1º BACHILLERATO/FÍSICA/CALOR Calcula el calor especifico Cuando suministramos {q} J de energía a {m} g de una sustancia a {ti} ºC pasa a estar a {tf} ºC. Calcula su calor específico en J/Kg·K

]]> 1.0000000 0.3333333 0 0 0 abc 0 {q}*1000/({m}*({tf}-{ti})) 0.02 1 1 3 0 0.1000000 3 0 private q calculatedsimple uniform 1.0 10.0 1 20 1 1.4 2 5.0 3 6.9 4 1.6 5 6.8 6 3.7 7 7.9 8 8.9 9 1.8 10 7.8 11 6.2 12 3.7 13 3.4 14 4.2 15 8.1 16 2.3 17 8.4 18 3.0 19 5.2 20 6.9 20 private m calculatedsimple uniform 1.0 10.0 1 20 1 4.0 2 6.7 3 7.1 4 1.0 5 4.8 6 3.1 7 6.5 8 5.6 9 4.3 10 8.2 11 9.5 12 7.8 13 5.0 14 8.1 15 3.1 16 7.1 17 8.0 18 6.9 19 4.9 20 8.2 20 private tf calculatedsimple uniform 1.0 10.0 1 20 1 3.5 2 6.1 3 8.5 4 6.5 5 6.5 6 1.8 7 3.2 8 8.3 9 3.3 10 8.6 11 6.6 12 3.9 13 6.9 14 7.6 15 5.4 16 6.4 17 1.3 18 8.5 19 2.2 20 2.3 20 private ti calculatedsimple uniform 1.0 10.0 1 20 1 3.9 2 5.3 3 1.4 4 2.9 5 7.8 6 2.9 7 5.0 8 7.1 9 1.8 10 1.2 11 6.7 12 3.3 13 6.0 14 5.9 15 7.5 16 5.5 17 1.6 18 3.3 19 3.1 20 8.4 20 Calcula el calor especifico Cuando suministramos {q} J de energía a {m} g de una sustancia a {ti} ºC pasa a estar a {tf} ºC. Calcula su calor específico en J/Kg·K

]]> 1.0000000 0.3333333 0 0 0 abc 0 {q}*1000/({m}*({tf}-{ti})) 0.02 1 1 3 0 0.1000000 3 0 private q calculatedsimple uniform 1.0 10.0 1 20 1 1.4 2 5.0 3 6.9 4 1.6 5 6.8 6 3.7 7 7.9 8 8.9 9 1.8 10 7.8 11 6.2 12 3.7 13 3.4 14 4.2 15 8.1 16 2.3 17 8.4 18 3.0 19 5.2 20 6.9 20 private m calculatedsimple uniform 1.0 10.0 1 20 1 4.0 2 6.7 3 7.1 4 1.0 5 4.8 6 3.1 7 6.5 8 5.6 9 4.3 10 8.2 11 9.5 12 7.8 13 5.0 14 8.1 15 3.1 16 7.1 17 8.0 18 6.9 19 4.9 20 8.2 20 private tf calculatedsimple uniform 1.0 10.0 1 20 1 3.5 2 6.1 3 8.5 4 6.5 5 6.5 6 1.8 7 3.2 8 8.3 9 3.3 10 8.6 11 6.6 12 3.9 13 6.9 14 7.6 15 5.4 16 6.4 17 1.3 18 8.5 19 2.2 20 2.3 20 private ti calculatedsimple uniform 1.0 10.0 1 20 1 3.9 2 5.3 3 1.4 4 2.9 5 7.8 6 2.9 7 5.0 8 7.1 9 1.8 10 1.2 11 6.7 12 3.3 13 6.0 14 5.9 15 7.5 16 5.5 17 1.6 18 3.3 19 3.1 20 8.4 20 Calcula el calor necesario para calentar Calcula el calor necesario para calentar {m} gramos de una sustancia de {ti} ºC a {tf} ºC, si no cambia de estado en ese intervalo y el calor específico es de {ce} J/Kg·K

]]> 1.0000000 0.3333333 0 0 0 abc 0 {m}*pow(10,-3)*{ce}*({tf}-{ti}) 0.03 1 1 3 0 0.1000000 3 0 private m calculatedsimple uniform 1.0 10.0 1 30 1 5.2 2 3.4 3 6.1 4 7.1 5 9.9 6 6.5 7 7.6 8 1.7 9 9.5 10 1.0 11 5.8 12 2.2 13 8.6 14 5.0 15 3.7 16 7.3 17 1.0 18 6.7 19 9.9 20 4.1 21 7.8 22 4.8 23 7.1 24 1.9 25 2.1 26 9.4 27 6.9 28 9.1 29 3.4 30 6.0 30 private ce calculatedsimple uniform 1.0 10.0 1 30 1 8.5 2 6.1 3 4.6 4 2.6 5 6.6 6 6.5 7 9.6 8 1.4 9 5.3 10 9.6 11 5.1 12 2.0 13 4.3 14 7.9 15 6.2 16 7.1 17 8.7 18 3.9 19 8.9 20 3.3 21 2.2 22 7.4 23 3.4 24 5.7 25 7.8 26 3.8 27 9.7 28 8.8 29 8.3 30 7.2 30 private tf calculatedsimple uniform 1.0 10.0 1 30 1 3.6 2 2.3 3 2.7 4 3.5 5 2.6 6 2.2 7 9.0 8 4.6 9 2.1 10 7.9 11 8.9 12 9.4 13 6.0 14 4.4 15 2.8 16 5.9 17 4.8 18 5.1 19 8.7 20 3.3 21 1.4 22 4.1 23 5.6 24 4.3 25 1.1 26 8.1 27 8.3 28 7.5 29 9.9 30 7.9 30 private ti calculatedsimple uniform 1.0 10.0 1 30 1 8.5 2 7.2 3 8.6 4 7.0 5 7.7 6 5.1 7 9.0 8 9.1 9 8.7 10 6.5 11 2.5 12 6.8 13 2.8 14 5.1 15 3.7 16 8.4 17 6.2 18 4.8 19 2.0 20 8.9 21 7.2 22 7.5 23 7.6 24 1.4 25 4.4 26 3.9 27 1.3 28 2.5 29 5.5 30 6.3 30 calcula la temperatura de equilibrio Tenemos {m1} Kg de una sustancia de calor específico {ce1} J/Kg·K a {t1} ºC y lo mezclamos con {m2} Kg de otra sustancia de calor específico {ce2} J/Kg·K a {t2} ºC. Calcula la temperatura de equilibrio

]]> 1.0000000 0.3333333 0 0 0 abc 0 (({m2}*{ce2}*{t2})+({m1}*{ce1}*{t1}))/(({m1}*{ce1})+({m2}*{ce2})) 0.02 1 1 3 0 0.1000000 3 0 private m2 calculatedsimple uniform 1.0 10.0 1 30 1 6.7 2 218.0 3 299.4 4 364.1 5 437.0 6 167.9 7 353.7 8 267.8 9 199.2 10 182.4 11 370.8 12 325.9 13 269.2 14 332.0 15 422.7 16 457.2 17 439.4 18 454.6 19 335.0 20 202.8 21 254.3 22 145.7 23 149.6 24 292.7 25 222.2 26 108.7 27 209.6 28 295.0 29 324.6 30 256.7 30 private ce2 calculatedsimple uniform 1.0 10.0 1 30 1 8.5 2 1460.5 3 591.7 4 1107.2 5 966.0 6 1067.7 7 595.7 8 1507.9 9 1020.0 10 813.3 11 1293.1 12 499.1 13 1509.4 14 997.8 15 1627.7 16 1442.8 17 1112.9 18 1489.8 19 1420.8 20 545.2 21 1315.2 22 1483.7 23 994.6 24 1109.9 25 911.9 26 813.1 27 1228.1 28 913.9 29 1345.9 30 1722.9 30 private t2 calculatedsimple uniform 1.0 10.0 1 30 1 8.5 2 37.3 3 36.5 4 24.0 5 36.1 6 24.3 7 15.7 8 38.7 9 34.7 10 26.4 11 25.6 12 39.1 13 38.6 14 20.8 15 27.1 16 36.7 17 33.7 18 16.8 19 23.5 20 22.8 21 20.2 22 12.1 23 10.2 24 31.6 25 16.0 26 20.8 27 27.4 28 22.6 29 16.4 30 38.6 30 private m1 calculatedsimple uniform 1.0 10.0 1 30 1 4.3 2 743.4 3 1102.1 4 464.4 5 807.4 6 1359.8 7 1000.7 8 951.6 9 489.2 10 1296.1 11 1070.8 12 1111.4 13 784.8 14 1580.1 15 972.7 16 773.5 17 1341.9 18 834.2 19 255.1 20 547.1 21 1298.5 22 896.6 23 1268.3 24 1294.2 25 1285.6 26 1093.3 27 626.9 28 1496.3 29 271.4 30 327.9 30 private ce1 calculatedsimple uniform 1.0 10.0 1 30 1 1.5 2 1298.8 3 1578.2 4 761.3 5 1415.7 6 1937.8 7 1303.3 8 1749.9 9 772.4 10 1208.5 11 1950.5 12 1793.3 13 1696.8 14 1056.3 15 1485.7 16 1733.5 17 1389.3 18 1697.9 19 757.8 20 1521.4 21 1072.5 22 1520.5 23 1354.0 24 1452.2 25 617.8 26 672.0 27 697.6 28 1510.7 29 944.2 30 1269.0 30 private t1 calculatedsimple uniform 1.0 10.0 1 30 1 6.6 2 83.6 3 93.8 4 81.1 5 56.8 6 81.7 7 75.3 8 73.5 9 55.7 10 84.6 11 56.7 12 85.9 13 57.7 14 59.8 15 74.3 16 87.3 17 83.2 18 71.9 19 55.7 20 73.7 21 62.2 22 94.3 23 91.3 24 94.8 25 62.8 26 67.6 27 61.9 28 60.2 29 52.2 30 64.0 30 calcula la temperatura de equilibrio (copia) Tenemos {m1} Kg de una sustancia de calor específico {ce1} J/Kg·K a {t1} ºC y lo mezclamos con {m2} Kg de otra sustancia de calor específico {ce2} J/Kg·K a {t2} ºC. Calcula la temperatura de equilibrio

]]> 1.0000000 0.3333333 0 0 0 abc 0 (({m2}*{ce2}*{t2})+({m1}*{ce1}*{t1}))/(({m1}*{ce1})+({m2}*{ce2})) 0.02 1 1 3 0 0.1000000 3 0 private m2 calculatedsimple uniform 1.0 10.0 1 30 1 6.7 2 218.0 3 299.4 4 364.1 5 437.0 6 167.9 7 353.7 8 267.8 9 199.2 10 182.4 11 370.8 12 325.9 13 269.2 14 332.0 15 422.7 16 457.2 17 439.4 18 454.6 19 335.0 20 202.8 21 254.3 22 145.7 23 149.6 24 292.7 25 222.2 26 108.7 27 209.6 28 295.0 29 324.6 30 256.7 30 private ce2 calculatedsimple uniform 1.0 10.0 1 30 1 8.5 2 1460.5 3 591.7 4 1107.2 5 966.0 6 1067.7 7 595.7 8 1507.9 9 1020.0 10 813.3 11 1293.1 12 499.1 13 1509.4 14 997.8 15 1627.7 16 1442.8 17 1112.9 18 1489.8 19 1420.8 20 545.2 21 1315.2 22 1483.7 23 994.6 24 1109.9 25 911.9 26 813.1 27 1228.1 28 913.9 29 1345.9 30 1722.9 30 private t2 calculatedsimple uniform 1.0 10.0 1 30 1 8.5 2 37.3 3 36.5 4 24.0 5 36.1 6 24.3 7 15.7 8 38.7 9 34.7 10 26.4 11 25.6 12 39.1 13 38.6 14 20.8 15 27.1 16 36.7 17 33.7 18 16.8 19 23.5 20 22.8 21 20.2 22 12.1 23 10.2 24 31.6 25 16.0 26 20.8 27 27.4 28 22.6 29 16.4 30 38.6 30 private m1 calculatedsimple uniform 1.0 10.0 1 30 1 4.3 2 743.4 3 1102.1 4 464.4 5 807.4 6 1359.8 7 1000.7 8 951.6 9 489.2 10 1296.1 11 1070.8 12 1111.4 13 784.8 14 1580.1 15 972.7 16 773.5 17 1341.9 18 834.2 19 255.1 20 547.1 21 1298.5 22 896.6 23 1268.3 24 1294.2 25 1285.6 26 1093.3 27 626.9 28 1496.3 29 271.4 30 327.9 30 private ce1 calculatedsimple uniform 1.0 10.0 1 30 1 1.5 2 1298.8 3 1578.2 4 761.3 5 1415.7 6 1937.8 7 1303.3 8 1749.9 9 772.4 10 1208.5 11 1950.5 12 1793.3 13 1696.8 14 1056.3 15 1485.7 16 1733.5 17 1389.3 18 1697.9 19 757.8 20 1521.4 21 1072.5 22 1520.5 23 1354.0 24 1452.2 25 617.8 26 672.0 27 697.6 28 1510.7 29 944.2 30 1269.0 30 private t1 calculatedsimple uniform 1.0 10.0 1 30 1 6.6 2 83.6 3 93.8 4 81.1 5 56.8 6 81.7 7 75.3 8 73.5 9 55.7 10 84.6 11 56.7 12 85.9 13 57.7 14 59.8 15 74.3 16 87.3 17 83.2 18 71.9 19 55.7 20 73.7 21 62.2 22 94.3 23 91.3 24 94.8 25 62.8 26 67.6 27 61.9 28 60.2 29 52.2 30 64.0 30 cambio estado (quitar qr) Queremos transformar #m gramos de hielo a - #th ºC a vapor de agua a #tv ºC. Calcula la energía necesaria en KJ.

DATOS:

Calor esp. agua líquida = 4180 J/Kg.K; hielo = 2091 J /Kg . K; vapor de agua = 1960 J / kg K..

Calores latentes del agua : fusión = 334000 J/Kg; vaporización = 2257000 J/Kg

]]> 1.0000000 0.3333333 0 0 #qt #qr <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>th</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tv</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>140</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mk</mi><mo>=</mo><mi>m</mi><mo>/</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qh</mi><mo>=</mo><mi>mk</mi><mo>*</mo><mn>2090</mn><mo>*</mo><mi>th</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qf</mi><mo>=</mo><mi>mk</mi><mo>*</mo><mn>334000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qa</mi><mo>=</mo><mi>mk</mi><mo>*</mo><mn>100</mn><mo>*</mo><mn>4180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qe</mi><mo>=</mo><mi>mk</mi><mo>*</mo><mn>2257000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qv</mi><mo>=</mo><mi>mk</mi><mo>*</mo><mn>1960</mn><mo>*</mo><mo>(</mo><mi>tv</mi><mo>-</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qt</mi><mo>=</mo><mi>qh</mi><mo>+</mo><mi>qf</mi><mo>+</mo><mi>qa</mi><mo>+</mo><mi>qe</mi><mo>+</mo><mi>qv</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qt</mi><mo>=</mo><mi>qt</mi><mo>/</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qr</mi><mo>=</mo><mi>qt</mi><mo>*</mo><mn>1000</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#qt</correctAnswer><correctAnswer id="1">#qr</correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> cambio estado 2 ((quiter qr) Queremos transformar #m gramos de hielo a - #th ºC a vapor de agua a 100 ºC. Calcula la energía necesaria en KJ.

DATOS:

Calor esp. agua líquida = 4180 J/Kg.K; hielo = 2091 J /Kg . K..

Calores latentes del agua : fusión = 334000 J/Kg; vaporización = 2257000 J/Kg

]]> 1.0000000 0.3333333 0 0 #qt #qr <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>th</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tv</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>140</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mk</mi><mo>=</mo><mi>m</mi><mo>/</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qh</mi><mo>=</mo><mi>mk</mi><mo>*</mo><mn>2090</mn><mo>*</mo><mi>th</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qf</mi><mo>=</mo><mi>mk</mi><mo>*</mo><mn>334000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qa</mi><mo>=</mo><mi>mk</mi><mo>*</mo><mn>100</mn><mo>*</mo><mn>4180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qe</mi><mo>=</mo><mi>mk</mi><mo>*</mo><mn>2257000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qt</mi><mo>=</mo><mi>qh</mi><mo>+</mo><mi>qf</mi><mo>+</mo><mi>qa</mi><mo>+</mo><mi>qe</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qt</mi><mo>=</mo><mi>qt</mi><mo>/</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qr</mi><mo>=</mo><mi>qt</mi><mo>/</mo><mn>1000</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#qt</correctAnswer><correctAnswer id="1">#qr</correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic" correctAnswer="1"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/CINEMÁTICA Desplazamiento y espacio recorrido Desde un punto de vista físico ¿En qué casos el espacio recorrido es igual al desplazmiento? (marca las opciones correctas)

]]> 1.0000000 0.1000000 0 true true abc Siempre Si el movimiento es circular Si el movimiento es rectilíneo Nunca Cuando el movimiento sea rectilíneo y en un solo sentido Si un cuerpo se mueve hacia la derecha Si consideramos positivo hacia la derecha y un cuerpo se mueve con velocidad positiva. La aceleración:

]]> 1.0000000 0.1000000 0 true true abc Es positiva Es negativa Puede ser positiva o negativa No tiene aceleración Un cuerpo que cae libremente de forma vertical Un cuerpo que cae libremente de forma vertical

]]> 1.0000000 0.1000000 0 true true abc No tiene aceleración Tiene aceleración normal pero no tangencial Tiene aceleración tangencial pero no normal Tiene aceleración normal y tangencial Un cuerpo que gia con rapidez constante Un cuerpo que gia con rapidez constante

]]> 1.0000000 0.1000000 0 true true abc No tiene aceleración No tiene aceleración tangencial, pero si normal No tiene aceleración normal pero si tangencial Tiene aceleración tangencial y normal un giro acelerado Un punto situado a una cierta distancia fija del eje gira con una rapidez que crece uniformemente. Indica las afirmaciones correctas:

]]> 1.0000000 0.1000000 0 false true abc No tiene aceleración tangencial No tiene aceleración normal su aceleración tangencial es constante Su aceleración normal es constante Su aceleración normal es creciente Su aceleración normal es decreciente su aceleración normal es proporcional a la velocidad su aceleración normal es proporcional al cuadrado de la velocidad Velocidad y aceleración cero Una partícula con velocidad cero ¿Puede tener aceleración ditinta de cero?. Y si su aceleración es cero ¿Puede cambiar el módulo de la velocidad?

]]> 1.0000000 0.1000000 0 true true abc No. Si Si. Si Si. No No. No Velocidad, aceleración tangencial y normal Indica la certeza o falsedad de las siguientes operaciones:

]]> 1.0000000 0.1000000 0 true La velocidad es siempre tangente a la trayectoria

]]> cierta La velocidad es siempre perpendicular a la trayectoria

]]> falsa La velocidad no tiene por qué ser ni tangente ni perpendicular a la trayectoria normalmente

]]> falsa La aceleración es tangente a la trayectoria

]]> falsa la aceleración es perpendicular a la trayectoria

]]> falsa La aceleración no tiene por qué ser ni tangente ni perpendicular a la trayectoria

]]> cierta la suma de los módulos de la aceleración normal y tangencial es igual a la aceleración

]]> falsa la suma de la aceleración tangencial y normal es igual a la aceleración

]]> cierta En un movimiento curvo la aceleración va siempre hacia el interior de la curva

]]> cierta En un movimiento curvo la aceleración va siempre hacia el exterior de la curva

]]> falsa 1º BACHILLERATO/FÍSICA/CINEMÁTICA/CINEMÁTICA VECTORIAL Integrar Un cuerpo tiene una aceleración a= #b j.

Calcula el módulo de su velocidad para un t = #t si para t=0 la velocidad es v = #c k
Calcula su distancia al origen para t = #t, si para t=0 está en el punto r= #d j +3 k

]]> 1.0000000 0.3333333 0 0 velocidad = #v1distancia al origen = #r1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup><mo>/</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vz</mi><mo>=</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rx</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>t</mi><mn>3</mn></msup><mo>/</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ry</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup><mo>/</mo><mn>2</mn><mo>)</mo><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rz</mi><mo>=</mo><mo>(</mo><mi>c</mi><mo>*</mo><mi>t</mi><mo>)</mo><mo>+</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>rx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ry</mi><mn>2</mn></msup><mo>+</mo><msup><mi>rz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mn>1</mn><mspace linebreak="newline"/><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mi>o</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Integrar Un cuerpo tiene una aceleración a= #a t i + #b j.

Calcula el módulo de su velocidad para un t = #t si para t=0 la velocidad es v = #c k
Calcula su distancia al origen para t = #t, si para t=0 está en el punto r= #d j +2 k

]]> 1.0000000 0.3333333 0 0 velocidad = #v1distancia al origen = #r1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup><mo>/</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>b</mi><mo>*</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vz</mi><mo>=</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rx</mi><mo>=</mo><mi>a</mi><mo>*</mo><msup><mi>t</mi><mn>3</mn></msup><mo>/</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ry</mi><mo>=</mo><mo>(</mo><mi>b</mi><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup><mo>/</mo><mn>2</mn><mo>)</mo><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rz</mi><mo>=</mo><mo>(</mo><mi>c</mi><mo>*</mo><mi>t</mi><mo>)</mo><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>rx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ry</mi><mn>2</mn></msup><mo>+</mo><msup><mi>rz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mn>1</mn><mspace linebreak="newline"/><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mi>o</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Posición de velocidad cero La posición de una partícula material que se desplaza sobre el eje OX, viene dada en función del tiempo por la ecuación:

r= #a t² + #b t + #c (SI)

Calcula el espacio que recorre en el primer segundo.
Calcula el espacio que recorre en el segundo segundo.

]]> 1.0000000 0.3333333 0 0 Espacio del primer segundo = #r01Espacio del segundo segundo = #r12]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r0</mi><mo>=</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><mn>4</mn><mo>)</mo><mo>+</mo><mo>(</mo><mi>b</mi><mo>*</mo><mn>2</mn><mo>)</mo><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r01</mi><mo>=</mo><mi>r1</mi><mo>-</mo><mi>r0</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r12</mi><mo>=</mo><mi>r2</mi><mo>-</mo><mi>r1</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">E</mi><mi mathvariant="normal">s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>o</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mo> </mo><mi>p</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi>n</mi><mi>d</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mn>01</mn><mspace linebreak="newline"/><mi mathvariant="normal">E</mi><mi mathvariant="normal">s</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>o</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mo> </mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi>n</mi><mi>d</mi><mi>o</mi><mo> </mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi>n</mi><mi>d</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mn>12</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Posición de velocidad cero La posición de una partícula material que se desplaza sobre el eje OX, viene dada en función del tiempo por la ecuación:

r= #a t² - #b t + #c (SI)

Calcula el valor de t, en segundos, para el que se para.
Calcula en qué posición, en metros, se detiene.

]]> 1.0000000 0.3333333 0 0 tiempo = #t1Posición = #r1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>b</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mo>(</mo><mi>a</mi><mo>*</mo><msup><mi>t1</mi><mn>2</mn></msup><mo>)</mo><mo>-</mo><mo>(</mo><mi>b</mi><mo>*</mo><mi>t1</mi><mo>)</mo><mo>+</mo><mi>c</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>1</mn><mspace linebreak="newline"/><mi>P</mi><mi>o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Posición de velocidad cero La posición de una partícula material que se desplaza sobre el eje OX, viene dada en función del tiempo por la ecuación:

r= #a t² - #b t + #c (SI)

Calcula el valor de t, en segundos, para el que se para.
Calcula en qué posición, en metros, se detiene.

r= #a t² - #b t + #c (SI)

Calcula su posición en el momento inicial.
Calcula su velocidad inicial.

]]> 1.0000000 0.3333333 0 0 Posición = #r1Velocidad = #v1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mo>-</mo><mi>b</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">V</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> vector de posición y movimiento El vector de posición de un objeto es:

r = ( 2t^#a+3) i + (3t^#b-5) j - 2 k

Indica las afirmaciones correctas:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> La aceleración es #av

]]> La aceleración es #af

]]> La velocidad es #vv

]]> La velocidad es #vf

]]> La posición es #pv

]]> La posición es #pf

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>av</mi><mo>=</mo><mo>"</mo><mi>variable</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>af</mi><mo>=</mo><mo>"</mo><mi>variable</mi><mo>"</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>vv</mi><mo>=</mo><mo>"</mo><mi>variable</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>vf</mi><mo>=</mo><mo>"</mo><mi>variable</mi><mo>"</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>pv</mi><mo>=</mo><mo>"</mo><mi>variable</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>pf</mi><mo>=</mo><mo>"</mo><mi>variable</mi><mo>"</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>a</mi><mo>=</mo><mn>3</mn><mo> </mo><mo>∨</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>3</mn><mo>)</mo></mrow><mtable><mtr><mtd><mi>af</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>vf</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>pf</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>a</mi><mo>=</mo><mn>2</mn><mo> </mo><mo>∨</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>2</mn><mo>)</mo></mrow><mtable><mtr><mtd><mi>av</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>vf</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>pf</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>1</mn><mo> </mo><mo>∨</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>av</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>vv</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>pf</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>av</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>vv</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>pv</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> vector de posición y movimiento El vector de posición de un objeto es:

r = ( 2t^#a+3) i + (3t^#b-5) j

Indica las afirmaciones correctas:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> La aceleración es #av

]]> La aceleración es #af

]]> La velocidad es #vv

]]> La velocidad es #vf

]]> La posición es #pv

]]> La posición es #pf

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800">librería</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>av</mi><mo>=</mo><mo>"</mo><mi>variable</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>af</mi><mo>=</mo><mo>"</mo><mi>variable</mi><mo>"</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>vv</mi><mo>=</mo><mo>"</mo><mi>variable</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>vf</mi><mo>=</mo><mo>"</mo><mi>variable</mi><mo>"</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mtable><mtr><mtd><mi>pv</mi><mo>=</mo><mo>"</mo><mi>variable</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>pf</mi><mo>=</mo><mo>"</mo><mi>variable</mi><mo>"</mo></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>a</mi><mo>=</mo><mn>3</mn><mo> </mo><mo>∨</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>3</mn><mo>)</mo></mrow><mtable><mtr><mtd><mi>af</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>vf</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>pf</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>a</mi><mo>=</mo><mn>2</mn><mo> </mo><mo>∨</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>2</mn><mo>)</mo></mrow><mtable><mtr><mtd><mi>av</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>vf</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>pf</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mn>1</mn><mo> </mo><mo>∨</mo><mo> </mo><mi>b</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>av</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>vv</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>pf</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>av</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>vv</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>pv</mi><mo>=</mo><mo>"</mo><mi>constante</mi><mo>"</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> velocidad y aceleración a partir del vector de posición El vector de posición de un móvil es:

r= #a t²i +#b t³j+(#c t²+#d t)k (SI)

Calcula:

Su velocidad para t= #t1 segundos
Su aceleración para t= #t2 segundos

]]> 1.0000000 0.3333333 0 0 velocidad =#vaceleración =#ac]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>t1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>b</mi><mo>*</mo><msup><mi>t1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vz</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>c</mi><mo>*</mo><mi>t1</mi><mo>)</mo><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mn>6</mn><mo>*</mo><mi>b</mi><mo>*</mo><mi>t2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mspace linebreak="newline"/><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>c</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> velocidad y aceleración a partir del vector de posición El vector de posición de un móvil es:

r= #a ti +(#b t + #c )j + #d t² k (SI)

Calcula:

El módulo de su velocidad para t= #t1 segundos
El módulo de su aceleración para t= #t2 segundos

]]> 1.0000000 0.3333333 0 0 velocidad =#vaceleración =#ac]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vz</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>d</mi><mo>*</mo><mi>t1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mspace linebreak="newline"/><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>c</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> velocidad y aceleración a partir del vector de posición El vector de posición de un móvil es:

r= #a t²i +#b t²j+(#c t³+#d t})k (SI)

Calcula:

El módulo de su velocidad para t= #t1 segundos
El módulo de su aceleración para t= #t2 segundos

]]> 1.0000000 0.3333333 0 0 velocidad =#vaceleración =#ac]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>t1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>*</mo><mi>t1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vz</mi><mo>=</mo><mo>(</mo><mn>3</mn><mo>*</mo><mi>c</mi><mo>*</mo><msup><mi>t1</mi><mn>2</mn></msup><mo>)</mo><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mn>6</mn><mo>*</mo><mi>c</mi><mo>*</mo><mi>t2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mspace linebreak="newline"/><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>c</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> velocidad y aceleración a partir del vector de posición El vector de posición de un móvil es:

r= #a sen( #b t)i +#c t³j+ #d t k (SI) (ángulo en radianes)

Calcula:

El módulo de su velocidad para t= #t1 segundos
El módulo de su aceleración para t= #t2 segundos

]]> 1.0000000 0.3333333 0 0 velocidad =#vaceleración =#ac]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>b</mi><mo>*</mo><mi>t1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>c</mi><mo>*</mo><msup><mi>t1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vz</mi><mo>=</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><msup><mi>b</mi><mn>2</mn></msup><mi>sin</mi><mo>(</mo><mi>b</mi><mo>*</mo><mi>t2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mn>6</mn><mo>*</mo><mi>c</mi><mo>*</mo><mi>t2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mspace linebreak="newline"/><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>c</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> velocidad y aceleración a partir del vector de posición El vector de posición de un móvil es:

r= #a t²i +#b t³j+(#c t²+#d t})k (SI)

Calcula:

El módulo de su velocidad para t= #t1 segundos
El módulo de su aceleración para t= #t2 segundos

]]> 1.0000000 0.3333333 0 0 velocidad =#vaceleración =#ac]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>t1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>b</mi><mo>*</mo><msup><mi>t1</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vz</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>c</mi><mo>*</mo><mi>t1</mi><mo>)</mo><mo>+</mo><mi>d</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mn>6</mn><mo>*</mo><mi>b</mi><mo>*</mo><mi>t2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mspace linebreak="newline"/><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>c</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/CINEMÁTICA/CINEMÁTICA VECTORIAL/ACELERACIONES Aceleración normal y tangencial Marque las afirmaciones correctas para un cuerpo que se mueve por una trayectoria rectilínea con rapidez variable.

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Aceleración distinta de cero

]]> Aceleración normal = 0

]]> Aceleración normal distinta de cero

]]> Aceleración=0

]]> Aceleración tangencial =0

]]> Aceleración tangencial distinta de cero

]]> Aceleración normal y tangencial Marque las afirmaciones correctas para un cuerpo que se mueve por una trayectoria curva con rapidez constante.

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Aceleración distinta de cero

]]> Aceleración normal = 0

]]> Aceleración normal distinta de cero

]]> Aceleración=0

]]> Aceleración tangencial =0

]]> Aceleración tangencial distinta de cero

]]> Aceleración normal y tangencial Marque las afirmaciones correctas para un cuerpo que se mueve por una trayectoria rectilínea con rapidez constante.

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Aceleración distinta de cero

]]> Aceleración normal = 0

]]> Aceleración normal distinta de cero

]]> Aceleración=0

]]> Aceleración tangencial =0

]]> Aceleración tangencial distinta de cero

]]> Aceleración normal y tangencial Marque las afirmaciones correctas para un cuerpo que se mueve por una trayectoria curva con rapidez variable.

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Aceleración distinta de cero

]]> Aceleración normal = 0

]]> Aceleración normal distinta de cero

]]> Aceleración=0

]]> Aceleración tangencial =0

]]> Aceleración tangencial distinta de cero

]]> aceleración y trayectoria Marca las afirmaciones que son correctas:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Un movimiento curvo siempre es acelerado

]]> Un movimiento rectilíneo no tiene aceleración tangencial

]]> Un movimiento con aceleración normal distinta de cero tiene rapidez variable

]]> Un movimiento con aceleración normal distinta de cero tiene rapidez constante

]]> Un movimiento curvo tiene aceleración normal distinta de cero

]]> La aceleración es siempre tangente a la trayectoria

]]> La velocidad es siempre tangente a la trayectoria

]]> 1º BACHILLERATO/FÍSICA/CINEMÁTICA/COMPOSICIÓN DE MOVIMIENTOS Alcance Un jugador de fútbol lanza una pelota desde el suelo con una inclinación de #ang º sobre la horizontal. Si la pelota sale con una velocidad de #vel m/s. Determina la distancia horizontal, en m, a la que cae al suelo.

]]> 1.0000000 0.3333333 0 0 #dh]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vel</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>ang</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dh</mi><mo>=</mo><msup><mi>vel</mi><mn>2</mn></msup><mo>*</mo><mi>sin</mi><mo>(</mo><mn>2</mn><mo>*</mo><mi>anr</mi><mo>)</mo><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>d</mi><mi mathvariant="normal">h</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Barca y rio Para cruzar un río una barca se mueve perpendicularmente a la corriente con una velocidad constante de #vb m/s. Si la corriente tiene una velocidad de #vc m/s y el río tiene una anchura de #anc m. Calcula:

¿A qué distancia rio abajo atracará en la otra orilla?
¿Qué distancia recorrerá la barca?

]]> 1.0000000 0.3333333 0 0 Distancia rio abajo= #dr Distancia recorrida = #db]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>anc</mi><mo>/</mo><mi>vb</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dr</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>t</mi><mo>*</mo><mi>vc</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>db</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>anc</mi><mn>2</mn></msup><mo>+</mo><msup><mi>dr</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mi>r</mi><mi mathvariant="normal">i</mi><mi>o</mi><mo> </mo><mi>a</mi><mi mathvariant="normal">b</mi><mi>a</mi><mi mathvariant="normal">j</mi><mi>o</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi>r</mi><mspace linebreak="newline"/><mo> </mo><mi>D</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>o</mi><mi>r</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi mathvariant="normal">b</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Desde un avión disparamos un misil Desde un helicóptero en reposo situado a #hin metros de altura disparamos un misil con una inclinación de #an º sobre la horizontal. Si el misil sale con una velocidad de #vel m/s. Determina:

Distancia horizontal, en metros, a la que cae al agua.
Módulo de la velocidad, en m/s, de impacto con el agua.

]]> 1.0000000 0.3333333 0 0 Distancia =#xfvelocidad=#mv]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hin</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>600</mn><mo>)</mo><mo>*</mo><mn>10</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vel</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>vel</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>vel</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ra</mi><mo>=</mo><mo>-</mo><msqrt><mrow><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>hin</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>(</mo><mi>ra</mi><mo>-</mo><mi>vy</mi><mo>)</mo><mo>/</mo><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xf</mi><mo>=</mo><mi>vx</mi><mo>*</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vyf</mi><mo>=</mo><mi>vy</mi><mo>-</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>t</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mv</mi><mo>=</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vyf</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mi>f</mi><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo>=</mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>v</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Desde un avión disparamos un misil Desde un helicóptero en reposo situado a #hin metros de altura disparamos un misil con una inclinación de #an º bajo la horizontal. Si el misil sale con una velocidad de #vel m/s. Determina:

Distancia horizontal, en metros, a la que cae al agua.
Módulo de la velocidad, en m/s, de impacto con el agua.

]]> 1.0000000 0.3333333 0 0 Distancia =#xfvelocidad=#mv]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hin</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>600</mn><mo>)</mo><mo>*</mo><mn>10</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vel</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>vel</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mo>-</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>vel</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mo>-</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ra</mi><mo>=</mo><mo>-</mo><msqrt><mrow><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>hin</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>(</mo><mi>ra</mi><mo>-</mo><mi>vy</mi><mo>)</mo><mo>/</mo><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xf</mi><mo>=</mo><mi>vx</mi><mo>*</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vyf</mi><mo>=</mo><mi>vy</mi><mo>-</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>t</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mv</mi><mo>=</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vyf</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mi>f</mi><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo>=</mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>v</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Desde un helicóptero Desde un helicóptero en reposo situado a #hin metros de altura dejamos caer una bomba. Si el viento tiene una velocidad de #vv m/s, determina:

Módulo de la velocidad, en m/s, cuando impacta con el suelo.
Ángulo de impacto, en grados respecto a la horizontal, con el suelo.

]]> 1.0000000 0.3333333 0 0 Módulo =#mvÁngulo =#avg ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hin</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>600</mn><mo>,</mo><mn>900</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vv</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><msqrt><mrow><mi>hin</mi><mo>/</mo><mn>4</mn><mo>.</mo><mn>9</mn></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mv</mi><mo>=</mo><msqrt><mrow><msup><mi>vv</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>av</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>vy</mi><mo>/</mo><mi>vv</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>avg</mi><mo>=</mo><mi>av</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>v</mi><mspace linebreak="newline"/><mi>Á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>v</mi><mi mathvariant="normal">g</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Desde una mesa Por una mesa horizontal situada a #hin metros de altura rueda una bola con una velocidad de #vin m/s y llega al borde. Determina:

Distancia horizontal, en m, a la que cae al suelo.
Rapidez, en m/s, de impacto con el suelo.

]]> 1.0000000 0.3333333 0 0 Distancia =#xfRapidez =#mv ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hin</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>90</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vin</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><msqrt><mrow><mi>hin</mi><mo>/</mo><mn>4</mn><mo>.</mo><mn>9</mn></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mv</mi><mo>=</mo><msqrt><mrow><msup><mi>vin</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xf</mi><mo>=</mo><mi>vin</mi><mo>*</mo><mi>t</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mi>f</mi><mspace linebreak="newline"/><mi>R</mi><mi>a</mi><mi>p</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi mathvariant="normal">e</mi><mi>z</mi><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>v</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Jugador de fútbol y valla Un jugador de fútbol lanza una pelota desde el suelo con una inclinación de #an º sobre la horizontal y desea superar una valla situada a #dx metros de distancia con una altura de #dy metros. Calcula la velocidad mínima, en m/s, del lanzamiento.

]]> 1.0000000 0.3333333 0 0 #mv]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dy</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><msqrt><mrow><mo>(</mo><mo>(</mo><mi>dx</mi><mo>*</mo><mi>tan</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo><mo>-</mo><mi>dy</mi><mo>)</mo><mo>/</mo><mn>4</mn><mo>.</mo><mn>9</mn></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mv</mi><mo>=</mo><mi>dx</mi><mo>/</mo><mo>(</mo><mi>t</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>v</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Parabólico desde acantilado Desde un acantilado situado a #hi metros de altura disparamos un cañón con una inclinación de #an º sobre la horizontal. Si la bala sale con una velocidad de #vi m/s. Determina:

Distancia horizontal a la que cae al agua.
Velocidad de impacto con el agua.

]]> 1.0000000 0.3333333 0 0 distancia X =#dxVelocidad impacto =#vf]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hi</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>vi</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>vi</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>raiz1</mi><mo>=</mo><msqrt><mrow><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>hi</mi><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>(</mo><mi>vy</mi><mo>+</mo><mi>raiz1</mi><mo>)</mo><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dx</mi><mo>=</mo><mi>t</mi><mo>*</mo><mi>vx</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vyf</mi><mo>=</mo><mi>vy</mi><mo>-</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>t</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vf</mi><mo>=</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vyf</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mi>X</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>d</mi><mi>x</mi><mspace linebreak="newline"/><mi>V</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>o</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>f</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Parabólico desde acantilado Desde un acantilado situado a #hi metros de altura disparamos un cañón con una inclinación de #an º sobre la horizontal. Si la bala sale con una velocidad de #vi m/s. Determina:

Distancia horizontal a la que cae al agua.
Velocidad de impacto con el agua.

]]> 1.0000000 0.3333333 0 0 distancia X =#dxVelocidad impacto =#vf]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hi</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>vi</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>vi</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>raiz1</mi><mo>=</mo><msqrt><mrow><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>hi</mi><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>(</mo><mi>vy</mi><mo>+</mo><mi>raiz1</mi><mo>)</mo><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dx</mi><mo>=</mo><mi>t</mi><mo>*</mo><mi>vx</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vyf</mi><mo>=</mo><mi>vy</mi><mo>-</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>t</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vf</mi><mo>=</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vyf</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mi>X</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>d</mi><mi>x</mi><mspace linebreak="newline"/><mi mathvariant="normal">V</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>o</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>f</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Parabólico desde avión Desde un avión situado a #hi metros de altura que se mueve a #va m/s, disparamos un misil con una inclinación de #an º bajo la horizontal. Si la bala sale con una velocidad de #vm m/s. Determina:

Distancia horizontal a la que cae al suelo.
Velocidad de impacto con el suelo.

]]> 1.0000000 0.3333333 0 0 distancia X =#dxVelocidad impacto =#vf]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hi</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>5000</mn><mo>,</mo><mn>9000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>va</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vm</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mo>-</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mo>(</mo><mi>vm</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo><mo>+</mo><mi>va</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>vm</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>raiz1</mi><mo>=</mo><msqrt><mrow><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>hi</mi><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>(</mo><mi>vy</mi><mo>+</mo><mi>raiz1</mi><mo>)</mo><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dx</mi><mo>=</mo><mi>t</mi><mo>*</mo><mi>vx</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vyf</mi><mo>=</mo><mi>vy</mi><mo>-</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>t</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vf</mi><mo>=</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vyf</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mi>X</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>d</mi><mi>x</mi><mspace linebreak="newline"/><mi mathvariant="normal">V</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>o</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>f</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Parabólico desde pozo Desde una hondonada de #hip metros de profundidad disparamos un cohete con una inclinación de #an º sobre la horizontal. Si sale con una velocidad de #vi m/s. Determina:

Distancia horizontal a la que cae al suelo exterior.
Velocidad de impacto con el agua.

]]> 1.0000000 0.3333333 0 0 distancia X =#dxVelocidad impacto =#vf]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hip</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hi</mi><mo>=</mo><mo>-</mo><mi>hip</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>vi</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>vi</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>raiz1</mi><mo>=</mo><msqrt><mrow><msup><mi>vy</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>hi</mi><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>(</mo><mi>vy</mi><mo>+</mo><mi>raiz1</mi><mo>)</mo><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dx</mi><mo>=</mo><mi>t</mi><mo>*</mo><mi>vx</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vyf</mi><mo>=</mo><mi>vy</mi><mo>-</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>t</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vf</mi><mo>=</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vyf</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mi>X</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>d</mi><mi>x</mi><mspace linebreak="newline"/><mi mathvariant="normal">V</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>a</mi><mi>c</mi><mi>t</mi><mi>o</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>f</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> velocidad y posicion en un tiempo Un jugador de fútbol lanza una pelota desde el suelo con una inclinación de #ang º sobre la horizontal. Si la pelota sale con una velocidad de #vel m/s. Determina.

Velocidad en el punto más alto
Posición al cabo de #t segundos

]]> 1.0000000 0.3333333 0 0 1.- Velocidad = #vx2.- Posición: x= #x y = #y]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vel</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>ang</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>vel</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>vel</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>vx</mi><mo>*</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>(</mo><mi>vy</mi><mo>*</mo><mi>t</mi><mo>)</mo><mo>-</mo><mn>4</mn><mo>.</mo><mn>9</mn><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo>-</mo><mo> </mo><mi mathvariant="normal">V</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mi>x</mi><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo>-</mo><mo> </mo><mi>P</mi><mi>o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo>:</mo><mo> </mo><mi>x</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> velocidad y posicion en un tiempo (copia) Un jugador de fútbol lanza una pelota desde el suelo con una inclinación de #ang º sobre la horizontal. Si la pelota sale con una velocidad de #vel m/s. Determina, al cabo de #t segundos

Rapidez (m/s)
Posición (metros)

]]> 1.0000000 0.3333333 0 0 1.- Rapidez = #v2.- Posición: x= #x y = #y]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vel</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>ang</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>vel</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>vel</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vyf</mi><mo>=</mo><mi>vy</mi><mo>-</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>t</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vyf</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>vx</mi><mo>*</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>(</mo><mi>vy</mi><mo>*</mo><mi>t</mi><mo>)</mo><mo>-</mo><mn>4</mn><mo>.</mo><mn>9</mn><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo>-</mo><mo> </mo><mi>R</mi><mi>a</mi><mi>p</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi mathvariant="normal">e</mi><mi>z</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo>-</mo><mo> </mo><mi>P</mi><mi>o</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo>:</mo><mo> </mo><mi>x</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 1º BACHILLERATO/FÍSICA/CINEMÁTICA/MOVIMIENTOS CIRCULARES aceleración angular Un disco, partiendo del reposo, alcanza #w rpm en #t segundos. Determina:

Su aceleración angular en rd/s².
El ángulo girado en radianes.

]]> 1.0000000 0.3333333 0 0 Aceleración angular =#aanÁngulo girado =#agi]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>500</mn><mo>,</mo><mn>4000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>wi</mi><mo>=</mo><mi>w</mi><mo>*</mo><pi/><mo>/</mo><mn>30</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aan</mi><mo>=</mo><mo> </mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>wi</mi><mo>/</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>agi</mi><mo>=</mo><mi>aan</mi><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup><mo>/</mo><mn>2</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mi>a</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>a</mi><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>a</mi><mi>n</mi><mspace linebreak="newline"/><mi>Á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mi mathvariant="normal">g</mi><mi mathvariant="normal">i</mi><mi>rad</mi><mi>o</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">i</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Aceleración normal y tangencial Un disco pasa de #v1 a #v2 rpm en #t segundos. Calcula:

la aceleración tangencial, en m/s², de un punto del borde a #di cm del eje.
La aceleración normal, en m/s², de ese mismo punto en el momento final

]]> 1.0000000 0.3333333 0 0 Aceleración tangencial =#atAceleración normal =#an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>70</mn><mo>,</mo><mn>110</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>v1</mi><mo>*</mo><pi/><mo>/</mo><mn>30</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>v2</mi><mo>*</mo><pi/><mo>/</mo><mn>30</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>at</mi><mo>=</mo><mi>di</mi><mo>*</mo><mo>(</mo><mi>w2</mi><mo>-</mo><mi>w1</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>t</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><msup><mi>w2</mi><mn>2</mn></msup><mo>*</mo><mi>di</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mi>t</mi><mi>a</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>t</mi><mspace linebreak="newline"/><mi>A</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mi>n</mi><mi>o</mi><mi>r</mi><mi mathvariant="normal">m</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Ángulo girado Un disco gira a una velocidad constante de #r rpm. Calcula:

El ángulo, en radianes, que girará en #t segundos
El tiempo que tarda en dar #v vueltas

]]> 1.0000000 0.3333333 0 0 Ángulo =#anTiempo= #tie]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>2000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>130</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>=</mo><mi>r</mi><mo>*</mo><pi/><mo>/</mo><mn>30</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>rr</mi><mo>*</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tie</mi><mo>=</mo><mi>v</mi><mo>*</mo><mn>2</mn><mo>.</mo><mn>0</mn><mo>*</mo><pi/><mo>/</mo><mi>rr</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mi>n</mi><mspace linebreak="newline"/><mi mathvariant="normal">T</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Dos discos con cinta Dos discos A y B están conectados por una cadena que los rodea. Si sus radios son #r1 y #r2 cm respectivamente y un punto del borde del disco A gira con una velocidad angular constante de #w1 rpm. Calcula la velocidad, en rd/s, de un punto del borde del disco B

]]> 1.0000000 0.3333333 0 0 #w2 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>wr1</mi><mo>=</mo><mi>w1</mi><mo>*</mo><pi/><mo>/</mo><mn>30</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>wr1</mi><mo>*</mo><mi>r1</mi><mo>/</mo><mi>r2</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#w2</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Dos discos con eje común Dos discos A y B están soldados a un eje común. Si sus radios son #r1 y #r2 cm respectivamente y un punto del borde del disco A gira con una velocidad constante de #v1 m/s. Calcula la velocidad, en m/s, de un punto del borde del disco B

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 1.0000000 0.3333333 0 0 #w2 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>wr1</mi><mo>=</mo><mi>w1</mi><mo>*</mo><pi/><mo>/</mo><mn>30</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo>=</mo><mi>wr1</mi><mo>/</mo><mn>8</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#w2</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Frecuencia y periodo Un disco gira a una velocidad de #r rpm. Calcula su frecuencia en Hz (ciclos/segundo) y su periodo (tiempo que tarda en dar un ciclo)

]]> 1.0000000 0.3333333 0 0 Frecuencia =#frePeriodo = #pe]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fre</mi><mo>=</mo><mi>r</mi><mo>/</mo><mn>60</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pe</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>/</mo><mi>fre</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>f</mi><mi>r</mi><mi mathvariant="normal">e</mi><mspace linebreak="newline"/><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>d</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>p</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Planeta Tierra El radio medio del planeta Tierra es de 6371 Km. Calcula, teniendo en cuenta sólo la rotación terrestre, la velocidad en Km/h que tendría un objeto:

Situado en el Ecuador
Situado a una latitud de #la º

]]> 1.0000000 0.3333333 0 0 1.-= #vec2.-= #vla]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vec</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mn>6371</mn><mo>*</mo><pi/><mo>/</mo><mn>12</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>la</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rla</mi><mo>=</mo><mn>6371</mn><mo>*</mo><mi>cos</mi><mo>(</mo><mi>la</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vla</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>rla</mi><mo>*</mo><pi/><mo>/</mo><mn>12</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo>-</mo><mo>=</mo><mo> </mo><mo> </mo><mo>#</mo><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo>-</mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mi mathvariant="normal">l</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Reloj Las dos manecillas de un reloj coinciden a las 12 en punto. ¿Cuántos minutos después vuelven a coincidir?

]]> 1.0000000 0.3333333 0 0 #mi]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mi</mi><mo>=</mo><mn>60</mn><mo>+</mo><mo>(</mo><mn>30</mn><mo>/</mo><mn>5</mn><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Taladro Un taladro pasa de #w1 a #w2 rpm en #t segundos. Calcula el número de vueltas girado en ese tiempo.

]]> 1.0000000 0.3333333 0 0 #an <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo> </mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>700</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>wr1</mi><mo>=</mo><mi>w1</mi><mo>*</mo><pi/><mo>/</mo><mn>30</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>wr2</mi><mo>=</mo><mi>w2</mi><mo>*</mo><pi/><mo>/</mo><mn>30</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mo>(</mo><mi>wr2</mi><mo>-</mo><mi>wr1</mi><mo>)</mo><mo>/</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mo>(</mo><mi>wr1</mi><mo>*</mo><mi>t</mi><mo>)</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>*</mo><mi>aa</mi><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>an</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><pi/><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#an</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Taladro Un taladro pasa de #w1 a #w2 rpm en #t segundos. Calcula el número de vueltas girado en ese timepo.

]]> 1.0000000 0.3333333 0 0 #an <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi><mo> </mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>700</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>wr1</mi><mo>=</mo><mi>w1</mi><mo>*</mo><pi/><mo>/</mo><mn>30</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>wr2</mi><mo>=</mo><mi>w2</mi><mo>*</mo><pi/><mo>/</mo><mn>30</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mo>(</mo><mi>wr2</mi><mo>-</mo><mi>wr1</mi><mo>)</mo><mo>/</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mo>(</mo><mi>wr1</mi><mo>*</mo><mi>t</mi><mo>)</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>*</mo><mi>aa</mi><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>an</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><pi/><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#an</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator"></option><option name="imaginary_unit"></option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/CINEMÁTICA/MOVIMIENTOS RECTILÍNEOS/MOVIMIENTOS ACELERADOS Aceleración Un coche circula por una autopista con una velocidad de #v1 Km/h. #di m más adelante tiene una velocidad de #v2 Km/h. Calcula:

Aceleración en m/s².
Tiempo de movimiento en segundos.

]]> 1.0000000 0.3333333 0 0 aceleración = #atiempo = #t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>90</mn><mo>,</mo><mn>130</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>80</mn><mo>,</mo><mn>140</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1ms</mi><mo>=</mo><mi>v1</mi><mo>/</mo><mn>3</mn><mo>.</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2ms</mi><mo>=</mo><mi>v2</mi><mo>/</mo><mn>3</mn><mo>.</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><msup><mi>v2ms</mi><mn>2</mn></msup><mo>-</mo><msup><mi>v1ms</mi><mn>2</mn></msup><mo>)</mo><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>di</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>(</mo><mi>v2ms</mi><mo>-</mo><mi>v1ms</mi><mo>)</mo><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gx</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>/</mo><mi>a</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mi>t</mi><mo>)</mo><mo>/</mo><mi>t</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mi>gx</mi><mo> </mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>devolver</mi><mo> </mo><mi>gx</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Aceleración móvil Un móvil circula por una pista con una velocidad #vi m/s, frena durante #t segundos y al final tiene una velocidad de #vf m/s. Calcula:

Su aceleración en m/s²
El espacio recorrido en metros

]]> 1.0000000 0.3333333 0 0 aceleración =#aDistancia =#d]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vf</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>35</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>vf</mi><mo>-</mo><mi>vi</mi><mo>)</mo><mo>/</mo><mi>t</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mo> </mo><mo>(</mo><mi>vi</mi><mo>*</mo><mi>t</mi><mo>)</mo><mo>+</mo><mo>(</mo><mi>a</mi><mo>*</mo><mi>t</mi><mo>*</mo><mi>t</mi><mo>)</mo><mo>/</mo><mn>2</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>D</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>d</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Frenado Un coche circula por una autopista con una velocidad de #vi Km/h. Ve un obstáculo y, 0.5 segundos más tarde, frena con una aceleración de frenado de #af m/s². Calcula:

Distancia, en m, hasta que se para.
Tiempo de frenado en segundos.

]]> 1.0000000 0.3333333 0 0 distancia = #ditiempo = #t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>af</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>90</mn><mo>,</mo><mn>130</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vms</mi><mo>=</mo><mi>vi</mi><mo>/</mo><mn>3</mn><mo>.</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di</mi><mo>=</mo><mo>(</mo><mi>vms</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>)</mo><mo>-</mo><msup><mi>vms</mi><mn>2</mn></msup><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>af</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>-</mo><mi>vms</mi><mo>/</mo><mi>af</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gx</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>di</mi><mo>)</mo><mo>/</mo><mi>di</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mi>t</mi><mo>)</mo><mo>/</mo><mi>t</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mi>gx</mi><mo> </mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>devolver</mi><mo> </mo><mi>gx</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi mathvariant="normal">i</mi><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Frenado Un coche circula por una autopista con una velocidad de #vi Km/h. Ve un obstáculo y frena en #di m. Calcula:

Aceleración en m/s².
Tiempo de frenado en segundos.

]]> 1.0000000 0.3333333 0 0 aceleración = #atiempo = #t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>90</mn><mo>,</mo><mn>130</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vms</mi><mo>=</mo><mi>vi</mi><mo>/</mo><mn>3</mn><mo>.</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><msup><mi>vms</mi><mn>2</mn></msup><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>di</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>-</mo><mi>vms</mi><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gx</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>/</mo><mi>a</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mi>t</mi><mo>)</mo><mo>/</mo><mi>t</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mi>gx</mi><mo> </mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>devolver</mi><mo> </mo><mi>gx</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Frenado Un coche circula por una autopista con una velocidad de #vi Km/h. Ve un obstáculo y frena en #di m. Calcula:

Aceleración en m/s².
Tiempo de frenado en segundos.

]]> 1.0000000 0.3333333 0 0 aceleración = #atiempo = #t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>90</mn><mo>,</mo><mn>130</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vms</mi><mo>=</mo><mi>vi</mi><mo>/</mo><mn>3</mn><mo>.</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>-</mo><msup><mi>vms</mi><mn>2</mn></msup><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>di</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>-</mo><mi>vms</mi><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gx</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>a</mi><mo>)</mo><mo>/</mo><mi>a</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mi>t</mi><mo>)</mo><mo>/</mo><mi>t</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mi>gx</mi><mo> </mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>devolver</mi><mo> </mo><mi>gx</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/CINEMÁTICA/MOVIMIENTOS RECTILÍNEOS/PERSECUCIONES Persecución Un móvil circula con una velocidad de #v1 m/s. #t1 segundos más tarde y desde el mismo punto de partida, sale otro en su persecución con una velocidad de #v2 m/s. Calcula:

¿Qué distancia, en metros, habrá recorrido el primer móvil cuando se encuentren?
¿Cuánto tiempo habrá estado circulando el primer móvil?

]]> 1.0000000 0.3333333 0 0 distancia = #ditiempo = #t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>incre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mi>incre</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di1</mi><mo>=</mo><mi>v1</mi><mo>*</mo><mi>t1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>v2</mi><mo>*</mo><mi>t1</mi><mo>/</mo><mi>incre</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>v1</mi><mo>*</mo><mi>t</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi mathvariant="normal">i</mi><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Persecución (II) Un móvil circula con una velocidad de #v1 m/s desde un punto A. Al mismo tiempo, desde un punto B situado #d1 metros más atrás, sale otro en su persecución con una velocidad de #v2 m/s. Calcula:

¿Qué distancia, en metros, habrá recorrido el primer móvil cuando se encuentren?
¿Cuánto tiempo habrá estado circulando el primer móvil?

]]> 1.0000000 0.3333333 0 0 distancia = #ditiempo = #t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>incre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mi>incre</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>120</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>d1</mi><mo>/</mo><mi>incre</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>v1</mi><mo>*</mo><mi>t</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi mathvariant="normal">i</mi><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Persecución (II) Un móvil circula con una velocidad de #v1 m/s desde un punto A. Al mismo tiempo, desde un punto B situado #d1 metros más atrás, sale otro en su persecución con una velocidad de #v2 m/s. Calcula:

¿Qué distancia, en metros, habrá recorrido el primer móvil cuando se encuentren?
¿Cuánto tiempo habrá estado circulando el primer móvil?

]]> 1.0000000 0.3333333 0 0 distancia = #ditiempo = #t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>incre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mi>incre</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>120</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>d1</mi><mo>/</mo><mi>incre</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>v1</mi><mo>*</mo><mi>t</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi mathvariant="normal">i</mi><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Persecución (III) Un móvil circula con una velocidad de #v1 m/s desde un punto A. #t1 segundos más tarde, desde un punto B situado #d1 metros más atrás, sale otro en su persecución con una velocidad de #v2 m/s. Calcula:

¿Qué distancia, en metros, habrá recorrido el primer móvil cuando se encuentren?
¿Cuánto tiempo habrá estado circulando el primer móvil?

]]> 1.0000000 0.3333333 0 0 distancia = #ditiempo = #t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>incre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mi>incre</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>120</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>id1</mi><mo>=</mo><mi>t1</mi><mo>*</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>id1</mi><mo>+</mo><mi>d1</mi><mo>)</mo><mo>/</mo><mi>incre</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>t2</mi><mo>+</mo><mi>t1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>v1</mi><mo>*</mo><mi>t</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi mathvariant="normal">i</mi><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Persecución (III) acelerado Un móvil circula con una velocidad de #v1 m/s desde un punto A. Al mismo tiempo, desde un punto B situado #d1 metros más atrás, sale otro en su persecución con una velocidad de #v2 m/s y una aceleración #a m/s². Calcula:

¿Qué distancia, en metros, habrá recorrido el primer móvil cuando se encuentren?
¿Cuánto tiempo habrá estado circulando el primer móvil?

]]> 1.0000000 0.3333333 0 0 distancia = #ditiempo = #t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>incre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mi>incre</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>120</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>raiz1</mi><mo>=</mo><msqrt><mrow><msup><mi>incre</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>d1</mi><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mo>-</mo><mi>incre</mi><mo>+</mo><mi>raiz1</mi><mo>)</mo><mo>/</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>v1</mi><mo>*</mo><mi>t</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi mathvariant="normal">i</mi><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Persecución al encuentro (I) Dos móviles A y B salen simultáneamente de dos puntos que distan #d1 metros uno al encuentro de otro con velocidades #v1 y #v2 m/s respectivamente. Calcula:

¿A qué distancia de A, en metros, se encuentran?
¿Cuánto tiempo habrá estado circulando?

]]> 1.0000000 0.3333333 0 0 distancia = #ditiempo = #t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>incre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mi>incre</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>500</mn><mo>,</mo><mn>1200</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>d1</mi><mo>/</mo><mo>(</mo><mi>v1</mi><mo>+</mo><mi>v2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>v1</mi><mo>*</mo><mi>t</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi mathvariant="normal">i</mi><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Persecución al encuentro (II) Dos móviles A y B salen de dos puntos que distan #d1 metros uno al encuentro de otro con velocidades #v1 y #v2 m/s respectivamente. Si A sale #t1 segundos antes que B, calcula:

¿A qué distancia de A, en metros, se encuentran?
¿Cuánto tiempo habrá estado circulando A?

]]> 1.0000000 0.3333333 0 0 distancia = #ditiempo = #t2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>incre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mi>incre</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>500</mn><mo>,</mo><mn>1200</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>d1</mi><mo>-</mo><mo>(</mo><mi>v1</mi><mo>*</mo><mi>t1</mi><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>v1</mi><mo>+</mo><mi>v2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>t</mi><mo>+</mo><mi>t1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>di</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>v1</mi><mo>*</mo><mi>t2</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi mathvariant="normal">i</mi><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/CINEMÁTICA/MOVIMIENTOS RECTILÍNEOS/SUBIDA Y CAÍDA LIBRE Desde el fondo de un pozo Desde el fondo de un pozo de #hp m de profundidad lanzamos un objeto hacia arriba con una velocidad de #vi m/s. Calcula a qué altura, en metros, estará sobre la superficie del suelo cuando se mueve a #vf m/s

]]> 1.0000000 0.3333333 0 0 #h <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hp</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vf</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mo>-</mo><mo>(</mo><mo>(</mo><mi>vf</mi><mo>*</mo><mi>vf</mi><mo>-</mo><mi>vi</mi><mo>*</mo><mi>vi</mi><mo>)</mo><mo>/</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo>)</mo><mo>-</mo><mi>hp</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#h</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Subida libre Lanzamos un cuerpo hacia arriba desde un balcón a #hi metros con una velocidad de #vi m/s. Calcula:

Su posición al cabo de #t segundos.
Su velocidad en ese instante

]]> 1.0000000 0.3333333 0 0 altura sobre el suelo = #p1velocidad = #v2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hi</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>25</mn><mo>,</mo><mn>48</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>hi</mi><mo>+</mo><mo>(</mo><mi>vi</mi><mo>*</mo><mi>t</mi><mo>)</mo><mo>-</mo><mo>(</mo><mn>4</mn><mo>.</mo><mn>9</mn><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>vi</mi><mo>-</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>t</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>a</mi><mo> </mo><mi mathvariant="normal">s</mi><mi>o</mi><mi>b</mi><mi>r</mi><mi mathvariant="normal">e</mi><mo> </mo><mi mathvariant="normal">e</mi><mi>l</mi><mo> </mo><mi mathvariant="normal">s</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Subida libre Lanzamos un cuerpo hacia arriba desde un balcón a #hi metros con una velocidad de #vi m/s. Calcula:

Su posición al cabo de #t segundos.
Su velocidad en ese instante

]]> 1.0000000 0.3333333 0 0 altura sobre el suelo = #p1velocidad = #v2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hi</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>25</mn><mo>,</mo><mn>48</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>hi</mi><mo>+</mo><mo>(</mo><mi>vi</mi><mo>*</mo><mi>t</mi><mo>)</mo><mo>-</mo><mo>(</mo><mn>4</mn><mo>.</mo><mn>9</mn><mo>*</mo><msup><mi>t</mi><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>vi</mi><mo>-</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>t</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>l</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>a</mi><mo> </mo><mi mathvariant="normal">s</mi><mi>o</mi><mi>b</mi><mi>r</mi><mi mathvariant="normal">e</mi><mo> </mo><mi mathvariant="normal">e</mi><mi>l</mi><mo> </mo><mi mathvariant="normal">s</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Subida libre Lanzamos un cuerpo desde un balcón a #hi metros con una velocidad de #vi m/s. Calcula el tiempo, en segundos, que tardaría en llegar al suelo si:

Lo lanzamos hacia arriba.
Lo lanzamos hacia abajo.

]]> 1.0000000 0.3333333 0 0 tiempo 1 = #t1tiempo 2 = #t2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hi</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>raiz1</mi><mo>=</mo><msqrt><mrow><msup><mi>vi</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>hi</mi><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>(</mo><mi>vi</mi><mo>+</mo><mi>raiz1</mi><mo>)</mo><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>vi</mi><mo>+</mo><mi>raiz1</mi><mo>)</mo><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gx</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>t1</mi><mo>)</mo><mo>/</mo><mi>t1</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mi>t2</mi><mo>)</mo><mo>/</mo><mi>t2</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mi>gx</mi><mo> </mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><mi>devolver</mi><mo> </mo><mi>gx</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>1</mn><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Subida libre balcón Lanzamos un cuerpo desde un balcón a #hi metros con una velocidad de #vi m/s. Calcula el tiempo, en segundos, que tardaría en llegar al suelo si:

Lo lanzamos hacia arriba.
Lo lanzamos hacia abajo.

]]> 1.0000000 0.3333333 0 0 tiempo 1 = #t1tiempo 2 = #t2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hi</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>raiz1</mi><mo>=</mo><msqrt><mrow><msup><mi>vi</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>hi</mi><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>(</mo><mi>vi</mi><mo>+</mo><mi>raiz1</mi><mo>)</mo><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>vi</mi><mo>+</mo><mi>raiz1</mi><mo>)</mo><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>1</mn><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Subida libre globo Lanzamos un cuerpo hacia arriba desde un globo a #hi metros con una velocidad de #v1 m/s. Calcula el tiempo, en segundos, que tardaría en llegar al suelo si el globo en ese momento:

Sube con #v2 m/s.
Baja con #v2 m/s.

]]> 1.0000000 0.3333333 0 0 tiempo 1 = #t1tiempo 2 = #t2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hi</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi1</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mi>v2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi2</mi><mo>=</mo><mi>v1</mi><mo>-</mo><mi>v2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>raiz1</mi><mo>=</mo><msqrt><mrow><msup><mi>vi1</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>hi</mi><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>(</mo><mi>vi1</mi><mo>+</mo><mi>raiz1</mi><mo>)</mo><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rai2</mi><mo>=</mo><msqrt><mrow><msup><mi>vi2</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mn>19</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>hi</mi><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>(</mo><mi>vi2</mi><mo>+</mo><mi>rai2</mi><mo>)</mo><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mn>1</mn><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>1</mn><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mn>2</mn><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Subida libre pozo Lanzamos un cuerpo hacia arriba desde el borde de un pozo de #hi metros de profundidad con una velocidad de #vi m/s. Calcula:

El tiempo en segundos necesario para alcanzar su altura máxima.
El tiempo, en segundos, que tardaría en caer al suelo, en el fondo del pozo

]]> 1.0000000 0.3333333 0 0 tiempo = #t1tiempo = #t2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hi</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>25</mn><mo>,</mo><mn>48</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>vi</mi><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>raiz1</mi><mo>=</mo><mo>-</mo><msqrt><mrow><msup><mi>vi</mi><mn>2</mn></msup><mo>+</mo><mo>(</mo><mn>2</mn><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>hi</mi><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mo>(</mo><mi>vi</mi><mo>-</mo><mi>raiz1</mi><mo>)</mo><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>1</mn><mspace linebreak="newline"/><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Subida libre se deja caer desde azotea Desde una azotea situada a #hi metros de altura se nos cae un objeto a la calle. Calcula:

El tiempo, en segundos, que tarda en llegar al suelo.
Su velocidad en ese instante

]]> 1.0000000 0.3333333 0 0 Tiempo de caida= #t1velocidad = #v1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>hi</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>25</mn><mo>,</mo><mn>48</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><msqrt><mrow><mn>19</mn><mo>.</mo><mn>6</mn><mo>*</mo><mi>hi</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>v1</mi><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>c</mi><mi>a</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>1</mn><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Subida libre suelo Lanzamos un cuerpo desde el suelo con una velocidad de #vi m/s. Calcula:

El tiempo, en segundos, que tardaría en volver al suelo.
La altura máxima que alcanzaría, en metros.

]]> 1.0000000 0.3333333 0 0 Tiempo= #tAltura = #y1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>vi</mi><mo>/</mo><mn>4</mn><mo>.</mo><mn>9</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><msup><mi>vi</mi><mn>2</mn></msup><mo>/</mo><mn>19</mn><mo>.</mo><mn>6</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mspace linebreak="newline"/><mi>A</mi><mi>l</mi><mi>t</mi><mi>u</mi><mi>r</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/FUERZAS DE LA NATURALEZA/CAMPO ELÉCTRICO Atracción entre dos cargas iguales Dos cargas iguales, que se encuentran a una distancia de #d metros, se repelen con una fuerza de #f N. Calcula el valor de las cargas en mC

]]> 1.0000000 0.3333333 0 0 #q <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>80</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><mn>1000</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><mi>f</mi><mo>*</mo><mi>d</mi><mo>*</mo><mi>d</mi><mo>/</mo><mo>(</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>)</mo></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#q</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.01))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> distribución de cargas (Terminar) En la distribución de cargas de la figura sabemos que A= #qa μC, B= #qb μC, C = #qc μC,. Si las distancia x = #dx m e y = #dy m. Calcula el módulo de la intensidad de campo, en N/C, que se ejercerá sobre el vértice que falta.

]]> 1.0000000 0.3333333 0 0 #et]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dy</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>dx</mi><mo>/</mo><mi>dy</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ea</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>3</mn></msup><mo>*</mo><mi>qa</mi><mo>/</mo><msup><mi>dy</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eb</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>3</mn></msup><mo>*</mo><mi>qb</mi><mo>/</mo><mo>(</mo><msup><mi>dy</mi><mn>2</mn></msup><mo>+</mo><msup><mi>dx</mi><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>3</mn></msup><mo>*</mo><mi>qc</mi><mo>/</mo><msup><mi>dx</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>etx</mi><mo>=</mo><mi>ea</mi><mo>+</mo><mo>(</mo><mi>eb</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ety</mi><mo>=</mo><mi>ec</mi><mo>+</mo><mo>(</mo><mi>eb</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>et</mi><mo>=</mo><msqrt><mrow><msup><mi>etx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ety</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Dos cargas Tenemos un sistema formado por dos cargas: una de #q1 mC situada en el punto ( #x1 , 0) y otra de #q2 mC situada en el punto ( #x2 , 0). Calcula el módulo de la intensidad de campo, en N/C, en el punto ( #xp , #yp) (Las distancias están en metros)

]]> 1.0000000 0.3333333 0 0 #et]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xp</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>yp</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>*</mo><mi>q1</mi><mo>/</mo><mo>(</mo><mo>(</mo><mi>xp</mi><mo>-</mo><mi>x1</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><msup><mi>yp</mi><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>*</mo><mi>q2</mi><mo>/</mo><mo>(</mo><mo>(</mo><mi>xp</mi><mo>-</mo><mi>x2</mi><msup><mo>)</mo><mn>2</mn></msup><mo>+</mo><msup><mi>yp</mi><mn>2</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>yp</mi><mo>/</mo><mo>(</mo><mi>xp</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>yp</mi><mo>/</mo><mo>(</mo><mi>xp</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>)</mo><mo>+</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ex</mi><mo>=</mo><mi>e1</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>+</mo><mi>e2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ey</mi><mo>=</mo><mi>e1</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>a1</mi><mo>)</mo><mo>+</mo><mi>e2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>et</mi><mo>=</mo><msqrt><mrow><msup><mi>ex</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ey</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Intensidad de campo. Dos cargas pos neg Tenemos dos cargas puntuales A y B cuyos valores son #qa mC y #qb mC situadas en los puntos (#xa,0) y (#xb,0) respectivamente. Calcula la intensidad de campo(E), en N/C, en el origen de corrodenadas, indicando si será positiva o negativa.

]]> 1.0000000 0.3333333 0 0 #e]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xb</mi><mo>=</mo><mo>-</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ea</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>*</mo><mi>qa</mi><mo>/</mo><msup><mi>xa</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eb</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>*</mo><mi>qb</mi><mo>/</mo><msup><mi>xb</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>eb</mi><mo>+</mo><mi>ea</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Intensidad de campo. Dos cargas puntuales sobre un eje Tenemos dos cargas puntuales A y B cuyos valores son #qa mC y #qb mC situadas en los puntos (#xa,0) y (#xb,0) respectivamente. Calcula la intensidad de campo(E), en N/C, en el origen de corrodenadas, indicando si será positiva o negativa.

]]> 1.0000000 0.3333333 0 0 #e]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ea</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>*</mo><mi>qa</mi><mo>/</mo><msup><mi>xa</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eb</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>*</mo><mi>qb</mi><mo>/</mo><msup><mi>xb</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>eb</mi><mo>+</mo><mi>ea</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Modelo de Bohr En el modelo de Rutherford del átomo de hidrógeno, el electrón gira describiendo órbitas circulares alrededor de un protón. Si la órbita de un electrón tiene un radio de #r pm, calcúlese la fuerza de atracción (N)protón-electrón y la velocidad (m/s) del electrón para que la órbita sea estable.

Datos: masa del electrón = 9.1·10^-31 Kg; carga del electrón = 1.6·10^-19 C

]]> 1.0000000 0.3333333 0 0 Fuerza = #fVelcocidad = #v]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>re</mi><mo>=</mo><mi>r</mi><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>12</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qe</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>19</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>1</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>*</mo><mi>qe</mi><mo>*</mo><mi>qe</mi><mo>/</mo><msup><mi>re</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mrow><mi>f</mi><mo>*</mo><mi>re</mi><mo>/</mo><mi>me</mi></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>z</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>f</mi><mspace linebreak="newline"/><mi>V</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>c</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/FUERZAS DE LA NATURALEZA/GRAVITACIÓN Calcular la masa de un planeta Un determinado planeta tiene un radio de #r km. Calcula cuál será su masa, si un objeto de #mo Kg pesa #p N en su superficie

]]> 1.0000000 0.3333333 0 0 #mp <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>150</mn><mo>)</mo><mo>*</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mp</mi><mo>=</mo><mi>p</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>/</mo><mo>(</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>*</mo><mi>mo</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#mp</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.02))</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Dos planetas Si el radio de la órbita de la Tierra alrededor del Sol es de 150 millones de kilómetros. Calcula el radio de la órbita (km) de un planeta que tarde #t años en girar alrededor del Sol

]]> 1.0000000 0.3333333 0 0 #r2 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mn>150</mn><mo>.</mo><mn>0</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>r1</mi><mo>*</mo><mroot><msup><mi>t</mi><mn>2</mn></msup><mn>3</mn></mroot></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r2</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Gravedad en un planeta Calcula la aceleración de la gravedad, en m/s², en un planeta cuyo radio es #r Km y cuya masa es #m Kg.

]]> 1.0000000 0.3333333 0 0 #g]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>950</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>20</mn><mo>)</mo><mo>*</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>g1</mi><mo>*</mo><msup><mi>r</mi><mn>2</mn></msup><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>/</mo><mo>(</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>*</mo><mi>m</mi><mo>/</mo><mo>(</mo><msup><mi>r</mi><mn>2</mn></msup><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">g</mi><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Satélite El radio de la Tierra es de 6370 Km y su masa es de 5.97·10²⁴Kg. Calcula la velocidad que deberá tener un satélite (m/s) para que su órbita ecuatorial sea estable a #h Km sobre el suelo

]]> 1.0000000 0.3333333 0 0 #v <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3000</mn><mo>,</mo><mn>8000</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mrow><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>14</mn></mrow></msup><mo>*</mo><mn>5</mn><mo>.</mo><mn>97</mn><mo>*</mo><msup><mn>10</mn><mn>24</mn></msup><mo>/</mo><mo>(</mo><mi>h</mi><mo>+</mo><mn>6370</mn><mo>)</mo></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#v</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un cuerpo a una cierta altura El radio de la Tierra es de 6370 Km y su masa es de 5.97·10²⁴Kg. Calcula el peso, en N, de una persona de #m kg si lo situamos a una altura de #h Km sobre la superficie terrestre

]]> 1.0000000 0.3333333 0 0 #p <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>800</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>17</mn></mrow></msup><mo>*</mo><mn>5</mn><mo>.</mo><mn>97</mn><mo>*</mo><msup><mn>10</mn><mn>24</mn></msup><mo>*</mo><mi>m</mi><mo>/</mo><mo>(</mo><mi>h</mi><mo>+</mo><mn>6370</mn><msup><mo>)</mo><mn>2</mn></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#p</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/FUERZAS EN GENERAL Calcular coeficiente de rozamiento Un bloque de #m gramos se desliza por una mesa horizontal con una velocidad de #v cm/s. Si se detiene en #d cm. ¿Cuál será el coeficiente de rozamiento?

]]> 1.0000000 0.3333333 0 0 #mu]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>80</mn><mo>,</mo><mn>250</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>*</mo><mi>v</mi><mo>*</mo><mi>v</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>d</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>a</mi><mo>/</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>u</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcular el módulo de la aceleración La única fuerza que se ejerce sobre un cuerpo tiene dos componentes F_x= #fx N y F_y = #fy N. Calcule el módulo de su aceleración em m/s² si su masa es #m Kg

]]> 1.0000000 0.3333333 0 0 #a <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fy</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><mi>fx</mi><mo>*</mo><mi>fx</mi><mo>+</mo><mi>fy</mi><mo>*</mo><mi>fy</mi></mrow></msqrt><mo>/</mo><mi>m</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Determinar la fuerza, en N, necesaria para tirar de un cuerpo de #m Kg hacia arriba de forma que baje con una aceleración de #a m/s2 (copia) Determinar la fuerza, en N, necesaria para tirar de un cuerpo de #m Kg hacia arriba de forma que baje con una aceleración de #a m/s²

El valor en N de la fuerza resultante.
El ángulo positivo que forma la fuerza resultante con la fuerza A

]]> 1.0000000 0.3333333 0 0 Fuerza = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>z</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Una locomotora tira de un tren Una locomotora de #ml Kg tira de un vagón de #mt1 Kg con una aceleración de #a m/s² como máximo por una vía horizontal. ¿Cuál será la aceleración máxima si tira de un vagón de #mt2 Kg?

]]> 1.0000000 0.3333333 0 0 #af <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ml</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mt1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>*</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mt2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>18</mn><mo>)</mo><mo>*</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>af</mi><mo>=</mo><mi>a</mi><mo>*</mo><mo>(</mo><mi>ml</mi><mo>+</mo><mi>mt1</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>ml</mi><mo>+</mo><mi>mt2</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#af</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/FUERZAS EN GENERAL/CUERPOS EN SUPERFICIES Cuerpo en superficie vertical Un cuerpo de #m g está apoyado sobre una superficie vertical. Si el coeficiente de rozamiento es #mu ¿Qué fuerza horizontal, en N, tendremos que ejercer, como mínimo, contra el objeto para que no resbale y caiga?

El valor de la aceleración, en m/s² con la que se moverá horizontalmente en ausencia de rozamientos.
El valor de la fuerza normal en N

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 1.0000000 0.3333333 0 0 aceleración = #acN = #fn]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mas</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mi>fu</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>/</mo><mi>mas</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fn</mi><mo>=</mo><mo>(</mo><mi>fu</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>mas</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>c</mi><mspace linebreak="newline"/><mi mathvariant="normal">N</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>f</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Plano inclinado y fuerza Por un plano inclinado #an º tiramos hacia arriba, con una fuerza paralela al mismo, de una caja de masa #m Kg. Si el coeficiente de rozamiento de la caja con el plano es de #k, calcula la fuerza mínima, en N, que tendremos que ejercer para que ésta siga:

Subiendo con velocidad constante
Bajando con velocidad constante

]]> 1.0000000 0.3333333 0 0 1.- Subida = #fs2.- Bajada = #fb]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>peso</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>px</mi><mo>=</mo><mi>peso</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fr</mi><mo>=</mo><mi>peso</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fs</mi><mo>=</mo><mi>px</mi><mo>+</mo><mi>fr</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fb</mi><mo>=</mo><mi>px</mi><mo>-</mo><mi>fr</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo>-</mo><mo> </mo><mi>S</mi><mi>u</mi><mi mathvariant="normal">b</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>f</mi><mi mathvariant="normal">s</mi><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo>-</mo><mo> </mo><mi>B</mi><mi>a</mi><mi mathvariant="normal">j</mi><mi>a</mi><mi>d</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>f</mi><mi mathvariant="normal">b</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sobre una superficie horizontal empujamos una caja Sobre una superficie horizontal empujamos una caja de masa #m Kg con una fuerza de #fe N. Calcula la aceleración de la caja, en m/s2, si el coeficiente de rozamiento es #mu

]]> 1.0000000 0.3333333 0 0 #a <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fe</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>160</mn><mo>,</mo><mn>190</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>fe</mi><mo>/</mo><mi>m</mi><mo>)</mo><mo>-</mo><mo>(</mo><mi>mu</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.02</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sobre una superficie inclinada empujamos una caja baja(copia) (copia) Sobre una superficie inclinada #an º queremos frenar la caida de una caja de masa #m Kg con una fuerza de #fe N. Calcula la aceleración de la caja, en m/s², si el coeficiente de rozamiento es #mu

]]> 1.0000000 0.3333333 0 0 #a <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fe</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pt</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>pt</mi><mo>-</mo><mi>fe</mi><mo>-</mo><mi>pr</mi><mo>)</mo><mo>/</mo><mi>m</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sobre una superficie inclinada empujamos una caja (copia) Sobre una superficie inclinada #an º hacemos subir una caja de masa #m Kg con una fuerza de #fe N. Calcula la aceleración de la caja, en m/s², si el coeficiente de rozamiento es #mu

]]> 1.0000000 0.3333333 0 0 #a <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fe</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>250</mn><mo>,</mo><mn>280</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pt</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>fe</mi><mo>-</mo><mi>pt</mi><mo>-</mo><mi>pr</mi><mo>)</mo><mo>/</mo><mi>m</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#a</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/FUERZAS EN GENERAL/LEY DE HOOKE Calcula la longitud Calcula la longitud de un muelle, en cm, cuya constante elástica de de #k N/m y cuya longitud en reposo es de #lo cm, si tiramos de él con una fuerza de #f N

]]> 1.0000000 0.3333333 0 0 #l <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1000</mn><mo>,</mo><mn>2000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mo>(</mo><mi>f</mi><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>/</mo><mi>k</mi><mo>)</mo><mo>+</mo><mi>lo</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#l</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Constante elástica de un muelle Un determinado muelle mide #l1 cm si tiramos de él con una fuerza de #f1 N y #l2 cm si tiramos con una fuerza de #f2 N. Calcula su constante elástica, en N/m, y su longitud en reposo en cm

]]> 1.0000000 0.3333333 0 0 K =#kL0 =#lo]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>25</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>22</mn><mo>,</mo><mn>45</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>lo</mi><mo>+</mo><mi>l1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>lo</mi><mo>+</mo><mi>l2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>k</mi><mo>*</mo><mo>(</mo><mi>l1</mi><mo>-</mo><mi>lo</mi><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>k</mi><mo>*</mo><mo>(</mo><mi>l2</mi><mo>-</mo><mi>lo</mi><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>f1</mi><mo>-</mo><mi>f2</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>l1</mi><mo>-</mo><mi>l2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo</mi><mo>=</mo><mn>100</mn><mo>*</mo><mo>(</mo><mo>(</mo><mi>k</mi><mo>*</mo><mi>l1</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>-</mo><mi>f1</mi><mo>)</mo><mo>/</mo><mi>k</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>K</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>k</mi><mspace linebreak="newline"/><msub><mi>L</mi><mrow><mn>0</mn><mo> </mo></mrow></msub><mo>=</mo><mo>#</mo><mi>l</mi><mi>o</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Objeto colgando de un muelle Un muelle mide en reposo #lo cm y, si colgamos de él un objeto de #m g, mide #l1 cm. Calcula su constante elástica en N/m

]]> 1.0000000 0.3333333 0 0 #k <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>65</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>800</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>98</mn><mo>/</mo><mo>(</mo><mi>l1</mi><mo>-</mo><mi>lo</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#k</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Objeto colgando de un muelle (copia) Un muelle mide en reposo #lo cm y, si colgamos de él un objeto de #m g, mide #l1 cm. Calcula su constante elástica en N/m

]]> 1.0000000 0.3333333 0 0 #k <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>65</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>800</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>98</mn><mo>/</mo><mo>(</mo><mi>l1</mi><mo>-</mo><mi>lo</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#k</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un objeto con dos muelles Un objeto está en una superficie horizontal sujeto a dos paredes enfrentadas por dos muelles cuyos datos se indican el la tabla. Si las paredes distan #lp cm. Calcula la longitud del muelle A en cm


	A	B
L₀ (cm)	#lo1	#lo2
K(N/m)	#k1	#k2

]]> 1.0000000 0.3333333 0 0 #la <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lp</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>150</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>150</mn><mo>,</mo><mn>200</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>300</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>lo1</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>lo2</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>lp</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>la</mi><mo>=</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mo>(</mo><mi>k2</mi><mo>*</mo><mi>d</mi><mo>)</mo><mo>+</mo><mo>(</mo><mi>k1</mi><mo>*</mo><mi>l1</mi><mo>)</mo><mo>-</mo><mo>(</mo><mi>k2</mi><mo>*</mo><mi>l2</mi><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>k1</mi><mo>+</mo><mi>k2</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#la</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/FUERZAS EN GENERAL/SISTEMAS DE CUERPOS Plano con tres cuerpos En la imagen de la figura, las masas de A, B y C son respectivamente #ma, #mb y #mc Kg. Si el ángulo α es de #an º, calcula:

La aceleración del sistema hacia la derecha, en m/s.
La tensión de las cuerdas A-B y B-C en N.

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1.0000000 0.3333333 0 0 1.- Aceleración = #a2.- Tensión A-B =#t1 Tensión B-C = #t2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>mc</mi><mo>-</mo><mo>(</mo><mi>ma</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>/</mo><mo>(</mo><mi>ma</mi><mo>+</mo><mi>mb</mi><mo>+</mo><mi>mc</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mo>(</mo><mi>a</mi><mo>+</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>mc</mi><mo>*</mo><mo>(</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>-</mo><mi>a</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo>-</mo><mo> </mo><mi>A</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo>-</mo><mo> </mo><mi>T</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mi>A</mi><mo>-</mo><mi>B</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>t</mi><mn>1</mn><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi>T</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>s</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mi>B</mi><mo>-</mo><mi>C</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Plano con tres cuerpos rozamiento En la imagen de la figura, las masas de A, B y C son respectivamente #ma, #mb y #mc Kg. Si el ángulo α es de #an º y el coeficiente de rozamiento entre los cuerpos y la superficie es de #k, calcula:

La aceleración del sistema hacia la derecha, en m/s².
La tensión de las cuerdas A-B y B-C en N.

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1.0000000 0.3333333 0 0 1.- Aceleración = #a2.- Tensión A-B =#t1 Tensión B-C = #t2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pxa</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fra</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>frb</mi><mo>=</mo><mi>mb</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pc</mi><mo>=</mo><mi>mc</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>pc</mi><mo>-</mo><mi>frb</mi><mo>-</mo><mi>fra</mi><mo>-</mo><mi>pxa</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>ma</mi><mo>+</mo><mi>mb</mi><mo>+</mo><mi>mc</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mo>(</mo><mi>ma</mi><mo>*</mo><mi>a</mi><mo>)</mo><mo>+</mo><mi>pxa</mi><mo>+</mo><mi>fra</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>pc</mi><mo>-</mo><mo>(</mo><mi>mc</mi><mo>*</mo><mi>a</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo>-</mo><mo> </mo><mi mathvariant="normal">A</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo>-</mo><mo> </mo><mi mathvariant="normal">T</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mi mathvariant="normal">A</mi><mo>-</mo><mi>B</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>t</mi><mn>1</mn><mspace linebreak="newline"/><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mo> </mo><mi mathvariant="normal">T</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mi>B</mi><mo>-</mo><mi mathvariant="normal">C</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Plano con tres cuerpos rozamiento mínimo En la imagen de la figura, las masas de A, B y C son respectivamente #ma, #mb y #mc Kg. Si el ángulo α es de #an º calcula el coeficiente de rozamiento mínimo entre los cuerpos y la superficie para que el sistema no se mueva.

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1.0000000 0.3333333 0 0 #k <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mo>(</mo><mi>mc</mi><mo>-</mo><mo>(</mo><mi>ma</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>mb</mi><mo>+</mo><mo>(</mo><mi>ma</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#k</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Plano inclinado y recto En el sistema de la figura el coeficiente de rozamiento entre las superficies es de #mu. Si el ángulo del plano inclinado es de #an º y las masas se A y B son, respectivamente #ma y #mb Kg. Calcula la fuerza necesaria para que suba con velocidad constante

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1.0000000 0.3333333 0 0 #f <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fra</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pta</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>frb</mi><mo>=</mo><mi>mb</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>fra</mi><mo>+</mo><mi>pta</mi><mo>+</mo><mi>frb</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#f</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Plano inclinado y recto (copia) En el sistema de la figura el coeficiente de rozamiento entre las superficies es de #mu. Si el ángulo del plano inclinado es de #an º y las masas se A y B son, respectivamente #ma y #mb Kg. Calcula la aceleración del sistema,(m/s²) y la tensión de la cuerda (N)

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1.0000000 0.3333333 0 0 aceleración =#aTensión =#t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fra</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pta</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>frb</mi><mo>=</mo><mi>mb</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>pta</mi><mo>-</mo><mi>fra</mi><mo>-</mo><mi>frb</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>ma</mi><mo>+</mo><mi>mb</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mo>(</mo><mi>mb</mi><mo>*</mo><mi>a</mi><mo>)</mo><mo>+</mo><mi>frb</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>T</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Plano inclinado y vertical En el sistema de la figura el coeficiente de rozamiento entre las superficies es de #mu. Si el ángulo del plano inclinado es de #an º y las masas se A y B son, respectivamente #ma y #mb Kg. Calcula la aceleración del sistema,(m/s²) y la tensión de la cuerda (N)

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1.0000000 0.3333333 0 0 aceleración =#aTensión =#t]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fra</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pta</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pb</mi><mo>=</mo><mi>mb</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo>(</mo><mi>pb</mi><mo>-</mo><mi>fra</mi><mo>-</mo><mi>pta</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>ma</mi><mo>+</mo><mi>mb</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>pb</mi><mo>-</mo><mo>(</mo><mi>mb</mi><mo>*</mo><mi>a</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi mathvariant="normal">T</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 1º BACHILLERATO/FÍSICA/DINÁMICA/MOMENTO LINEAL Bolas que chocan con ángulo Dos bolas A y B de masas #ma Kg y #mb Kg respectivamente chocan según indica la figura y se quedan unidas. Si α= #aa º y β = #ab º. Si la Bola A se mueve inicialmetne a #va m/s. Calcula, en m/s:

La velocidad de B
La velocidad del conjunto después del choque

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1.0000000 0.3333333 0 0 Velocidad de B = #vbVelocidad del conjunto = #vt]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ab</mi><mo> </mo><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>va</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aar</mi><mo>=</mo><mi>aa</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>abr</mi><mo>=</mo><mi>ab</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vb</mi><mo>=</mo><mi>ma</mi><mo>*</mo><mi>va</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>aar</mi><mo>)</mo><mo>/</mo><mo>(</mo><mi>mb</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>abr</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vt</mi><mo>=</mo><mo>(</mo><mo>(</mo><mi>ma</mi><mo>*</mo><mi>va</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>aar</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>mb</mi><mo>*</mo><mi>vb</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>abr</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>ma</mi><mo>+</mo><mi>mb</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>B</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mi>b</mi><mspace linebreak="newline"/><mi>V</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mi>l</mi><mo> </mo><mi>c</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">j</mi><mi>u</mi><mi>n</mi><mi>t</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Bomba que cae y explota Una bomba de masa #mi Kg cae durante #t1 segundos libremente. En ese momento explota dividiéndose en dos trozos. #t2 segundos después el trozo mayor ( #po % de la masa) se mueve con una velocidad #v1 m/s y un ángulo de #a1 º bajo la horizontal. Calcula la rapidez, en m/s, del otro trozo en ese instante

]]> 1.0000000 0.3333333 0 0 #v2 <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>po</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>mi</mi><mo>*</mo><mi>po</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mi>mi</mi><mo>-</mo><mi>m1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>80</mn><mo>,</mo><mn>120</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>70</mn><mo>,</mo><mn>85</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1r</mi><mo>=</mo><mo>-</mo><mi>a1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pt</mi><mo>=</mo><mi>mi</mi><mo>*</mo><mo>(</mo><mo>-</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>)</mo><mo>*</mo><mo>(</mo><mi>t1</mi><mo>+</mo><mi>t2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mo>-</mo><mo>(</mo><mi>m1</mi><mo>*</mo><mi>v1</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>a1r</mi><mo>)</mo><mo>)</mo><mo>/</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mo>(</mo><mo>-</mo><mi>pt</mi><mo>+</mo><mo>(</mo><mi>m1</mi><mo>*</mo><mi>v1</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>a1r</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>/</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#v2</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Bomba que explota Una bomba de #mini Kg explota y se divide en dos trozos de #m1 y #m2 Kg. El primero se mueve hacia la derecha con una velocidad de #v1 m/s. Calcula la velocidad del otro trozo, si la bomba inicialmente:

Estaba en reposo.
Se movía hacia la derecha con una velocidad #vb m/s

]]> 1.0000000 0.3333333 0 0 Si está en reposo = #vf1Si se movía inicialmente = #vf2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mini</mi><mo>=</mo><mi>m1</mi><mo>+</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vf1</mi><mo>=</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>m1</mi><mo>*</mo><mi>v1</mi><mo>/</mo><mi>m2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vf2</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mo>(</mo><mi>vb</mi><mo>*</mo><mi>mini</mi><mo>)</mo><mo>-</mo><mo>(</mo><mi>m1</mi><mo>*</mo><mi>v1</mi><mo>)</mo><mo>)</mo><mo>/</mo><mi>m2</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mi mathvariant="normal">i</mi><mo> </mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>á</mi><mo> </mo><mi mathvariant="normal">e</mi><mi>n</mi><mo> </mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>p</mi><mi>o</mi><mi mathvariant="normal">s</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mi>f</mi><mn>1</mn><mspace linebreak="newline"/><mi>S</mi><mi mathvariant="normal">i</mi><mo> </mo><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mo> </mo><mi mathvariant="normal">m</mi><mi>o</mi><mi>v</mi><mi>í</mi><mi>a</mi><mo> </mo><mi mathvariant="normal">i</mi><mi>n</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mi>lm</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mi>f</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Coche y camón al encuentro Por una carretera horizontal un camión, de masa #mca Kg va con una velocidad de #vca m/s. Un coche, de masa #mco Kg se dirige a su encuentro a una velocidad de #vco m/s. tras chocar se quedan unidos. Calcula la rapidez del conjunto.

]]> 1.0000000 0.3333333 0 0 #v <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mco</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>600</mn><mo>,</mo><mn>900</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vco</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mca</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3000</mn><mo>,</mo><mn>6000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vca</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mo>(</mo><mi>mca</mi><mo>*</mo><mi>vca</mi><mo>)</mo><mo>-</mo><mo>(</mo><mi>mco</mi><mo>*</mo><mi>vco</mi><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>mca</mi><mo>+</mo><mi>mco</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#v</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Coche y camón uno detrás de otro Por una carretera horizontal un camión, de masa #mca Kg va con una velocidad de #vca m/s. Un coche, de masa #mco Kg tiene la misma dirección y sentido a una velocidad de #vco m/s. tras chocar se quedan unidos. Calcula la rapidez del conjunto.

]]> 1.0000000 0.3333333 0 0 #v <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mco</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>600</mn><mo>,</mo><mn>900</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vco</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mca</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3000</mn><mo>,</mo><mn>6000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vca</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mo>(</mo><mi>mca</mi><mo>*</mo><mi>vca</mi><mo>)</mo><mo>+</mo><mo>(</mo><mi>mco</mi><mo>*</mo><mi>vco</mi><mo>)</mo><mo>)</mo><mo>/</mo><mo>(</mo><mi>mca</mi><mo>+</mo><mi>mco</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#v</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Dos bolas Dos bolas A y B de igual masa se dirigen una al encuentro de la otra a la misma velocidad #v1 m/s formando un ángulo de 90º. Tras chocar, una de ellas se desvía #a º y sale con una velocidad #v2 m/s. Calcula la velocidad de la segunda

]]> 1.0000000 0.3333333 0 0 #vf <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ar</mi><mo>=</mo><mi>a</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vx</mi><mo>=</mo><mi>v1</mi><mo>-</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ar</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vy</mi><mo>=</mo><mi>v1</mi><mo>-</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ar</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vf</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>vx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>vy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#vf</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/ENERGÍA/CAMPOS Calcular potencial eléctrico Tenemos dos cargas de #q1 y #q2 mC situadas en los puntos (0,#y1) y (#x2,0), distancias en metros, respectivamente. Calcula el valor del potencial eléctrico (V) en:

El origen de coordenadas.
En el punto (#x2,#y1)

]]> 1.0000000 0.3333333 0 0 1. Potencial =#v1 2. Potencial =#v2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>28</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>17</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v11</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>*</mo><mi>q1</mi><mo>/</mo><mi>y1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v21</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>*</mo><mi>q2</mi><mo>/</mo><mi>x2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v12</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>*</mo><mi>q1</mi><mo>/</mo><mi>x2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v22</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>*</mo><mi>q2</mi><mo>/</mo><mi>y1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>v11</mi><mo>+</mo><mi>v21</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>v12</mi><mo>+</mo><mi>v22</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo> </mo><mi>P</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mn>1</mn><mspace linebreak="newline"/><mo> </mo><mn>2</mn><mo>.</mo><mo> </mo><mi>P</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Calcular potencial eléctrico pos neg Tenemos dos cargas de #q1 y #q2 mC situadas en los puntos (0,#y1) y (#x2,0), distancias en metros, respectivamente. Calcula el valor del potencial eléctrico (V) en:

El origen de coordenadas.
En el punto (#x2,#y1)

]]> 1.0000000 0.3333333 0 0 1. Potencial =#v1 2. Potencial =#v2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mo>-</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>28</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>17</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>13</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v11</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>*</mo><mi>q1</mi><mo>/</mo><mi>y1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v21</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>*</mo><mi>q2</mi><mo>/</mo><mi>x2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v12</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>*</mo><mi>q1</mi><mo>/</mo><mi>x2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v22</mi><mo>=</mo><mn>9</mn><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>*</mo><mi>q2</mi><mo>/</mo><mi>y1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>v11</mi><mo>+</mo><mi>v21</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>v12</mi><mo>+</mo><mi>v22</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo> </mo><mi>P</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mn>1</mn><mspace linebreak="newline"/><mo> </mo><mn>2</mn><mo>.</mo><mo> </mo><mi>P</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Diferencia entres suelo y altura (Ep) Calcula la diferencia de energía potencial (J) que habrá para un objeto de #m Kg entre el suelo y una altura de:

#d1 Km
#d2 Km

Datos: radio de la Tierra = 6370 Km; Masa de la Tierra = 5.97· 10²⁴ Kg

]]> 1.0000000 0.3333333 0 0 1. ΔEp = #dep12. ΔEp = #dep2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo><mo>*</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dep1</mi><mo>=</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>d1</mi><mo>*</mo><msup><mn>10</mn><mn>3</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dep2</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>*</mo><mn>5</mn><mo>.</mo><mn>97</mn><mo>*</mo><msup><mn>10</mn><mn>24</mn></msup><mo>*</mo><mi>m</mi><mo>*</mo><mo>(</mo><mo>(</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>/</mo><mn>6370</mn><mo>)</mo><mo>-</mo><mo>(</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>/</mo><mo>(</mo><mn>6370</mn><mo>+</mo><mi>d2</mi><mo>)</mo><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo> </mo><mi>Δ</mi><mi>E</mi><mi>p</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>p</mi><mn>1</mn><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo> </mo><mi>Δ</mi><mi>E</mi><mi>p</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>p</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Energía potencial campo gravitatorio Calcula la energía potencial gravitatoria de un objeto de #m Kg situado a #d km del centro de un planeta de #ba·10³⁰ Kg

]]> 1.0000000 0.3333333 0 0 #ep]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>80</mn><mo>)</mo><mo>*</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ba</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ep</mi><mo>=</mo><mo>-</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>*</mo><mi>m</mi><mo>*</mo><mi>ba</mi><mo>*</mo><msup><mn>10</mn><mn>30</mn></msup><mo>/</mo><mo>(</mo><mi>d</mi><mo>*</mo><msup><mn>10</mn><mn>3</mn></msup><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Energía total de un objeto en la superficie de la Tierra Tenemos una persona de #m Kg en reposo en el Ecuador sobre la superficie de la Tierra. Calcula (J):

Su energía cinética debida a la rotación terrestre
Su energía potencial gravitatoria. absoluta (suponemos que el efecto de los demás objetos del universo es despreciable).
Su energía total.

Datos: radio Tierral = 6370 Km ; Masa de la Tierra= 5.98·10²⁴ Kg

]]> 1.0000000 0.3333333 0 0 Energía cinética = #ecEnergía potencial = #epEnergía total =#et]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variabl</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mn>2</mn><mo>*</mo><pi/><mo>*</mo><mn>6370</mn><mo>*</mo><msup><mn>10</mn><mn>3</mn></msup><mo>/</mo><mo>(</mo><mn>24</mn><mo>*</mo><mn>3600</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec</mi><mo>=</mo><mi>m</mi><mo>*</mo><msup><mi>v</mi><mn>2</mn></msup><mo>/</mo><mn>2</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ep</mi><mo>=</mo><mo>-</mo><mn>6</mn><mo>.</mo><mn>67</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>11</mn></mrow></msup><mo>*</mo><mi>m</mi><mo>*</mo><mn>5</mn><mo>.</mo><mn>98</mn><mo>*</mo><msup><mn>10</mn><mn>24</mn></msup><mo>/</mo><mo>(</mo><mn>6370</mn><mo>*</mo><msup><mn>10</mn><mn>3</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>et</mi><mo>=</mo><mi>ec</mi><mo>+</mo><mi>ep</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>g</mi><mi>í</mi><mi>a</mi><mo> </mo><mi>c</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi>é</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>c</mi><mspace linebreak="newline"/><mi>E</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>g</mi><mi>í</mi><mi>a</mi><mo> </mo><mi>p</mi><mi>o</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mi>l</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>p</mi><mspace linebreak="newline"/><mi>E</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>g</mi><mi>í</mi><mi>a</mi><mo> </mo><mi>t</mi><mi>o</mi><mi>t</mi><mi>a</mi><mi>l</mi><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/ENERGÍA/CINÉTICA Y POTENCIAL cuerpo que sube y baja Desde una altura de #h1 m se lanza verticalmente hacia arriba una pelota de #m g con una velocidad de #v1 m/s. Calcula su energía mecánica, sobre el suelo y en J, cuando se encuentra a #h2 m sobre el suelo. ¿Cuál es su velocidad, en m/s, cuando llega al suelo?

]]> 1.0000000 0.3333333 0 0 Energía mecánica = #emVelocidad en el suelo =#v2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>12</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>11</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>12</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>m</mi><mo>/</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>em</mi><mo>=</mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>*</mo><mi>m1</mi><mo>*</mo><msup><mi>v1</mi><mn>2</mn></msup><mo>)</mo><mo>+</mo><mo>(</mo><mi>m1</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>h1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><msqrt><mrow><mn>2</mn><mo>*</mo><mi>em</mi><mo>/</mo><mi>m1</mi></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">E</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi mathvariant="normal">g</mi><mi>í</mi><mi>a</mi><mo> </mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>á</mi><mi>n</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mspace linebreak="newline"/><mi>V</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mi mathvariant="normal">e</mi><mi>n</mi><mo> </mo><mi mathvariant="normal">e</mi><mi>l</mi><mo> </mo><mi mathvariant="normal">s</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_literal"><param name="usecase">false</param><param name="usespaces">false</param></assertion></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cuerpo sube y baja Desde un punto situado a #h1 m de altura lanzamos un cuerpo con una velocidad de #v1 m/s. Calcula su velocidad (m/s) cuando está a #h2 m de altura sobre el suelo

]]> 1.0000000 0.3333333 0 0 #ec]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>30</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>18</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec</mi><mo>=</mo><mi>f</mi><mo>*</mo><mi>t</mi><mo>/</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.024</mn></math></output></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>c</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Muelle horizontal Un muelle horizontal, cuya constante elástica es #ke N/m, se comprime #l cm e impulsa un objeto de #m Kg que se mueve por una superficie horizontal cuyo coeficiente de rozamiento con el cuerpo es #mu. Calcula la distancia, en m, que recorre hasta que se para

]]> 1.0000000 0.3333333 0 0 #d <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ke</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>ke</mi><mo>*</mo><msup><mi>l</mi><mn>2</mn></msup><mo>/</mo><mo>(</mo><mn>20000</mn><mo>*</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>mu</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#d</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un muelle con objeto colgando (arreglar) En un muelle colgado del techo colocamos un objeto de masa #m Kg. Una vez en equilibrio, lo estiramos #l cm y lo soltamos. Calcula:

La longitud del muelle, en cm, en la situación de equilibrio.
La velocidad, en m/s, que tendrá el objeto cuando pasa por la posición inicial.

Datos constante elástica = #k N/m; longitud en reposo del muelle = #lo cm

]]> 1.0000000 0.3333333 0 0 longitud en equilibrio =#l1Velocidad = #v]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>12</mn><mo>,</mo><mn>18</mn><mo>)</mo><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>lo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mo>(</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mn>100</mn><mo>/</mo><mi>k</mi><mo>)</mo><mo>+</mo><mi>lo</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eo</mi><mo>=</mo><mo>-</mo><mo>(</mo><mi>m</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>l</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>+</mo><mo>(</mo><mi>k</mi><mo>*</mo><mo>(</mo><mi>l</mi><mo>+</mo><mi>l1</mi><mo>-</mo><mi>lo</mi><msup><mo>)</mo><mn>2</mn></msup><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><msup><mn>10</mn><mn>4</mn></msup><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>efe</mi><mo>=</mo><mi>k</mi><mo>*</mo><mo>(</mo><mi>l1</mi><mo>-</mo><mi>lo</mi><msup><mo>)</mo><mn>2</mn></msup><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><msup><mn>10</mn><mn>4</mn></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><msqrt><mrow><mn>2</mn><mo>*</mo><mo>(</mo><mi>eo</mi><mo>-</mo><mi>efe</mi><mo>)</mo><mo>/</mo><mi>m</mi></mrow></msqrt></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>u</mi><mi>d</mi><mo> </mo><mi mathvariant="normal">e</mi><mi>n</mi><mo> </mo><mi mathvariant="normal">e</mi><mi>q</mi><mi>u</mi><mi mathvariant="normal">i</mi><mi>l</mi><mi mathvariant="normal">i</mi><mi>b</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>o</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>V</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/INTRODUCCIÓN MATEMÁTICA/CONVERSIÓN DE COORDENADAS Polares a cartesianas Sea un vector A de módulo #mo unidades que forma un ángulo de #anº con el semieje positivo de X. Calcula sus componentes.

]]> 1.0000000 0.3333333 0 0 x =#x1y = #y1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>355</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>an</mi><mo>=</mo><mn>90</mn><mo> </mo><mo>∨</mo><mo> </mo><mi>an</mi><mo>=</mo><mn>180</mn><mo> </mo><mo>∨</mo><mo> </mo><mi>an</mi><mo>=</mo><mn>270</mn></mrow><mrow><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>355</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data><data name="inputCompound">true</data></localData></question> Polares a cartesianas Sea un vector A de módulo #mo unidades que forma un ángulo de #anº con el semieje positivo de X. Calcula sus componentes.

]]> 1.0000000 0.3333333 0 0 x =#x1y = #y1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>355</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Polares a cartesianas Sea un vector A de módulo #mo unidades que forma un ángulo de #anº con el semieje positivo de X. Calcula sus componentes.

]]> 1.0000000 0.3333333 0 0 x =#x1y = #y1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>355</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data><data name="inputCompound">true</data></localData></question> Polares a cartesianas (radianes) Sea un vector A de módulo #mo que forma un ángulo de #an radianes con el semieje positivo de X. Calcula sus componentes.

]]> 1.0000000 0.3333333 0 0 x =#x1y = #y1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>355</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Polares a cartesianas (radianes) Sea un vector A de módulo #mo que forma un ángulo de #an radianes con el semieje positivo de X. Calcula sus componentes.

]]> 1.0000000 0.3333333 0 0 x =#x1y = #y1]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>35</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>anr</mi><mo>=</mo><mi>an</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>mo</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>anr</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Rectangulares a polares Sea el vector:

A = #xs i + #ys j

Halla su módulo y el ángulo, en grados, positivo que forma con el semieje positivo de X

]]> 1.0000000 0.3333333 0 0 módulo = #moángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>angulo</mi><mo>(</mo><mo>[</mo><mi>xs</mi><mo>,</mo><mi>ys</mi><mo>]</mo><mo>,</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo><mo>)</mo><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>xs</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ys</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>an</mi></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Rectangulares a polares Sea el vector:

A = #xs i + #ys j

Halla su módulo y el ángulo, en grados, positivo que forma con el semieje positivo de X

]]> 1.0000000 0.3333333 0 0 módulo = #moángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>angulo</mi><mo>(</mo><mo>[</mo><mi>xs</mi><mo>,</mo><mi>ys</mi><mo>]</mo><mo>,</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo><mo>)</mo><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>xs</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ys</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>an</mi></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Rectangulares a polares Sea el vector:

A = #xs i + #ys j

Halla su módulo y el ángulo positivo, en grados, que forma con el semieje positivo de X

]]> 1.0000000 0.3333333 0 0 módulo = #moángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>angulo</mi><mo>(</mo><mo>[</mo><mi>xs</mi><mo>,</mo><mi>ys</mi><mo>]</mo><mo>,</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo><mo>)</mo><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>xs</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ys</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>an</mi></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Rectangulares a polares (radianes) Sea el vector:

A = #xs i + #ys j

Halla su módulo y el ángulo positivo, en radianes,que forma con el semieje positivo de X

]]> 1.0000000 0.3333333 0 0 módulo = #moángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mi>ys</mi><mrow><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>angulo</mi><mo>(</mo><mo>[</mo><mi>xs</mi><mo>,</mo><mi>ys</mi><mo>]</mo><mo>,</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>xs</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ys</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>*</mo><pi/><mo>)</mo><mo>-</mo><mi>an</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Rectangulares a polares (radianes) Sea el vector:

A = #xs i + #ys j

Halla su módulo y el ángulo, en radianes, positivo que forma con el semieje positivo de X

]]> 1.0000000 0.3333333 0 0 módulo = #moángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>angulo</mi><mo>(</mo><mo>[</mo><mi>xs</mi><mo>,</mo><mi>ys</mi><mo>]</mo><mo>,</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>xs</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ys</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>*</mo><pi/><mo>)</mo><mo>-</mo><mi>an</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Rectangulares a polares (radianes) Sea el vector:

A = #xs i + #ys j

Halla su módulo y el ángulo, en radianes, positivo que forma con el semieje positivo de X

]]> 1.0000000 0.3333333 0 0 módulo = #moángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>xs</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>xs</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>30</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>ys</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>angulo</mi><mo>(</mo><mo>[</mo><mi>xs</mi><mo>,</mo><mi>ys</mi><mo>]</mo><mo>,</mo><mo>[</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>]</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mo</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msqrt><mrow><msup><mi>xs</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ys</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>ys</mi><mo><</mo><mn>0</mn></mrow><mrow><mi>an</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>*</mo><pi/><mo>)</mo><mo>-</mo><mi>an</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/INTRODUCCIÓN MATEMÁTICA/DERIVADAS Derivada polinomio Sea la función polinómica:

f(x) = #c1 + #c2 x + #c3 x^#e3 + #c4 x^#e4

Calcula:

El valor de la derivada para x= #v1
El valor de la derivada para x= #v2

]]> 1.0000000 0.3333333 0 0 a= #x1b= #x2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>c2</mi><mo>+</mo><mo>(</mo><mi>e3</mi><mo>*</mo><mi>c3</mi><mo>*</mo><msup><mi>v1</mi><mrow><mo>(</mo><mi>e3</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo><mo>+</mo><mo>(</mo><mi>c4</mi><mo>*</mo><mi>e4</mi><mo>*</mo><msup><mi>v1</mi><mrow><mo>(</mo><mi>e4</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mo>(</mo><mi>c2</mi><mo>+</mo><mo>(</mo><mi>e3</mi><mo>*</mo><mi>c3</mi><mo>*</mo><msup><mi>v2</mi><mrow><mo>(</mo><mi>e3</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo><mo>+</mo><mo>(</mo><mi>c4</mi><mo>*</mo><mi>e4</mi><mo>*</mo><msup><mi>v2</mi><mrow><mo>(</mo><mi>e4</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Derivada polinomio Sea la función polinómica:

f(x) = #c1 + #c2 x + #c3 x^#e3

Calcula:

El valor de la derivada para x= #v1
El valor de la derivada para x= #v2

]]> 1.0000000 0.3333333 0 0 a= #x1b= #x2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>c2</mi><mo>+</mo><mo>(</mo><mi>e3</mi><mo>*</mo><mi>c3</mi><mo>*</mo><msup><mi>v1</mi><mrow><mo>(</mo><mi>e3</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>c2</mi><mo>+</mo><mo>(</mo><mi>e3</mi><mo>*</mo><mi>c3</mi><mo>*</mo><msup><mi>v2</mi><mrow><mo>(</mo><mi>e3</mi><mo>-</mo><mn>1</mn><mo>)</mo></mrow></msup><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Derivadas Sea la función (ángulo en radianes):

f(x) = #a1 x + tan(#a2 - #a3 x)

Si el ángulo está en radianes, Calcula:

Su valor y derivada para x= #v1
Su valor y derivada para x= #v2

f(x) = #a1 x + cos(#a2 + #a3 x)

Si el ángulo está en radianes, Calcula:

El valor de la derivada para x= #v1
El valor de la derivada para x= #v2

f(x) = #a1 x + ln(#a2 - #a3 x)

Si el ángulo está en radianes, Calcula:

Su valor y derivada para x= #v1
Su valor y derivada para x= #v2

]]> 1.0000000 0.3333333 0 0 a =#x1b =#x2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>ln</mi><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a3</mi><mo>*</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>v1</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>v2</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Derivadas (función) Sea la función (ángulo en radianes):

f(x) = #a1 x + tan(#a2 - #a3 x)

Si el ángulo está en radianes, Calcula:

El valor de la derivada para x= #v1
El valor de la derivada para x= #v2

]]> 1.0000000 0.3333333 0 0 a =#x1b =#x2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>tan</mi><mo>(</mo><mi>a2</mi><mo>-</mo><mi>a3</mi><mo>*</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>v1</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>v2</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>gx</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>x1</mi><mo>)</mo><mo>/</mo><mi>x1</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></apply></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>y</mi><mo>-</mo><mi>x2</mi><mo>)</mo><mo>/</mo><mi>x2</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo></mrow><mrow><mi>gx</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>+</mo><mi>gx</mi></mrow></apply></mtd></mtr><mtr><mtd><mi>devolver</mi><mo> </mo><mi>gx</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Derivadas (función) Sea la función:

f(x) = #a1 x + ln(#a3 x)

Si el ángulo está en radianes, Calcula:

El valor de la derivada para x= #v1
El valor de la derivada para x= #v2

]]> 1.0000000 0.3333333 0 0 a =#x1b =#x2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v1</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v2</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>ln</mi><mo>(</mo><mi>a3</mi><mo>*</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>v1</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>=</mo><mi>f</mi><mo>'</mo><mo>(</mo><mi>v2</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>x</mi><mn>2</mn><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/INTRODUCCIÓN MATEMÁTICA/INTEGRALES Integral definida Sea la función:

f(x) = #a1 x^#e1 + #a2«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msqrt»«mi»x«/mi»«/msqrt»«/math»

Calcula:

Su valor para x = #v1
Su integral entre x = #v1 y x= #v2

]]> 1.0000000 0.3333333 0 0 f(x) =#y1Integral = #in12]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>a1</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>)</mo><mo>+</mo><mo>(</mo><mi>a2</mi><mo>*</mo><msqrt><mi>x</mi></msqrt><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>v1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in12</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msubsup><mo>∫</mo><mi>v1</mi><mi>v2</mi></msubsup><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>ⅆ</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>I</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>r</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">i</mi><mi>n</mi><mn>12</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.03))</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Integral definida Sea la función (ángulos en radianes):

f(x) = #a1·sen x + #a2·cos x

Calcula:

Su valor para x = #v1
Su integral entre x = #v1 y x= #v2

]]> 1.0000000 0.3333333 0 0 f(x) =#y1Integral = #in12]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>a1</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>a2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>v1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in12</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msubsup><mo>∫</mo><mi>v1</mi><mi>v2</mi></msubsup><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>ⅆ</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>I</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>r</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">i</mi><mi>n</mi><mn>12</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.03))</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Integral definida Sea la función:

f(x) = #a1 x + #a2 / x

Calcula:

Su valor para x = #v1
Su integral entre x = #v1 y x= #v2

]]> 1.0000000 0.3333333 0 0 f(x) =#y1Integral = #in12]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>)</mo><mo>+</mo><mo>(</mo><mi>a2</mi><mo>/</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>v1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in12</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msubsup><mo>∫</mo><mi>v1</mi><mi>v2</mi></msubsup><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>ⅆ</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>I</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>r</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">i</mi><mi>n</mi><mn>12</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.03))</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Integral definida Sea la función:

f(x) = #a1 x + #a2 / x

Calcula:

Su valor para x = #v1
Su integral entre x = #v1 y x= #v2

]]> 1.0000000 0.3333333 0 0 f(x) =#y1Integral = #in12]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>)</mo><mo>+</mo><mo>(</mo><mi>a2</mi><mo>/</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>v1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in12</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msubsup><mo>∫</mo><mi>v1</mi><mi>v2</mi></msubsup><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>ⅆ</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>I</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>r</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">i</mi><mi>n</mi><mn>12</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.03))</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Integral definida Sea la función:

f(x) = #a1 x + #a2 · x ^#e1

Calcula:

Su valor para x = #v1
Su integral entre x = #v1 y x= #v2

]]> 1.0000000 0.3333333 0 0 f(x) =#y1Integral = #in12]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mi>a1</mi><mo>*</mo><mi>x</mi><mo>)</mo><mo>+</mo><mo>(</mo><mi>a2</mi><mo>*</mo><msup><mi>x</mi><mi>e1</mi></msup><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>f</mi><mo>(</mo><mi>v1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>in12</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><msubsup><mo>∫</mo><mi>v1</mi><mi>v2</mi></msubsup><mrow><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow><mo>ⅆ</mo><mi>x</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn><mspace linebreak="newline"/><mi>I</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">g</mi><mi>r</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">i</mi><mi>n</mi><mn>12</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.03))</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/INTRODUCCIÓN MATEMÁTICA/OPERACIONES CON VECTORES Producto escalar Dados los vectores A = #ax i+ #ay j+ #az k y B= #bx i+ #by j+ #bz k . Calcula:

Su producto escalar.
El ángulo que forman en grados.

]]> 1.0000000 0.3333333 0 0 Producto escalar =#pesángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>by</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bz</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pes</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>bx</mi><mo>+</mo><mi>ay</mi><mo>*</mo><mi>by</mi><mo>+</mo><mi>az</mi><mo>*</mo><mi>bz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu1</mi><mo>=</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu2</mi><mo>=</mo><msqrt><mrow><msup><mi>bx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>by</mi><mn>2</mn></msup><mo>+</mo><msup><mi>bz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>acos</mi><mo>(</mo><mi>pes</mi><mo>/</mo><mo>(</mo><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>)</mo><mo>)</mo><mo>/</mo><pi/></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>r</mi><mi>o</mi><mi>d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi>o</mi><mo> </mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi>c</mi><mi>a</mi><mi mathvariant="normal">l</mi><mi>a</mi><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Producto escalar Dados los vectores A = #ax i+ #ay j+ #az k y B= #bx i+ #by j+ #bz k . Calcula:

Su producto escalar.
El ángulo que forman en grados.

]]> 1.0000000 0.3333333 0 0 Producto escalar =#pesángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>by</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bz</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pes</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>bx</mi><mo>+</mo><mi>ay</mi><mo>*</mo><mi>by</mi><mo>+</mo><mi>az</mi><mo>*</mo><mi>bz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu1</mi><mo>=</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu2</mi><mo>=</mo><msqrt><mrow><msup><mi>bx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>by</mi><mn>2</mn></msup><mo>+</mo><msup><mi>bz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>acos</mi><mo>(</mo><mi>pes</mi><mo>/</mo><mo>(</mo><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>)</mo><mo>)</mo><mo>/</mo><pi/></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>r</mi><mi>o</mi><mi>d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi>o</mi><mo> </mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi>c</mi><mi>a</mi><mi mathvariant="normal">l</mi><mi>a</mi><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Producto escalar (copia) Dados los vectores A = #ax i+ #ay j+ #az k y B= #bx i+ #by j+ #bz k . Calcula:

Su producto escalar.
El ángulo que forman en grados.

]]> 1.0000000 0.3333333 0 0 Producto escalar =#pesángulo = #an]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>by</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bz</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pes</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>bx</mi><mo>+</mo><mi>ay</mi><mo>*</mo><mi>by</mi><mo>+</mo><mi>az</mi><mo>*</mo><mi>bz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu1</mi><mo>=</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu2</mi><mo>=</mo><msqrt><mrow><msup><mi>bx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>by</mi><mn>2</mn></msup><mo>+</mo><msup><mi>bz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>acos</mi><mo>(</mo><mi>pes</mi><mo>/</mo><mo>(</mo><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>)</mo><mo>)</mo><mo>/</mo><pi/></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>r</mi><mi>o</mi><mi>d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi>o</mi><mo> </mo><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mi>c</mi><mi>a</mi><mi mathvariant="normal">l</mi><mi>a</mi><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Producto vectorial Dados los vectores A = #ax i+ #ay j+ #az k y B= #bx i+ #by j+ #bz k . Calcula:

El ángulo que forman en grados.
El módulo de su producto vectorial.

]]> 1.0000000 0.3333333 0 0 ángulo = #anmódulo prod. vect. =#mve]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>by</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bz</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pes</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>bx</mi><mo>+</mo><mi>ay</mi><mo>*</mo><mi>by</mi><mo>+</mo><mi>az</mi><mo>*</mo><mi>bz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu1</mi><mo>=</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu2</mi><mo>=</mo><msqrt><mrow><msup><mi>bx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>by</mi><mn>2</mn></msup><mo>+</mo><msup><mi>bz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>pes</mi><mo>/</mo><mo>(</mo><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>an1</mi><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mve</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>an1</mi><mo>)</mo></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mspace linebreak="newline"/><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>d</mi><mo>.</mo><mo> </mo><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>v</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Producto vectorial Dados los vectores A = #ax i+ #ay j+ #az k y B= #bx i+ #by j+ #bz k . Calcula:

El ángulo que forman en grados.
El módulo de su producto vectorial.

]]> 1.0000000 0.3333333 0 0 ángulo = #anmódulo prod. vect. =#mve]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>by</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bz</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pes</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>bx</mi><mo>+</mo><mi>ay</mi><mo>*</mo><mi>by</mi><mo>+</mo><mi>az</mi><mo>*</mo><mi>bz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu1</mi><mo>=</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu2</mi><mo>=</mo><msqrt><mrow><msup><mi>bx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>by</mi><mn>2</mn></msup><mo>+</mo><msup><mi>bz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>pes</mi><mo>/</mo><mo>(</mo><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>an1</mi><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mve</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>an1</mi><mo>)</mo></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mspace linebreak="newline"/><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>d</mi><mo>.</mo><mo> </mo><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>v</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Producto vectorial (copia) Dados los vectores A = #ax i+ #ay j+ #az k y B= #bx i+ #by j+ #bz k . Calcula:

El ángulo que forman en grados.
El módulo de su producto vectorial.

]]> 1.0000000 0.3333333 0 0 ángulo = #anmódulo prod. vect. =#mve]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ax</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ay</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>az</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bx</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>by</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bz</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>8</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pes</mi><mo>=</mo><mi>ax</mi><mo>*</mo><mi>bx</mi><mo>+</mo><mi>ay</mi><mo>*</mo><mi>by</mi><mo>+</mo><mi>az</mi><mo>*</mo><mi>bz</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu1</mi><mo>=</mo><msqrt><mrow><msup><mi>ax</mi><mn>2</mn></msup><mo>+</mo><msup><mi>ay</mi><mn>2</mn></msup><mo>+</mo><msup><mi>az</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>modu2</mi><mo>=</mo><msqrt><mrow><msup><mi>bx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>by</mi><mn>2</mn></msup><mo>+</mo><msup><mi>bz</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>pes</mi><mo>/</mo><mo>(</mo><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an</mi><mo>=</mo><mn>180</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>an1</mi><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mve</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>modu1</mi><mo>*</mo><mi>modu2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>an1</mi><mo>)</mo></mrow></mfenced></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mspace linebreak="newline"/><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>d</mi><mo>.</mo><mo> </mo><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>v</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/INTRODUCCIÓN MATEMÁTICA/SUMA DE VECTORES Suma de vectores Tenemos tres vectores A, B y C de módulos #v1, #v2 y #v3 respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

El módulo del vector A+2B+C
El ángulo positivo que forma el vector resultante con el vector A

]]> 1.0000000 0.3333333 0 0 módulo = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma de vectores Tenemos tres vectores A, B y C de módulos #v1, #v2 y #v3 respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

El módulo del vector -A+5B-C
El ángulo positivo que forma el vector resultante con el vector A

]]> 1.0000000 0.3333333 0 0 módulo = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mo>-</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mn>5</mn><mo>*</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>-</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mn>5</mn><mo>*</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>)</mo><mo>-</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma de vectores Tenemos tres vectores A, B y C de módulos #v1, #v2 y #v3 respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

El módulo del vector A+B-C
El ángulo positivo que forma el vector resultante con el vector A

]]> 1.0000000 0.3333333 0 0 módulo = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>-</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>-</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma de vectores Tenemos tres vectores A, B y C de módulos #v1, #v2 y #v3 respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

El módulo del vector suma.
El ángulo positivo que forma el vector resultante con el vector A

]]> 1.0000000 0.3333333 0 0 módulo = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma de vectores Tenemos tres vectores A, B y C de módulos #v1, #v2 y #v3 respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

El módulo del vector suma.
El ángulo positivo que forma el vector resultante con el vector A

]]> 1.0000000 0.3333333 0 0 módulo = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Suma de vectores (copia) Tenemos tres vectores A, B y C de módulos #v1, #v2 y #v3 respectivamente. El ángulo entre A y B es de #an1 º y el que hay entre B y C es de #an2 º. Halla:

El módulo del vector suma.
El ángulo positivo que forma el vector resultante con el vector A

]]> 1.0000000 0.3333333 0 0 módulo = #msuángulo = #anr]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>8</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>160</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>an2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang1</mi><mo>=</mo><mi>an1</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ang2</mi><mo>=</mo><mi>an2</mi><mo>*</mo><pi/><mo>/</mo><mn>180</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resx</mi><mo>=</mo><mi>v1</mi><mo>+</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resy</mi><mo>=</mo><mo>(</mo><mi>v2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>)</mo><mo>)</mo><mo>+</mo><mo>(</mo><mi>v3</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>ang1</mi><mo>+</mo><mi>ang2</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msu</mi><mo>=</mo><msqrt><mrow><msup><mi>resx</mi><mn>2</mn></msup><mo>+</mo><msup><mi>resy</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>acos</mi><mo>(</mo><mi>resx</mi><mo>/</mo><mi>msu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>alfa1</mi><mo>=</mo><mi>alfa1</mi><mo>*</mo><mn>180</mn><mo>/</mo><pi/></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>resy</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>anr</mi><mo>=</mo><mi>alfa1</mi></mrow><mrow><mi>anr</mi><mo>=</mo><mn>360</mn><mo>-</mo><mi>alfa1</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">m</mi><mi>ó</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>u</mi><mspace linebreak="newline"/><mi>á</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>n</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/FÍSICA/MAS Ecuación armónico simple El movimiento de un oscilador armónico simple se ajusta a la ecuación:

x= #a * cos( #w * t + #delta) metros

¿Cuánto valen para t= #t segundos??

Elongación (m)
Velocidad (m/s)
Aceleración (m/s²)

]]> 1.0000000 0.3333333 0 0 Elongación = #xVelocidad = #vAceleración = #ac]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>13</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>delta</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>w</mi><mo>*</mo><mi>t</mi><mo> </mo><mo>+</mo><mo> </mo><mi>delta</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mo>-</mo><mi>w</mi><mo>*</mo><mi>a</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>w</mi><mo>*</mo><mi>t</mi><mo>+</mo><mi>delta</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ac</mi><mo>=</mo><mo>-</mo><msup><mi>w</mi><mn>2</mn></msup><mo>*</mo><mi>a</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>w</mi><mo>*</mo><mi>t</mi><mo>+</mo><mi>delta</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">E</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>x</mi><mspace linebreak="newline"/><mi mathvariant="normal">V</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mspace linebreak="newline"/><mi mathvariant="normal">A</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>c</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data><data name="inputCompound">true</data></localData></question> Ecuación armónico simple El movimiento de un oscilador armónico simple se ajusta a la ecuación:

x= #a * cos( #w * t + #delta) metros

¿Cuánto valen?

Amplitud (m)
Frecuencia angular (rd/s)
Constante de fase (rd)
Periodo (s)
Frecuencia (Hz)

]]> 1.0000000 0.3333333 0 0 Amplitud = #aFrecuencia angular = #wConstante de fase = #deltaPeriodo = #perFrecuencia =#frec]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>13</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>delta</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>per</mi><mo>=</mo><mn>2</mn><mo>*</mo><pi/><mo>/</mo><mi>w</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>frec</mi><mo>=</mo><mn>1</mn><mo>/</mo><mi>per</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">A</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>u</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>Fr</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mi>a</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">l</mi><mi>a</mi><mi>r</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>w</mi><mspace linebreak="newline"/><mi mathvariant="normal">C</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>f</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>t</mi><mi>a</mi><mspace linebreak="newline"/><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>d</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>p</mi><mi mathvariant="normal">e</mi><mi>r</mi><mspace linebreak="newline"/><mi>Fr</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>f</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>c</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Péndulo simple Un péndulo simple de #l m de longitud tiene un periodo de #per segundos para pequeñas oscilaciones. Calcula:

Intensidad del campo gravitatorio (m/s²)
Si la velocidad de la bolita en el punto de equilibrio es de #v m/s, calcula su amplitud

]]> 1.0000000 0.3333333 0 0 Intensidad de campo = #gAmplitud = #a]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>per</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>12</mn><mo>,</mo><mn>30</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mn>2</mn><mo>*</mo><pi/><mo>/</mo><mi>per</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><msup><mi>w</mi><mn>2</mn></msup><mo>*</mo><mi>l</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>v</mi><mo>*</mo><msqrt><mrow><mo>(</mo><mi>l</mi><mo>/</mo><mi>g</mi><mo>)</mo><mo>-</mo><mo>(</mo><msup><mi>v</mi><mn>2</mn></msup><mo>/</mo><mo>(</mo><mn>4</mn><mo>*</mo><mi>g</mi><mo>)</mo><mo>)</mo></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>I</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>c</mi><mi>a</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">g</mi><mspace linebreak="newline"/><mi mathvariant="normal">A</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>u</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Una partícula que oscila Una partícula que oscila con movimiento armónico simple se encuentra en x= #xo cm cuando t=0. En ese preciso instante, su velocidad es de - #v cm/s. Si su periodo de oscilación es de #per segundos, calcula:

La constante de fase, en rd, y la amplitud en cm.
La velocidad (cm/s) y la aceleración (cm/s²) para t= #t segundos.

]]> 1.0000000 0.3333333 0 0 constante de fase = #deltaamplitud = #avelocidad = #vtaceleración = #at]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>per</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mn>2</mn><mo>*</mo><pi/><mo>/</mo><mi>per</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>delta</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>v</mi><mo>/</mo><mo>(</mo><mi>xo</mi><mo>*</mo><mi>w</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>xo</mi><mo>/</mo><mi>cos</mi><mo>(</mo><mi>delta</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xt</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>w</mi><mo>*</mo><mi>t</mi><mo>+</mo><mi>delta</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vt</mi><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mi>w</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mo>(</mo><mi>w</mi><mo>*</mo><mi>t</mi><mo>)</mo><mo>+</mo><mi>delta</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>at</mi><mo>=</mo><mo>-</mo><msup><mi>w</mi><mn>2</mn></msup><mo>*</mo><mi>xt</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>f</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>t</mi><mi>a</mi><mspace linebreak="newline"/><mi>a</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>u</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mi>t</mi><mspace linebreak="newline"/><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi>t</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Una partícula que oscila máximos Una partícula que oscila con movimiento armónico simple se encuentra en x= #xo cm cuando t=0. En ese preciso instante, su velocidad es de - #v cm/s. Si su periodo de oscilación es de #per segundos, calcula:

La constante de fase, en rd, y la amplitud en cm.
La velocidad (cm/s) y la aceleración (cm/s²) máximas. (ambas positivas)

]]> 1.0000000 0.3333333 0 0 constante de fase = #deltaamplitud = #avelocidad máxima= #vmaceleración máxima= #am]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>xo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>per</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mn>2</mn><mo>*</mo><pi/><mo>/</mo><mi>per</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>delta</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>v</mi><mo>/</mo><mo>(</mo><mi>xo</mi><mo>*</mo><mi>w</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>xo</mi><mo>/</mo><mi>cos</mi><mo>(</mo><mi>delta</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vm</mi><mo>=</mo><mi>w</mi><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>am</mi><mo>=</mo><msup><mi>w</mi><mn>2</mn></msup><mo>*</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">s</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>f</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi mathvariant="normal">e</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>d</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>t</mi><mi>a</mi><mspace linebreak="newline"/><mi>a</mi><mi mathvariant="normal">m</mi><mi>p</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>u</mi><mi>d</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mo> </mo><mi mathvariant="normal">m</mi><mi>á</mi><mi>x</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi><mi>a</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mi mathvariant="normal">m</mi><mspace linebreak="newline"/><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mi>n</mi><mo> </mo><mi mathvariant="normal">m</mi><mi>á</mi><mi>x</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi><mi>a</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>a</mi><mi mathvariant="normal">m</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">0.03</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 1º BACHILLERATO/LE CHATELIER equilibrio con sólidos (copia) ¿Hacia dónde se desplazará el equilibrio?:

C _(s) + H₂O _(g) <=> CO _(g) + H₂ _(g) ΔH < 0

Si:

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Aumentamos la presión

]]> izquierda Aumentamos la temperatura

]]> izquierda Disminuimos la cantidad de CO

]]> derecha Aumentamos la cantidad de C

]]> No se desplaza Aumentamos la cantidad de agua

]]> derecha 1º BACHILLERATO/PRUEBA INICIAL/PRUEBA INICIAL. CALCULO f) El cloro es un gas a temperatura ambiente y el cloruro de potasio funde a 776ºC ¿Por qué el cloro es un gas a temperatura ambiente y el cloruro de potasio funde a algo menos de ochocientos grados?

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Porque el cloro tiene estructura covalente molecular y el cloruro de potasio es iónico

]]> Porque la atracción entre las moléculas de cloro (apolares) es menor que entre los iones muy cargados del cloruro de potasio

]]> Es falso

]]> Porque en el cloruro de potasio la diferencia del tamaño de los átomos es mayor que en el caso del cloro, en el que son todos iguales

]]> Porque el cloro prefiere estar con el potasio que consigo mismo

]]> h) ¿Por qué una disolución hierve a mayor temperatura que el disolvente puro? ¿Por qué una disolución hierve a mayor temperatura que el disolvente puro?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Porque tiene menor presión de vapor

]]> Porque el soluto normalmente es sólido y la temperatura media de ebullición entre los dos crece

]]> No siempre es así, puede ser mayor o menor, depende

]]> Normalmente es al revés

]]> la plata conduce la corriente eléctrica y el cloruro de plata sólido no ¿Cuáles de las siguientes afirmaciones sobre por qué la plata conduce la corriente eléctrica y el cloruro de plata sólido no, son correctas?

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Porque en el cloruro de plata los electrones no caben y no pueden pasar por la red de iones

]]> Porque la plata es un átomo muy poco electronegativo y los electrones están libres en la red , pero en el cloruro de plata el cloro, muy electronegativo, los atrae

]]> Porque la plata es un metal y el cloruro de plata es covalente atómico

]]> En estado sólido es cierto, pero en estado líquido ambos son conductores

]]> Porque el cloruro de plata es iónico pero la plata es un covalente atómico

]]> molécula BF3 ¿Cuál de las siguientes afirmaciones describe la estructura e hibridación del BF₃ y su polaridad?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Estructura de orbitales tetraédrica, de átomos pirámide trigonal y molécula polar

]]> Estructura de orbitales trigonal plana, de átomos trigonal plana y molécula apolar

]]> Estructura de orbitales tetraédrica, de átomos tetraédrica y molécula apolar

]]> Estructura de orbitales tetraédrica, de átomos pirámide trigonal y molécula apolar

]]> Estructura de orbitales lineal, de átomos lineal y molécula polar

]]> molécula NF3 ¿Cuál de las siguientes afirmaciones describe la estructura e hibridación del NF₃ y su polaridad?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Estructura de orbitales tetraédrica, de átomos pirámide trigonal y molécula polar

]]> Estructura de orbitales trigonal plana, de átomos trigonal plana y molécula polar

]]> Estructura de orbitales tetraédrica, de átomos tetraédrica y molécula apolar

]]> Estructura de orbitales tetraédrica, de átomos pirámide trigonal y molécula apolar

]]> Estructura de orbitales lineal, de átomos lineal y molécula polar

]]> Número cuánticos electrones del nitrógeno ¿Cuál o cuáles de las siguientes combinaciones de números cuánticos podrían corresponder a los tres últimos electrones del estado fundamental del nitrógeno?

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> (2, 1, 0, 1/2), (2, 1, 1, 1/2), (2, 1, -1, 1/2)

]]> (2, 1, 0, -1/2), (2, 1, 1, -1/2), (2, 1, -1, -1/2)

]]> (2, 1, 0, 1/2), (2, 1, 0, -1/2), (2, 1, 1, 1/2)

]]> (2, 1, -1, 1/2), (2, 1, -1, -1/2), (2, 1, 0, 1/2)

]]> (2, 1, 0, 1/2), (2, 1, 0, 1/2), (2, 1, 0, 1/2)

]]> Números cuánticos ¿Cuál o cuáles de las siguientes combinaciones de números cuánticos (n, l, m, s) son imposibles?:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> (3,-1,1,1/2)

]]> (1,0,2,1/2)

]]> (5,3,-3,1/2)

]]> (0,1,-1,1/2)

]]> (3,2,0,1/2)

]]> Pirita En una fábrica de ácido sulfúrico se tuesta la pirita (FeS₂) con oxígeno para dar óxido de hierro (III) y dióxido de azufre. Queremos obtener #mdi Kg por hora de dióxido de azufre, pero sabemos que el mineral tiene una riqueza del #rm % y que el rendimiento de la reacción es del #rr %:

FeS₂ + O₂ --> SO₂ + Fe₂O₃

¿Cuántos kg de mineral necesitaremos aportar por hora?
¿Cuántos Kg de óxido de hierro (III) se obtienen?
¿Qué volumen, en litros, ocupará el oxígeno usado en C.N. ?

Datos: masas atómicas: Fe = 55.8; O=16; S=32

]]> 1.0000000 0.3333333 0 0 1.- Masa mineral= #mmi2.- Masa de óxido de hierro (III)= #moh3.- Volumen de oxígeno= #vo]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mdi</mi><mo> </mo><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>80</mn><mo>)</mo><mo>*</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rm</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>70</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mmi</mi><mo>=</mo><mi>mdi</mi><mo>*</mo><mn>4</mn><mo>*</mo><mn>119</mn><mo>.</mo><mn>8</mn><mo>*</mo><mn>10000</mn><mo>/</mo><mo>(</mo><mn>8</mn><mo>*</mo><mn>64</mn><mo>*</mo><mi>rr</mi><mo>*</mo><mi>rm</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>moh</mi><mo>=</mo><mi>mdi</mi><mo>*</mo><mn>2</mn><mo>*</mo><mn>159</mn><mo>.</mo><mn>6</mn><mo>/</mo><mo>(</mo><mn>8</mn><mo>*</mo><mn>64</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vo</mi><mo>=</mo><mi>mdi</mi><mo>*</mo><mn>11</mn><mo>*</mo><mn>22</mn><mo>.</mo><mn>4</mn><mo>*</mo><mn>10000</mn><mo>/</mo><mo>(</mo><mn>8</mn><mo>*</mo><mn>64</mn><mo>*</mo><mi>rr</mi><mo>*</mo><mi>rm</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo>-</mo><mo> </mo><mi>M</mi><mi>a</mi><mi>s</mi><mi>a</mi><mo> </mo><mi>min</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>a</mi><mi>l</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>m</mi><mi>m</mi><mi mathvariant="normal">i</mi><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo>-</mo><mo> </mo><mi>M</mi><mi>a</mi><mi>s</mi><mi>a</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>ó</mi><mi>x</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>o</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>h</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>r</mi><mi>o</mi><mo> </mo><mo>(</mo><mi>I</mi><mi>I</mi><mi>I</mi><mo>)</mo><mo>=</mo><mo> </mo><mo>#</mo><mi>m</mi><mi>o</mi><mi>h</mi><mspace linebreak="newline"/><mn>3</mn><mo>.</mo><mo>-</mo><mo> </mo><mi>V</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>o</mi><mi>x</mi><mi>í</mi><mi>g</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>o</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mi>o</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sulfúrico y amoniaco 1) En un recipiente ponemos #va cc de una disolución #ca M de ácido sulfúrico (H₂SO₄) y #vb cc de una disolución cuya densidad es #cb g/cc con una riqueza del #rb % en hidróxido de amonio (NH₄OH). Calcula:

H₂SO₄+ NH₄OH --> (NH₄)₂SO₄ + H₂O

Molaridad de la disolución de hidróxido de amonio
Si reaccionan para dar sulfato amónico y agua. Calcula la concentración resultante de sulfato de amonio (suponemos que el volumen permanece constante)

Datos: masas atómicas = H=1; N=14; O=16; S=32

]]> 1.0000000 0.3333333 0 0 1.- Molaridad hidróxido de amonio= #mb2.- Molaridad sulfato de amonio = #csa]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>va</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>30</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ca</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>18</mn><mo>,</mo><mn>32</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>101</mn><mo>,</mo><mn>110</mn><mo>)</mo><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rb</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mb</mi><mo>=</mo><mi>cb</mi><mo>*</mo><mn>1000</mn><mo>*</mo><mi>rb</mi><mo>/</mo><mo>(</mo><mn>100</mn><mo>*</mo><mn>35</mn><mo>.</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vt</mi><mo>=</mo><mi>va</mi><mo>+</mo><mi>vb</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>csa1</mi><mo>=</mo><mi>mb</mi><mo>*</mo><mi>vb</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>vt</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>csa2</mi><mo>=</mo><mi>va</mi><mo>*</mo><mi>ca</mi><mo>/</mo><mi>vt</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>csa1</mi><mo>></mo><mi>csa2</mi></mrow><mrow><mi>csa</mi><mo>=</mo><mi>csa2</mi></mrow><mrow><mi>csa</mi><mo>=</mo><mi>csa1</mi></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>.</mo><mo>-</mo><mo> </mo><mi>M</mi><mi>o</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo> </mo><mi>h</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>r</mi><mi>ó</mi><mi>x</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>o</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>a</mi><mi>m</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">i</mi><mi>o</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>m</mi><mi>b</mi><mspace linebreak="newline"/><mn>2</mn><mo>.</mo><mo>-</mo><mo> </mo><mi>M</mi><mi>o</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">d</mi><mi>a</mi><mi mathvariant="normal">d</mi><mo> </mo><mi>s</mi><mi>u</mi><mi>l</mi><mi>f</mi><mi>a</mi><mi>t</mi><mi>o</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>a</mi><mi>m</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">i</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>c</mi><mi>s</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> tamaño iones Ordena de forma creciente el tamaño de los iones Cl^-, Na⁺, S^2-y Al³⁺

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Cl^-, Na⁺, S^2-, Al³⁺

]]> Cl^-, Al³⁺, Na⁺, S^2-

]]> Na⁺, S^2-, Al³⁺, Cl^-

]]> Cl^-, Na⁺, S^2-y Al³⁺

]]> Al³⁺, Na⁺, S^2-, Cl^-

]]> Al³⁺, Na⁺, Cl^-. S^2-,

]]> 1º BACHILLERATO/PRUEBA INICIAL/PRUEBA INICIAL. TEXTO Error 1 Resume brevemente el error nº 1 que cometemos al estudiar, según el artículo

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 Error 2 Resume brevemente el error nº 2 que cometemos al estudiar, según el artículo

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 Error 3 Resume brevemente el error nº 3 que cometemos al estudiar, según el artículo

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 Error 4 Resume brevemente el error nº 4 que cometemos al estudiar, según el artículo

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 Instrcucciones Lee el artículo sobre técnicas de estudio y responde a las siguientes preguntas:

]]> 0.0000000 0.0000000 0 Método 1 Resume brevemente el primero de los métodos de estudio más aconsejable citados en el artículo

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 Método 2 Resume brevemente el segundo de los métodos de estudio más aconsejable citados en el artículo

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 Método 3 Resume brevemente el tercero de los métodos de estudio más aconsejable citados en el artículo

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 Método 4 Resume brevemente el cuarto de los métodos de estudio más aconsejable citados en el artículo

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 Método 5 Resume brevemente el quinto de los métodos de estudio más aconsejable citados en el artículo

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 Música ¿Qué dice el artículo sobre oír música mientras se estudia?

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 puntos más importantes ¿Cuáles son los puntos más importantes para el aprendizaje, según el artículo? Coméntalos

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 Regla de oro 1 Resume brevemente la primera regla de oro del estudio, según el artículo

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 Regla de oro 2 Resume brevemente la segunda regla de oro del estudio, según el artículo

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 Regla de oro 3 Resume brevemente la tercera regla de oro del estudio, según el artículo

]]> 1.0000000 0.0000000 0 editor 1 5 0 0 1º BACHILLERATO/QUÍMICA/ATOMO/BOHR Di si las siguientes afirmaciones son verdaderas o falsas Indica las afirmaciones correctas:

]]> 1.0000000 0.1000000 0 false true abc El atomo es indivisible e inmutable El modelo de Thomson es incorrecto porque no explica la experiencia de Rutherdford La corteza electrónica es muy densa El protón, el neutrón y el electrón tienen aproximadamente la misma masa El átomo está práctcamente vacío El átomo no puede ser neutro porque contiene cargas eléctricas El modelo de Bohr establecía que las órbitas permitidas en las que podía moverse el electrón no podía ser cualesquiera ya que: El modelo de Bohr establecía que las órbitas permitidas en las que podía moverse el electrón no podía ser cualesquiera ya que:]]> 1.0000000 0.1000000 0 true true abc El átomo perdería el electrón Los niveles de energía tiene que ser mayores a medida que nos acercamos al núcleo Los niveles de energía dentro del átomo están cuantizados esto es, dependen del valor de un número cuántico Se produciría una colisión del electrón con el núcleo Los niveles de energía dentro del átomo están cuantizados esto es, dependen del valor del cuanto de enrgía de la radiación ultravioleta El modelo de Bohr para el hidrógeno: El modelo de Bohr para el hidrógeno:]]> 1.0000000 0.1000000 0 true true abc Fracasó porque no explicaba el proceso de emisión o absorción de la radiación electromagnética Fracasó porque explicaba el proceso de emisión o absorción de la luz visible, pero no de cualquier otro tipo de radiación electromagnética Fracasó porque era muy complicado matematicamente Explicó satisfactoriamente su espectro de emisión, pero fracasó cuando el átomo tenía más de un electrón Ninguna El modelo de Sommerfeld prevee órbitas elípticas, además de las circulares: El modelo de Sommerfeld prevee órbitas elípticas, además de las circulares:]]> 1.0000000 0.1000000 0 true true abc Para explicar el efecto Zeeman Para explicar satisfactoriamente el espectro de cualquier átomo En realidan no llegó a aexplicar absolutamente nada Se demostró que las órbitas electrónicas por razón de sus números cuánticos tenían que se siempre circulares Ninguna En el modelo de Bohr-Sommerfeld una órbita está caracterizada por: En el modelo de Bohr-Sommerfeld una órbita está caracterizada por:]]> 1.0000000 0.1000000 0 true true abc Un número cuántico llamado principal n Un número cuántico llamado de espín Tres números cuánticos n,l,m Cuatro números cuáticos n,l,m,s Ninguna Longitud de onda asociada Calcula la longitud de onda (en m) asociada a un electrón que se mueve a #v m/s ( masa del electrón = 9.1*10^-31 Kg)

]]> 1.0000000 0.3333333 0 0 #l]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>va</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>15</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>va</mi><mo>*</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>1</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>h</mi><mo>/</mo><mo>(</mo><mi>m</mi><mo>*</mo><mi>v</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Los espectros atómicos demostraban que los niveles de energía dentro del átomo: Los espectros atómicos demostraban que los niveles de energía dentro del átomo:]]> 1.0000000 0.1000000 0 true true abc Eran fijos y su valor no podía ser cualquiera Podían tener cualquier valor Dependían del estado en el que se encontraba el átomo Estaban formados por rayas de luz Ninguna Según Bohr, los electrones se mueven en unas órbitas determinadas a las que llamó Según Bohr, los electrones se mueven en unas órbitas determinadas a las que llamó

]]> 1.0000000 0.1000000 0 true true abc Orbitales Spín Azimutales Capas o niveles de energía Señala la opción incorrecta para completar la frase:
"Si un electrón ubicado en el segundo nivel de energía, recibe en estimulo externo....."

]]> 1.0000000 0.1000000 0 true true abc Puede ionizar al átomo Pude pasar al nivel 4 Puede pasar al nivel 3 Puede pasar al nivel 1 Si excitamos todos los electrones de una muestra de átomos Si excitamos todos los electrones de una muestra de átomos de hidrógeno hasta el nivel 4, al volver a estados de energía inferiores ¿Cuántas líneas apareceránen el espectro de emisión resultante? 1.0000000 0.1000000 0 true true abc 4 1 3 6 Un electrón en el nivel da un espectro de emisión de Un electrón de un átomo de hidrógeno situado en el nivel #n ¿Cuántas líneas tendrá en su espectro de emisión?

]]> 1.0000000 0.3333333 0 0 #l]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>n</mi><mo>*</mo><mo>(</mo><mi>n</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>/</mo><mn>2</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/QUÍMICA/ATOMO/CONFIGURACIÓN ELECTRÓNICA ¿Cuántos electrones desapareados tiene el ¿Cuántos electrones desapareados tiene?

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Na

]]> 1 Ca

]]> 0 P

]]> 3 Cu

]]> 1 Cr

]]> 6 Fe

]]> 4 Se

]]> 2 Cl

]]> 1 B

]]> 1 Algunos de los elementos que acomodan sus electrones en forma diferente a la esperada (ANOMALÍAS) son Algunos de los elementos que acomodan sus electrones en forma diferente a la esperada (ANOMALÍAS) son 1.0000000 0.1000000 0 true true abc cadmio y zinc Cobre, cromo Manganeso e hierro Potasio y Calcio Cuando hay disponibles varios orbitales del mismo tipo, los electrones se acomodan de uno en uno en spines paralelos, en cada orbital, hasta semillenar los orbitales y luego se van apareando hasta completarlos. El texto anterior se refiere a Cuando hay disponibles varios orbitales del mismo tipo, los electrones se acomodan de uno en uno en spines paralelos, en cada orbital, hasta semillenar los orbitales y luego se van apareando hasta completarlos. El texto anterior se refiere a:]]> 1.0000000 0.1000000 0 true true abc El principio de construcción progresiva El principio de Aufbau (regla de Möller) El principio de exclusión de Pauli La regla de Hund El ion calcio tiene El calcio tiene 1.0000000 0.1000000 0 true true abc 8 electrones de valencia 2 electrones de valencia 40 electrones de valencia Ninguna de las anteriores El sodio tiene El sodio tiene:

]]> 1.0000000 0.1000000 0 true true abc 11 electrones de valencia 1 electrón de valencia 8 electrones de valencia Ninguna de las anteriores El valor de los números cuánticos para el último electrón del circonio es El valor de los números cuánticos para el último electrón del circonio pueden ser: (n,l,m,s)]]> 1.0000000 0.1000000 0 true true abc (4,3,-1,1/2) (4,2,-1,1/2) (4,0,-2,-1/2) (5,2,-1,1/2) El valor de los números cuánticos para el último electrón del galio es El valor de los números cuánticos para el último electrón del galio puede ser (n,l,m,s)

]]> 1.0000000 0.1000000 0 true true abc (4,1,1,-1/2) (4,2,0,1/2) (4,0,0,1/2) (3,1,-1,-1/2) Es un término alemán que determina cómo se van llenando los electrones, en los diferentes niveles y subniveles, que va del menor al de mayor energía. El texto anterior corresponde a Es un término alemán que determina cómo se van llenando los electrones, en los diferentes niveles y subniveles, que va del menor al de mayor energía. El texto anterior corresponde a:

]]> 1.0000000 0.1000000 0 true true abc La Regla de Hund El principio de exclusión de Pauli El principio de Aufbau (regla de Möller) El principio de máxima multiplicidad La siguiente configuración electrónica [Xe] 6s2 5d1 4f 3, corresponde a La siguiente configuración electrónica de un átomo neutro [Xe] 6s² 5d¹ 4f³, corresponde a:

]]> 1.0000000 0.1000000 0 true true abc Pm

]]> W

]]> U

]]> Nd

]]> Para las siguientes configuraciones Indica, para las siguientes configuraciones del Sc ¿cuáles son fundamentales, excitados e imposibles? 1.0000000 0.1000000 0 true 1s2 2s2p6 3s2p6d1 4s2 Fundamental 1s2 2s2p6 3s2p6d3 excitada 1s2 2s2p6 3s2d9 excitada 1s2 2s2p6 3d11 imposible excitada imposible 1º BACHILLERATO/QUÍMICA/ATOMO/IONES Iones más estables Los criterios básicos de formación de los iones más estables de un elemento de un grupo principal son:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Adquisición de estructura de gas noble

]]> Último nivel lleno

]]> Que tenga más protones que neutrones

]]> Que los orbitales no estén llenos para evitar la repulsión entre electrones

]]> orden de colocación de alectrones Cuando se van añadiendo electrones a un átomo, éstos de colocan:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Siguiendo estrictamente la regla de Möeller (consecuencia de la regla de Aufbau) para ser más estable

]]> Siguiendo la regla de Möeller (consecuencia de la regla de Aufbau) pero, en determinados casos, sufre alteraciones para hacerse más estable

]]> Sigue siempre la regla de estabilidad orbital

]]> Se ordenan según el orden de los números cuánticos

]]> Ninguna de las otras opciones es cierta

]]> orden de colocación de alectrones en iones Cuando se van quitando electrones a un átomo, éstos de eliminan de:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Siguiendo estrictamente la regla de Möeller (consecuencia de la regla de Aufbau) en forma inversa para ser más estable

]]> Siguiendo la regla de Möeller (consecuencia de la regla de Aufbau) pero, en determinados casos, sufre alteraciones para hacerse más estable

]]> Sigue siempre la regla de estabilidad orbital

]]> Se van eliminando de las capas más externas a las más internas

]]> Se van eliminando de las capas más externas a las más internas, aunque, a veces, hay alteraciones para hacerlo más estable

]]> Parejas de iones De las siguientes parejas de iones ¿Cuál de ellos será el mayor?

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> N^-3 / O^-2

]]> El primero S^-2 / I^-

]]> El segundo S ^-2 / Ar

]]> El primero Son iguales de tamaño Tamaño de iones Para las siguientes parejas de iones, el primero es menor que el segundo porque:

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> F^- y O^2-

]]> Tiene igual configuración electrónica, pero el primero tiene mayor carga nuclear Tiene igual configuración electrónica, pero el primero tiene menor carga nuclear F^- y Cl^-

]]> Tiene menor número de capas Tiene mayor número de capas S^-2 y P^-3

]]> Tiene igual configuración electrónica, pero el primero tiene mayor carga nuclear F^- y K⁺

]]> Tiene menor número de capas Cl^- y Se ²^-

]]> Tiene menor número de capas Está a la izquierda y abajo Está a la derecha 1º BACHILLERATO/QUÍMICA/ATOMO/MODELO CUÁNTICO ¿Cuáles son los valores permitidos para el número cuántico principal? ¿Cuáles son los valores permitidos para el número cuántico principal?

]]> 1.0000000 0.1000000 0 true true abc Desde - l hasta + l Enteros positivos del 1 en adelante + 1/2, - 1/2 0, enteros positivos hasta n-1 a dualidad onda-corpúsculo consiste en que: La dualidad onda-corpúsculo consiste en que:]]> 1.0000000 0.1000000 0 true true abc Las ondas son materia Los corpúsculos emiten ondas Las ondas electromagnéticas chocan contra los corpúsculos a materia tiene una doble naturaleza, puede comportarse como partículas y como ondas Ninguna El número cuántico magnético (m) El número cuántico magnético (m) 1.0000000 0.1000000 0 true true abc Está relacionado con el número de probabilidades de orientación espacial. Éste número cuántico NO se deriva de la ecuación de Schördinger De él depende casi toda la energía del electrón. Está asociado a un momento magnético lo que le da el giro del electrón alrededor de sí mismo. 1.0000000 0.1000000 0 true true abc 5 3 7 Ninguno El pricipio de Incertidumbre de Heisenberg nos dice que: El principio de Incertidumbre de Heisenberg nos dice que:]]> 1.0000000 0.1000000 0 true true abc Al medir siempre se comete un error Que una onda se comporta como una partícula Es imposible conocer simultaneamente la posición y la velocidad del electrón dentro del átomo Es imposible conocer simultaneamente la velocidad y la aceleración del electrón dentro del átomo Ninguna Empareja el número cuántico con el aspecto orbital Empareja el número cuántico con la propiedad del orbital que le corresponde:

]]> 1.0000000 0.1000000 0 true Tamaño del orbital

]]> n Forma del orbital

]]> l Orientación del orbital

]]> m s no tiene nº cuántico asociado En el modelo atómico actual: Indica las frases que están de acuerdo con nuestra visión actual del átomo

]]> 1.0000000 0.1000000 0 false true abc Los electrones siguen órbitas elípticas con diferentes inclinaciones Los electrones están, a su vez, compuestos de otras partículas menores Los protones están, a su vez, compuestos de otras partículas menores Los electrones tiene características ondulatorias, pero los protones y neutrones no Los electrones en un orbital p se mueven en órbitas con forma de ocho El núcleo atrae a los electrones mediante fuerzas eléctricas Indica a que tipo de orbital pertenecen los electrones ( n,l,m,s) Indica el tipo de orbital pertenecen los electrones cuyos números cuánticos son ( n,l,m,s)

]]> 1.0000000 0.1000000 0 true (3,0,0,1/2)

]]> 3s (2,1,0,1/2)

]]> 2p ((3,2,2,1/2)

]]> 3d (2,0,1,1/2)

]]> Imposible (3,1,-1,-1/2)

]]> 3p 2s Indica el orden de energía de los siguientes electrones según sus número cuánticos Indica el orden de energía de los siguientes electrones según sus número cuánticos (1= menor; 5= mayor)

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> (1,0,0,1/2)

]]> 1 (2,1,1,1/2)

]]> 2 3,0,0,1/2)

]]> 3 4,0,0,1/2)

]]> 5 3,1,-1,1/2)

]]> 4 Indica si son posibles o imposibles los sigientes conjuntos de números cuánticos (n,l,m,s) Indica si son posibles o imposibles los sigientes conjuntos de números cuánticos (n,l,m,s):

]]> 1.0000000 0.1000000 0 true (1,0,0,1/2)

]]> Posible (3,1,-1,-1/2)

]]> Posible (4,2,-3,1/2)

]]> Imposible (5,3,-1,1/2)

]]> Posible (4,4,2,1/2)

]]> Imposible ((3,2,0,1)

]]> Imposible Posible Imposible l número cuántico que representa la forma del orbital, o nube electrónica asociada a un electrón, además de representar los subniveles de energía donde se localizan los electrones se denomina. El número cuántico que representa la forma del orbital, o nube electrónica asociada a un electrón, además de representar los subniveles de energía donde se localizan los electrones se denomina.]]> 1.0000000 0.1000000 0 true true abc Magnético Secundario (azimutal) Principal Spin 1º BACHILLERATO/QUÍMICA/ATOMO/ONDAS ¿Qué radiación se propaga más rápidamente en el vacío ¿Qué radiación se propaga más rápidamente en el vacío?

]]> 1.0000000 0.1000000 0 false true abc Rayos X Luz El sonido Ondas de radio calcula la frecuencia Calcula la frecuencia (en Hz) y el periodo (en s) de una onda electromagnética de longitud de onda #f #un

]]> 1.0000000 0.3333333 0 0 Frecuencia(Hz) =#l Periodo(s) = #t ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tu</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>nm</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>μm</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>mm</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu</mi><mo>=</mo><mo>(</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>un</mi><mo>=</mo><msub><mi>tu</mi><mi>iu</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fcu</mi><mo>=</mo><msub><mi>fu</mi><mi>iu</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>0</mn><mo>*</mo><mn>10</mn><mo>^</mo><mn>8</mn><mo>/</mo><mo>(</mo><mi>f</mi><mo>*</mo><mi>fcu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>/</mo><mo>(</mo><mi>l</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo>(</mo><mi>Hz</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">l</mi><mo> </mo><mspace linebreak="newline"/><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>d</mi><mi>o</mi><mo>(</mo><mi mathvariant="normal">s</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> calcula la frecuencia Calcula la frecuencia (en Hz) y el periodo (en s) de una onda electromagnética de longitud de onda #f #un

]]> 1.0000000 0.3333333 0 0 Frecuencia(Hz) = #l Periodo(s) = #t ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tu</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>nm</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>μm</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>mm</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu</mi><mo>=</mo><mo>(</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>un</mi><mo>=</mo><msub><mi>tu</mi><mi>iu</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fcu</mi><mo>=</mo><msub><mi>fu</mi><mi>iu</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>0</mn><mo>*</mo><mn>10</mn><mo>^</mo><mn>8</mn><mo>/</mo><mo>(</mo><mi>f</mi><mo>*</mo><mi>fcu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>/</mo><mo>(</mo><mi>l</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mi>F</mi><mi>r</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>u</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>a</mi><mo>(</mo><mi>Hz</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">l</mi><mo> </mo><mspace linebreak="newline"/><mo> </mo><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>d</mi><mi>o</mi><mo>(</mo><mi mathvariant="normal">s</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> calcula la longitud de onda Calcula la longitud de onda (en m) y el periodo (en s) de una onda electromagnética de frecuencia #f #un

]]> 1.0000000 0.3333333 0 0 Longitud de onda(m)=#l Periodo(s) = #t ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tu</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>THz</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>GHz</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>KHz</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu</mi><mo>=</mo><mo>(</mo><mn>10</mn><mo>^</mo><mn>12</mn><mo>,</mo><mn>10</mn><mo>^</mo><mn>9</mn><mo>,</mo><mn>10</mn><mo>^</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>un</mi><mo>=</mo><msub><mi>tu</mi><mi>iu</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fcu</mi><mo>=</mo><msub><mi>fu</mi><mi>iu</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>0</mn><mo>*</mo><mn>10</mn><mo>^</mo><mn>8</mn><mo>/</mo><mo>(</mo><mi>f</mi><mo>*</mo><mi>fcu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>/</mo><mo>(</mo><mi>f</mi><mo>*</mo><mi>fcu</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mi mathvariant="normal">L</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>u</mi><mi>d</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>o</mi><mi>n</mi><mi>d</mi><mi>a</mi><mo>(</mo><mi mathvariant="normal">m</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">l</mi><mo> </mo><mspace linebreak="newline"/><mo> </mo><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>d</mi><mi>o</mi><mo>(</mo><mi mathvariant="normal">s</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> calcula la longitud de onda Calcula la longitud de onda (en m) y el periodo (en s) de una onda electromagnética de frecuencia #f #un

]]> 1.0000000 0.3333333 0 0 Longitud de onda(m) = #lPeriodo(s) = #t ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>iu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tu</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>THz</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>GHz</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>KHz</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu</mi><mo>=</mo><mo>(</mo><mn>10</mn><mo>^</mo><mn>12</mn><mo>,</mo><mn>10</mn><mo>^</mo><mn>9</mn><mo>,</mo><mn>10</mn><mo>^</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>un</mi><mo>=</mo><msub><mi>tu</mi><mi>iu</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fcu</mi><mo>=</mo><msub><mi>fu</mi><mi>iu</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mn>3</mn><mo>.</mo><mn>0</mn><mo>*</mo><mn>10</mn><mo>^</mo><mn>8</mn><mo>/</mo><mo>(</mo><mi>f</mi><mo>*</mo><mi>fcu</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>/</mo><mo>(</mo><mi>f</mi><mo>*</mo><mi>fcu</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mi mathvariant="normal">L</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>u</mi><mi>d</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>o</mi><mi>n</mi><mi>d</mi><mi>a</mi><mo>(</mo><mi mathvariant="normal">m</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">l</mi><mspace linebreak="newline"/><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>d</mi><mi>o</mi><mo>(</mo><mi mathvariant="normal">s</mi><mo>)</mo><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cuanrtos más fotones emita una fuente electromagnética Cuantos más fotones emita una fuente de radiación electromagnética que haga emitir electrones a un determinado metal:

]]> 1.0000000 0.1000000 0 true true abc Más electrones emite Más rápido se mueven los electrones Emite más electrones, pero más lentos Emite menos electrones, pero más rápidos Entre dos niveles electrónicos Calcula la frecuencia (en Hz) que tendrá un fotón emitido por un electrón cuando pasa de un nivel de -#n1 eV a otro de -#n2 eV (1 eV = 1.6*10^-19 J )

]]> 1.0000000 0.3333333 0 0 #f ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>n1a</mi><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>n2a</mi><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mo>(</mo><mi>n2</mi><mo>-</mo><mi>n1</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>19</mn><mo>/</mo><mo>(</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>34</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>#</mo><mi>f</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">4</option><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Entre dos niveles electrónicos Calcula la frecuencia (en Hz) que tendrá un fotón emitido por un electrón cuando pasa de un nivel de -#n1 eV a otro de -#n2 eV (1 eV = 1.6*10^-19 J )

]]> 1.0000000 0.3333333 0 0 #f <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>n1a</mi><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2a</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>n2a</mi><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mo>(</mo><mi>n2</mi><mo>-</mo><mi>n1</mi><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>6</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>19</mn><mo>/</mo><mo>(</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>34</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#f</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">4</option><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La luz es La luz es: 1.0000000 0.1000000 0 true true abc Una onda Una partícula Un chorro de partículas Un ente físico que puede comportarse como una onda o como una partícula dependiendo del fenómeno que se trate No se sabe lo que es Un fotón es: Un fotón es:]]> 1.0000000 0.1000000 0 true true abc La cantidad de energía más pequeña que posee un átomo a cantidad de energía más grande que puede absorber un átomo Una partícula que forma la radiación electromagnética y que contiene una energía igual al cuanto de energía de Planck Una partícula que forma la radiación electromagnética y que contiene una energía que es múltiplo del cuanto de energía de Planck Ninguna 1º BACHILLERATO/QUÍMICA/ATOMO/PLANCK Calcula el trabajo de extracción de un electrón (frec,frec) Calcula el trabajo de extracción (en Julios) de un electrón para un determinado metal sabiendo que si lo iluminamos con una radiación cuya frecuencia es #f·10¹² Hz emite electrones que se mueven a #v m/s ( masa del electrón = 9.1·10^-31 Kg)

]]> 1.0000000 0.3333333 0 0 #te ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>va</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>va</mi><mo>*</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>34</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ei</mi><mo>=</mo><mi>h</mi><mo>*</mo><mi>f</mi><mo>*</mo><mn>10</mn><mo>^</mo><mn>12</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>*</mo><mi>v</mi><mo>*</mo><mi>v</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>1</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>31</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>te</mi><mo>=</mo><mi>ei</mi><mo>-</mo><mi>ec</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>t</mi><mi mathvariant="normal">e</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula el trabajo de extracción de un electrón (frec,frec) Calcula el trabajo de extracción (en Julios) de un electrón para un determinado metal sabiendo que si lo iluminamos con una radiación cuya frecuencia es #f·10¹² Hz emite electrones que se mueven a #v m/s ( masa del electrón = 9.1·10^-31 Kg)

]]> 1.0000000 0.3333333 0 0 #te ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>va</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>va</mi><mo>*</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>34</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ei</mi><mo>=</mo><mi>h</mi><mo>*</mo><mi>f</mi><mo>*</mo><mn>10</mn><mo>^</mo><mn>12</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>*</mo><mi>v</mi><mo>*</mo><mi>v</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>1</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>31</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>te</mi><mo>=</mo><mi>ei</mi><mo>-</mo><mi>ec</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>#</mo><mi>t</mi><mi mathvariant="normal">e</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula el trabajo de extracción de un electrón (long) Calcula el trabajo de extracción (en Julios) de un electrón para un determinado metal sabiendo que si lo iluminamos con una radiación cuya longitud de onda es #l nm emite electrones que se mueven a #v m/s ( masa del electrón = 9.1·10^-31 Kg)

]]> 1.0000000 0.3333333 0 0 #te ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>va</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>va</mi><mo>*</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>34</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ei</mi><mo>=</mo><mi>h</mi><mo>*</mo><mn>3</mn><mo>*</mo><mn>10</mn><mo>^</mo><mn>8</mn><mo>/</mo><mo>(</mo><mi>l</mi><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>*</mo><mi>v</mi><mo>*</mo><mi>v</mi><mo>*</mo><mn>9</mn><mo>.</mo><mn>1</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>31</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>te</mi><mo>=</mo><mi>ei</mi><mo>-</mo><mi>ec</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>t</mi><mi mathvariant="normal">e</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula la velocidad Calcula la velocidad (en m/s) de los electrones emitidos por un metal cuya frecuencia umbral es de #fu THz, si lo iluminamos con una radiación de frecuencia #fi THz (masa del electrón = 9.1*10^-31 Kg ).

Nota: si no hay emisión indica velocidad 0

]]> 1.0000000 0.3333333 0 0 #ve ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>120</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>120</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>34</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>1</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>31</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>fu</mi><mo>></mo><mo>=</mo><mi>fi</mi></mrow><mrow><mi>ve</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>ve</mi><mo>=</mo><msqrt><mrow><mn>2</mn><mo>*</mo><mi>h</mi><mo>*</mo><mo>(</mo><mi>fi</mi><mo>-</mo><mi>fu</mi><mo>)</mo><mo>*</mo><mn>10</mn><mo>^</mo><mn>12</mn><mo>/</mo><mi>m</mi></mrow></msqrt></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>v</mi><mi mathvariant="normal">e</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula la velocidad Calcula la velocidad (en m/s) de los electrones emitidos por un metal cuya frecuencia umbral es de #fu THz, si lo iluminamos con una radiación de frecuencia #fi THz (masa del electrón = 9.1*10^-31 Kg ).

Nota: si no hay emisión indica velocidad 0

]]> 1.0000000 0.3333333 0 0 #ve]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>120</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>120</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>34</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>1</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>31</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>fu</mi><mo>></mo><mo>=</mo><mi>fi</mi></mrow><mrow><mi>ve</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>ve</mi><mo>=</mo><msqrt><mrow><mn>2</mn><mo>*</mo><mi>h</mi><mo>*</mo><mo>(</mo><mi>fi</mi><mo>-</mo><mi>fu</mi><mo>)</mo><mo>*</mo><mn>10</mn><mo>^</mo><mn>12</mn><mo>/</mo><mi>m</mi></mrow></msqrt></mrow></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>v</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">3</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula le energía cinética Calcula la energía cinética (en Julios) de los electrones que emite un metal si su frecuencia umbral es d e#fu ·10⁹ Hz y lo iluminamos con una radiación de #fi·10⁹ Hz

]]> 1.0000000 0.3333333 0 0 #ec]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mrow style="color:#ffc800"><mtext xml:lang="es">variables</mtext><mi>fu</mi><mo>=</mo></mrow><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>14</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec</mi><mo>=</mo><mo>(</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><mn>10</mn><mo>^</mo><mo>-</mo><mn>34</mn><mo>)</mo><mo>*</mo><mn>10</mn><mo>^</mo><mn>9</mn><mo>*</mo><mo>(</mo><mi>fi</mi><mo>-</mo><mi>fu</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>c</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula le energía cinética Calcula la energía cinética (en Julios) de los electrones que emite un metal si su frecuencia umbral es d e#fu ·10⁹ Hz y lo iluminamos con una radiación de #fi·10⁹ Hz

]]> 1.0000000 0.3333333 0 0 #ec ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mrow style="color:#ffc800"><mtext xml:lang="es">variables</mtext><mi>fu</mi><mo>=</mo></mrow><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>14</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec</mi><mo>=</mo><mo>(</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup><mo>)</mo><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup><mo>*</mo><mo>(</mo><mi>fi</mi><mo>-</mo><mi>fu</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>c</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> frecuencia umbral ( incid vel) Calcula la frecuencia umbral (en Hz) de un determinado metal si al iluminarlo con una radiación de #f GHz emite electrones que se mueven a #v m/s (masa deñl electrón 9.1*10^-31 Kg

]]> 1.0000000 0.3333333 0 0 #fu <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>va</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>va</mi><mo>*</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ec</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>*</mo><mn>9</mn><mo>.</mo><mn>1</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>31</mn></mrow></msup><mo>*</mo><mi>v</mi><mo>*</mo><mi>v</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ei</mi><mo>=</mo><mi>h</mi><mo>*</mo><mi>f</mi><mo>*</mo><msup><mn>10</mn><mn>9</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eu</mi><mo>=</mo><mi>ei</mi><mo>-</mo><mi>ec</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fu</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>eu</mi><mo>/</mo><mi>h</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#fu</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Indica si se emiten electrones o no En la siguiente tabla están representadas las características de la onda umbral y de la incidente (por este orden). Indica si ha emisión o no de electroens

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Longitud de onda umbral = #l1 nm

Longitud de onda incidente = #l2 nm

]]> SI Longitud de onda umbral = #l3 nm

Longitud de onda incidente = #l4 nm

]]> NO Frecuencia umbral = #f5 THz

Frecuencia incidente = #f6 THz

]]> NO Frecuencia umbral = #f7 THz

Longitud de onda incidente = #l8 nm

]]> NO Frecuencia umbral = #f9 THz

Longitud de onda incidente = #l0 nm

]]> SI <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>160</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>160</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>180</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f6</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>170</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f7</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>210</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l8</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1600</mn><mo>,</mo><mn>3000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f9</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>140</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l0</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1100</mn><mo>,</mo><mn>2000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Indica si se emiten electrones o no En la siguiente tabla están representadas las características de la onda umbral y de la incidente (por este orden). Indica si ha emisión o no de electroens

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Longitud de onda umbral = #l1 nm

Longitud de onda incidente = #l2 nm

]]> SI Longitud de onda umbral = #l3 nm

Longitud de onda incidente = #l4 nm

]]> NO Frecuencia umbral = #f5 THz

Frecuencia incidente = #f6 THz

]]> NO Frecuencia umbral = #f7 THz

Longitud de onda incidente = #l8 nm

]]> NO Frecuencia umbral = #f9 THz

Longitud de onda incidente = #l0 nm

]]> SI <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>160</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>249</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>136</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>66</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>160</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>178</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>180</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>217</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f6</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>170</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>103</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f7</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>210</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>243</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l8</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1600</mn><mo>,</mo><mn>3000</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2530</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f9</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>140</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>l0</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1100</mn><mo>,</mo><mn>2000</mn><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1825</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Respecto al efecto fotoeléctrico, señala cuáles de las siguientes afirmaciones son verdaderas: Respecto al efecto fotoeléctrico, señala cuáles de las siguientes afirmaciones son verdaderas:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> La frecuencia límite depende del tipo de metal con el que se realice el experimento.

]]> La energía cinética de los electrones emitidos depende de la frecuencia de la radiación incidente.

]]> La energía cinética de los electrones emitidos no depende de la frecuencia de la radiación incidente.

]]> La intensidad de la radiación determina la energía de los electrones emitidos.

]]> La intensidad de la radiación determina el número de los electrones emitidos.

]]> Respecto al efecto fotoeléctrico, señala cuáles de las siguientes afirmaciones son verdaderas: Respecto al efecto fotoeléctrico, señala cuáles de las siguientes afirmaciones son verdaderas:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> La frecuencia límite no depende de la intensidad de la radiación.

]]> Todas las frecuencias permiten arrancar electrones.

]]> La frecuencia límite depende de la intensidad de la radiación

]]> Sólo hasta una cierta frecuencia se pueden arrancar electrones.

]]> Sólo a partir de una cierta frecuencia se pueden arrancar electrones.

]]> Si la radiación umbral de un metal es Si la radiación umbral de un metal tiene una longitud de onda de 450 nm, indica cuáles de las siguientes radicaciones provocarán emisión de electrones:

]]> 1.0000000 0.1000000 0 false true abc Una radiación de 200 nm Una radicación de 400 nm Una radiación de 0.6 micras Una radiación de 800 THz Una radiación de 1300 THz Una radiación de 1100 THz Si la radiación umbral de un metal es Si la radiación umbral de un metal tiene una longitud de onda de 300 nm, indica cuáles de las siguientes radicaciones provocarán emisión de electrones:

]]> 1.0000000 0.1000000 0 false true abc Una radiación de 200 nm Una radicación de 400 nm Una radiación de 0.6 micras Una radiación de 800 THz Una radiación de 1300 THz Una radiación de 1100 THz Una fuente de radiación tiene una potencia de Una fuente de radiación tiene una potencia de #pot watios emitiendo una radiación de #fi THz de frecuencia. Determina el número de fotones por segundo que emite

]]> 1.0000000 0.3333333 0 0 #nf <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pot</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>18</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ef</mi><mo>=</mo><mi>fi</mi><mo>*</mo><msup><mn>10</mn><mn>12</mn></msup><mo>*</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nf</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>pot</mi><mo>/</mo><mi>ef</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#nf</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Una fuente de radiación tiene una potencia de Una fuente de radiación tiene una potencia de #pot watios emitiendo una radiación de #fi THz de frecuencia. Determina el número de fotones por segundo que emite

]]> 1.0000000 0.3333333 0 0 #nf ]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pot</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>18</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ef</mi><mo>=</mo><mi>fi</mi><mo>*</mo><msup><mn>10</mn><mn>12</mn></msup><mo>*</mo><mn>6</mn><mo>.</mo><mn>625</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>34</mn></mrow></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nf</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>pot</mi><mo>/</mo><mi>ef</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>#</mo><mi>n</mi><mi>f</mi><mo> </mo></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/QUÍMICA/ATOMO/PROPIEDADES PERIÓDICAS Los electrones de valencia Los electrones de valencia: 1.0000000 0.1000000 0 true true abc Son los que lleva el átomo Son los de la última capa del átomo Son los que existen enel núcleo del átomo Son los que se distribuyen en capas Los electrones de valencia son Los electrones de valencia son: 1.0000000 0.1000000 0 true true abc las partículas más pequeñas de un elemento. los electrones que se ubican en las capas internas. los electrones que se ubican en las capas externas. Los que tienen un solo electrón Los metales están a la izquierda de la tabla periódica porque: Los metales están a la izquierda de la tabla periódica porque:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Mendeleiev los colocó así

]]> Es la zona de menor electronegatividad

]]> Forman redes y por eso están en esa zona

]]> En algún sitio había que colocarlos

]]> Son átomos relativamente grandes en los que los electrones de enlace están poco atraidos

]]> Ordena los siguientes átomos en función de su radio Ordena los siguientes átomos en función de su radio (1=Menor, 4= mayor) 1.0000000 0.1000000 0 true He 1 Ne 2 Ar 3 Kr 4 Potenciales de ionización sucesivos Los potenciales de ionización sucesivos para un mismo átomo:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Son siempre crecientes porque aumenta la carga

]]> Son siempre decrecientes porque disminuye el número de electrones

]]> Pueden crecer o disminuir, según el caso

]]> Crecen o disminuyen regularmente

]]> Crecen de forma irregular

]]> Razones del cambio de potencial de ionización El potencial de ionización del Cl es mayor que el del S porque:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Cl tiene menor radio que S

]]> Cl tiene mayor radio que S

]]> Cl es más electronegativo que S

]]> Cl es menos electronegativo que S

]]> 1º BACHILLERATO/QUÍMICA/ENLACE ¿Por qué se unen los átomos? ¿Por qué se unen los átomos?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> la sustancia que se obtiene con la unión consigue tener menos energía

]]> es la tendencia natural

]]> la sustancia que se obtiene consigue tener más energía

]]> ninguna es cierta

]]> Elementos de la tabla y electrones de valencia Indica, para los siguientes elementos de la tabla, el número de electrones de valencia

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> S

]]> 6 N

]]> 5 P

]]> 5 Cl

]]> 7 Sr

]]> 2 Al

]]> 3 Br

]]> 7 17 9 Indica cual de las siguientes afirmaciones es cierta Indica cuál o cuáles de las siguientes afirmaciones son ciertas

]]> 1.0000000 0.1000000 0 false true abc Al romperse un enlace químico se libera energía Al formarse un enlace químico se desprende energía Si se calienta agua hasta que se evapora, se rompen los enlaces O-H Las energías de enlace de las moléculas de Br 2 , H 2 y HBr son, respectivamente, de 193,87; 436,00 y 365,7 kJ/mol. De los siguientes enunciados señale el que considere correcto. Las energías de enlace de las moléculas de Br₂ , H₂ y HBr son, respectivamente, de 193,87; 436,00 y
365,7 kJ/mol. De los siguientes enunciados señale el que considere correcto.

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> La molécula de Br2 es más estable que las moléculas de H2 y HBr

]]> La molécula mas estable es la de H2.

]]> El Br₂ será más reactivo que el HBr

]]> El calor de formación de una molécula de HBr se obtiene como media aritmética de los calores de formación
del bromo e hidrógeno.

]]> Ordena en base a la polaridad los siguientes enlaces Ordena de mayor a menor polaridad, utilizando los valores de electronegatividad dados, los enlaces siguientes:

Elemento	F	O	Cl	N	C	S	H
Electronegatividad	4.0	3.5	3.0	3.0	2.5	2.5	2.1

]]> 1.0000000 0.1000000 0 true H-F

]]> 1 O-H

]]> 2 C-O

]]> 3 H-N

]]> 4 H-C

]]> 5 Para que se forme un enlace Para que se forme un enlace

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> necesariamente hay que aportar energía

]]> puede que se desprenda energía o que se necesite, depende de los elementos que se unan

]]> necesariamente debe haber un desprendimiento de energía

]]> Para que se pueda formar un enlace es necesario que: Para que se pueda formar un enlace es necesario que:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Tenga lugar una disminución de la energía del sistema

]]> Se produzca una hibridación de orbitales.

]]> Se produzca una transferencia de electrones entre los átomos que van a enlazarse.

]]> Se produzca un solapamiento de orbitales.

]]> Pares de elementos y tipos de enlace Indica, para las siguientes parejas de elementos, el tipo de enlace que formarán

]]> 1.0000000 0.1000000 0 true Na- Sn

]]> Metálico Sc-Zn

]]> Metálico S-Cd

]]> Iónico C-N

]]> Covalente polar Ca-Mg

]]> Metálico O-O

]]> Covalente apolar Iónico Covalente apolar Metálico Se tienen cuatro elementos A, B, C y D situados Se tienen cuatro elementos A, B, C y D situados en el mismo periodo. Su estructura de valencia es de 1, 3, 5 y 7 electrones respectivamente.

la estequiometría del compuesto de A con D será {1:MULTICHOICE:=AD~AD7~A7D~A7D7~Ninguna de ellas} y tendrá las características de un enlace {1:MULTICHOICE:=Iónico~Covalente apolar~Covalente polar~Metálico~Coordinado~Ninguna de ellas}
la estequiometría del compuesto de B con D será {1:MULTICHOICE:=BD3~B3D7~B7D3~B7D7~B3D3~Ninguna de ellas}
El compuesto formado por C y D será {1:MULTICHOICE:=CD3~C5D7~C7D5~C7D7~C5D5~Ninguna de ellas} y tendrá las características de un enlace {1:MULTICHOICE:=Covalente polar~Covalente apolar~Iónico~Metálico~Coordinado~Ninguna de ellas}

]]> 0.1000000 0 Teniendo en cuenta que los valores de la electronegatividad según la escala de Pauling de los elementos siguientes son: H: 2,1 ; O: 3,5 ; Na: 0,9 ; S: 2,5 y Cl: 3,0 ¿Cual de los siguientes enlaces es más polar? Teniendo en cuenta que los valores de la electronegatividad según la escala de Pauling de los
elementos siguientes son: H: 2,1 ; O: 3,5 ; Na: 0,9 ; S: 2,5 y Cl: 3,0 ¿Cual de los siguientes enlaces es más
polar?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> H-O

]]> H-Na

]]> H-S

]]> H-Cl

]]> Un elemento A tiene dos electrones en su última capa, y otro elemento B presenta en su capa de valencia la configuración 3s 2 3p 5 . Si estos dos elementos se combinan entre sí, la posible fórmula del compuesto que originan será: Un elemento A tiene dos electrones en su última capa, y otro elemento B presenta en su capa de
valencia la configuración ns² p⁵ . Si estos dos elementos se combinan entre sí, la posible fórmula del
compuesto que originan será:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> AB

]]> AB₂

]]> AB₅

]]> A2B

]]> A₂B₂

]]> 1º BACHILLERATO/QUÍMICA/ENLACE/ENLACE COVALENTE ¿Cómo una sustancia gaseosa apolar puede llegar a licuar? ¿Cómo una sustancia gaseosa apolar puede llegar a licuar?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Calentando

]]> bajando mucho la temperatura para crear dipolos inducidos

]]> a través la atracción de sus dipolos permanentes

]]> Ninguna de las otras

]]> El ácido sulfhídrico (H2S) es una molécula ... El ácido sulfhídrico (H₂S) es una molécula ...

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Pirámide trigonal

]]> Tetraédrica

]]> Trigonal

]]> Ninguna de las otras

]]> El enlace covalente se produce porque tiene lugar ... El enlace covalente se produce porque tiene lugar ...

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Una transferencia de electrones

]]> Una compartición de electrones

]]> Una atracción entre los cationes y las nubes electrónicas

]]> En el enlace covalente: En el enlace covalente:

]]> 1.0000000 0.1000000 0 true true abc Se forman unidades de pocos átomos Se forman redes tridimensionales con muchos iones del mismo tipo Se forman redes tridimensionales con iones positivos y negativos en el mismo número Pueden formar unidades pequeñas o redes tridimensionales En el enlace covalente: En el enlace covalente:

]]> 1.0000000 0.1000000 0 false true abc Tiene puntos de fusión bajos Tienen puntos de fusión altos Pueden tener puntos de ffusión bajos o altos dependiendo de la polaridad Pueden tener puntos de fusión bajos o altos dependiendo de si forman moléculas o redes Los compuestos de moléculas grandes tienen mayor punto de fusión que los de moléculas pequeñas Los compuestos de moléculas pequeñas tienen mayor punto de fusión que los de moléculas grandes La molécula de dióxido de carbono es La molécula de dióxido de carbono es:

]]> 1.0000000 0.1000000 0 true true abc Lineal con 2 enlaces simples Lineal con dos enlaces dobles Angular con dos enlaces simples angular con un enlace simple y uno doble Los compuesto covalentes: Los compuesto covalentes:

]]> 1.0000000 0.1000000 0 true true abc Conducen el calor y la electricidad siempre Conducen la electricidad si están disueltos en disolventes polares Conducen la electricidad si están disueltos en disolventes apolares No conducen la electricidad salvo alguna excepción Los compuestos covalentes son poco solubles en los disolventes polares porque: Los compuestos covalentes son poco solubles en los disolventes polares porque:

]]> 1.0000000 0.1000000 0 true true abc La moléculas de disolvente están más atraidas por ellas mismas que por el soluto Las molećulas de soluto están muy atraidas entre sí y poco por las de disolvente Esto sería verdad si la electronegatividad del soluto es mayor que la del disolvente Ninguna de las otras Para hallar la estructura geométrica de una molécula nos tenemos que basar en: Para hallar la estructura geométrica de una molécula nos tenemos que basar en:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> los dobles y/o triples enlaces que existan en la molécula

]]> los electrones que tiende a compartir el átomo central

]]> los pares de electrones enlazantes y no enlazantes que tiene el átomo central

]]> Si un átomo tiene 6 electrones de valencia y se combina con el hidrógeno Si un átomo tiene 6 electrones de valencia y se combina con el hidrógeno ¿Cuántos enlaces covalentes formará?

]]> 1.0000000 0.1000000 0 true true abc Ninguno. Serán iónicos 6 2 4 Una molécula covalente: Una molécula covalente:

]]> 1.0000000 0.1000000 0 false true abc Puede ser apolar aunque sus enlaces sean polares Puede ser polar aunque sus enlaces sean apolares La polaridad depende de los enlaces y de la estructura tridimensional Puede ser plana y apolar Una molécula será polar si ... Una molécula será polar si ...

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> los enlaces son polares y la molécula no tiene simetria

]]> los enlaces son polares y la molécula es simétrica

]]> los enlaces covalentes son apolares

]]> Los enlaces son polares. No importa la simetría

]]> 1º BACHILLERATO/QUÍMICA/ENLACE/ENLACE COVALENTE/GEOMETRÍA El ácido sulfhídrico (H2S) es una molécula ... El ácido sulfhídrico (H₂S) es una molécula ...

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Pirámide trigonal

]]> Tetraédrica

]]> Trigonal

]]> Ninguna de las otras

]]> El NF3 es menos polar que el NH3 porque: El NF₃ es menos polar que el NH₃ porque:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> La polaridad del enlace N-H es mayor que la del enlace N-F

]]> La estructura tridimensional es diferencrte

]]> El NF3 no tiene orbitales no enlazantes

]]> La polaridad de los enlaces N-F se anula parcialemente con la de los orbitales no enlazantes

]]> La molécula de dióxido de carbono es La molécula de dióxido de carbono es:

]]> 1.0000000 0.1000000 0 true true abc Lineal con 2 enlaces simples Lineal con dos enlaces dobles Angular con dos enlaces simples angular con un enlace simple y uno doble Para hallar la estructura geométrica de una molécula nos tenemos que basar en: Para hallar la estructura geométrica de una molécula nos tenemos que basar en:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> los dobles y/o triples enlaces que existan en la molécula

]]> los electrones que tiende a compartir el átomo central

]]> los pares de electrones enlazantes y no enlazantes que tiene el átomo central

]]> Una de las siguientes proposiciones acerca de la molécula de H-CN es incorrecta, señálela: Una de las siguientes proposiciones acerca de la molécula de H-CN es incorrecta, señálela:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Hay dos enlaces sigma y dos enlaces pi

]]> La molécula tiene geometría lineal

]]> El carbono utiliza orbitales híbridos sp²

]]> La molécula es polar

]]> 1º BACHILLERATO/QUÍMICA/ENLACE/ENLACE IÓNICO A medida que los iones de una sustancia ionica sean más pequeños y cargados, ... A medida que los iones de una sustancia ionica sean más pequeños y cargados, ...

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> serán más frágiles y se disolverán mejor

]]> serán más frágiles, pero se disolverán mejor

]]> serán más duros y se disolverán peor

]]> En el enlace ionico, las fuerzas de atracción electrostática ... En el enlace ionico, las fuerzas de atracción electrostática ...

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> No son direccionales

]]> Son direccionales (tienen direcciones de preferencia)

]]> No existen

]]> Los compuestos iónicos no son conductores en estado sólido porque Los compuestos iónicos son malos conductores eléctricos en estado sólido porque

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Los electrones no caben entre los iones

]]> Los electrones están muy atraidos por los aniones y repelidos por los cationes

]]> Los electrones están muy atraidos por los cationes y repelidos por los aniones

]]> Son buenos conductores eléctricos en estado sólido

]]> Los compuestos iónicos son aislantes en estado sólido Los compuestos iónicos son aislantes en estado sólido porque:

]]> 1.0000000 0.1000000 0 true true abc Los electrones no caben entre los iones que ocupan el maximo de espacio Los electrones no se pueden mover porque los iones están muy atraidos entre sí Los compuestos iónicos son conductores en estado sólido Ninguna de las otras Los compuestos iónicos son frágiles porque Los compuestos iónicos son frágiles porque

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Es su naturaleza

]]> Si desplazamos una capa de iones los iones del mismo signo se repelen entre sí

]]> No son frágiles

]]> Los cationes crean huecos entre los aniones

]]> Los sólidos iónicos son... Los sólidos iónicos son...

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Frágiles

]]> Resistentes

]]> Maleables

]]> Ninguna de las tres cosas

]]> Predice la carga del ión más estable de los siguientes átomos Predice la carga del ión más estable de los siguientes átomos.

]]> 1.0000000 0.1000000 0 true Ba

]]> +2 Br

]]> -1 Cs

]]> +1 Al

]]> +3 O

]]> -2 -5 -3 Se tienen cuatro elementos A, B, C y D situados Se tienen cuatro elementos A, B, C y D situados en el mismo periodo. Su estructura de valencia es de 1, 3, 5 y 7 electrones respectivamente.

la estequiometría del compuesto de A con D será {1:MULTICHOICE:=AD~AD7~A7D~A7D7~Ninguna de ellas} y tendrá las características de un enlace {1:MULTICHOICE:=Iónico~Covalente apolar~Covalente polar~Metálico~Coordinado~Ninguna de ellas}
la estequiometría del compuesto de B con D será {1:MULTICHOICE:=BD3~B3D7~B7D3~B7D7~B3D3~Ninguna de ellas}
El compuesto formado por C y D será {1:MULTICHOICE:=CD3~C5D7~C7D5~C7D7~C5D5~Ninguna de ellas} y tendrá las características de un enlace {1:MULTICHOICE:=Covalente polar~Covalente apolar~Iónico~Metálico~Coordinado~Ninguna de ellas}

]]> 0.1000000 0 1º BACHILLERATO/QUÍMICA/ENLACE/ENLACE METÁLICO ¿Cuál de las siguientes propiedades no es propia de los enlaces metálicos? ¿Cuál o cuáles de las siguientes propiedades no son propias de los enlaces metálicos?

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Maleables

]]> Conductores del calor

]]> Electrones externos con poca o nula movilidad

]]> Dúctiles

]]> Conductores eléctricos

]]> Solubles en disolventes polares

]]> Indique cual de las siguientes afirmaciones es falsa: "Los compuestos metálicos poseen todos ellos..."

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Una conductividad térmica elevada

]]> Una estructura cristalina

]]> Puntos de fusión muy elevados

]]> Los electrones de valencia son comunes a todo el orbital

]]> Una gran solubilidad en ácidos

]]> Refiriendose a los metales, señale la afirmación que considere correcta: Refiriendose a los metales, señale la afirmación que considere correcta:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> El retículo cristalino está formado por iones positivos

]]> Los electrones de valencia de los átomos están situados en orbitales localizados

]]> El retículo cristalino está formado por iones positivos y negativos

]]> El retículo cristalino está formado por átomos neutros

]]> El retículo cristalino está lleno de electrones muy libres

]]> Se sabe que los metales son buenos conductores del calor. Indique de cual de los siguientes factores depende fundamentalmente esta propiedad: Se sabe que los metales son buenos conductores del calor. Indique de cual de los siguientes factores
depende fundamentalmente esta propiedad:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Del número de protones y neutrones de su núcleo

]]> De la nube electrónica que se origina al formarse el enlace metálico.

]]> De los restos positivos que se distribuyen en los nodos del retículo.

]]> De los electrones que quedan en las capas internas y que no intervienen en la formación del enlace.

]]> Un sólido metálico está compuesto por: Un sólido metálico está compuesto por:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Iones positivos y negativos

]]> Átomos neutros que comparten electrones en enlaces dirigidos

]]> Iones positivos y una nube de electrones

]]> Iones negativos y una nube de electrones

]]> 1º BACHILLERATO/QUÍMICA/ENLACE/FUERZAS INTERMOLECULARES ¿Cuál de las siguientes afirmaciones no corresponde con un enlace de puente de hidrógeno? ¿Cuál o cuáles de las siguientes afirmaciones no corresponde con una unión de puente de hidrógeno?

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Siempre participa un átomo de hidrógeno

]]> Uno de los átomos de la molécula es pequeño y muy electronegativo

]]> Las uniones son más fuertes que los covalentes

]]> Las uniones son más fuertes que las fuerzas de Van der Waals

]]> ¿Qué gas tendrá mayor punto de ebullición, el Neón, el Argón o el Kripton? ¿Qué gas tendrá mayor punto de ebullición, el Neón, el Argón o el Kripton?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Neón

]]> Argón

]]> Kriptón

]]> Todos iguales. Son gases nobles

]]> ¿Qué gas tendrá mayor punto de ebullición, el Neón, el Argón o el Kripton? ¿Qué gas tendrá mayor punto de ebullición, el Neón, el Argón o el Kripton?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Neón

]]> Argón

]]> Kriptón

]]> Todos iguales. Son gases nobles

]]> A temperatura ambiente, metano (CH4) es un gas, hexano (C6H14) e A temperatura ambiente, CH₄ es un gas, C₆H₁₄ es líquido y C₂₀H₄₂ es sólido. Esto se debe a que:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Al número de hidrógenos

]]> Al número de átomos de la molécula

]]> Al aumento de la polaridad

]]> A que foman moléculas globulares

]]> La afirmación del enunciado es falsa

]]> Al evaporar agua ¿Qué uniones tenemos que romper? Al evaporar agua ¿Cuál es la unión más importante que tenemos que romper?

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Enlaces O -H

]]> Fuerzas de puente de hidrógeno

]]> Fuerzas de Van der Waals

]]> La agitación molecular

]]> No hay que romper uniones. Sólo separar las moléculas

]]> Dados los compuestos siguientes: H 2 O ; H 4 Si ; CH 3 OH ; HF y HI, podemos decir que formarán enlaces intermoleculares por puente de hidrógeno los siguientes: Dados los compuestos siguientes: H₂O ; SiH₄ ; CH₃OH ; HF y HI, podemos decir que tendrán

fuerzas intermoleculares de puente de hidrógeno los siguientes:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Todos ellos pues tienen H y otro elemento más electronegativo

]]> Solamente los H2O, SiH4, HF y HI

]]> Solamente los H2O, CH3OH y HF

]]> Solamente los que tienen el enlace O-H, es decir: el H2O y el CH3OH

]]> El etanal (HCOH) es solubles en agua, pero el metano (CH4 El etanal (HCOH) es solubles en agua, pero el metano (CH₄) no lo es. Este hecho se debe a que:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> El etanal forma puentes de hidrógeno con el agua y el metano no

]]> Los enlaces de puente de hidrógeno entre las moléculas de metano son más fuertes que los que forma con el agua

]]> Ambos son muy poco solubles en agua

]]> El metanal tiene oxígeno y el metano no

]]> El punto de fusión del nitrógeno es -209°C, a la presión normal y la energía de disociación es muy elevada: 943,8 Kj/mol. Teniendo en cuenta esto, indique cual de las siguientes afirmaciones es FALSA: El punto de fusión del nitrógeno es -209°C, a la presión normal y la energía de disociación es muy
elevada: 943,8 Kj/mol. Teniendo en cuenta esto, indique cual o cuáles de las siguientes afirmaciones son
FALSAS:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Las fuerzas intermoleculares en el nitrógeno líquido son fuerzas de Van der Waals débiles

]]> El enlace que se establece entre los dos átomos de nitrógeno que forman la molécula de N2 es muy fuerte

]]> En el nitrógeno molecular las fuerzas intermoleculares no son de tipo dipolo-dipolo.

]]> En el nitrógeno molecular, las fuerzas de Van der Waals entre las moléculas son más fuertes que las fuerzas
que mantienen unidos los átomos que forman la molécula.

]]> Indica qué moléculas tienen puentes de hidrógeno Indica qué moléculas tienen puentes de hidrógeno

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> H₂O₂

]]> SI H₂S

]]> NO CH₃-CH2OH

]]> SI CH₃-O-CH₃

]]> NO CH₃-COH

]]> NO CH₃-COOH

]]> SI NH₃

]]> SI CH₄

]]> NO Indica qué tipo de fuerzas intermoleculares serán dominantes en las uniones entre moléculas de: Indica qué tipo de fuerzas intermoleculares serán dominantes en las uniones entre moléculas de:

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> NH₃ y NH₃

]]> Puentes de hidrógeno H₂Se y H₂Se

]]> Dipolo-dipolo H₂O y O₂

]]> Dipolo - Dipolo inducido BF₃ y BF₃

]]> Dispersión I₂ y I₂

]]> Dispersión CH₄ y CH₄

]]> Dispersión HF y HF

]]> Puentes de hidrógeno Dipolo - Radical Apolares Indique cual de las siguientes afirmaciones es CIERTA: "Cuando el hidrógeno se licua los enlaces
que aparecen entre sus moléculas son:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Enlaces covalentes

]]> Enlaces intermoleculares por puente de hidrógeno

]]> No aparecen enlaces intermoleculares, solamente existen los enlaces entre los dos átomos que conforman
cada molécula.

]]> Enlaces intermoleculares por fuerzas de dispersión

]]> 1º BACHILLERATO/QUÍMICA/ENLACE/PROPIEDADES Dadas las siguientes sustancias en estado sólido: NaCl, C Cl 4 , SiO 2 ; CO 2 , CH 4 y H 2 O, señale la proposición que considere correcta entre las siguientes: Dadas las siguientes sustancias en estado sólido: NaCl, CCl4 , SiO2 ; CO2 , CH4 y H2O, señale la proposición que considere correcta entre las siguientes:

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> En las sustancias CCl4 , CO2 , y CH4 en estado sólido, las fuerzas intermoleculares de atracción son
debidas principalmente a fuerzas de Van der Waals

]]> El NaCl y el SiO2 dan lugar a sólidos iónicos

]]> El CCl4 , CH4 y H2O presentan enlaces intermoleculares por puente de hidrógeno

]]> El SiO2 y el CO2 dan lugar a compuestos sólidos covalentes o sólidos atómicos

]]> De las siguientes propiedades, referidas a los sólidos covalentes, señale la que considere correcta. De las siguientes propiedades, referidas a los sólidos covalentes, señale la que considere correcta.

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Los nudos del retículo cristalino están ocupados por partículas cargadas eléctricamente.

]]> Sus átomos tienen alta electronegatividad

]]> Son muy blandos

]]> Son conductores de la electricidad

]]> La frase: "El enlace covalente en los compuestos moleculares es más débil que el enlace iónico, ya que los compuestos iónicos funden a mayor temperatura que los covalentes"

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Es cierta. Una forma de ver la fuerza de los enlaces es analizar los puntos de cambios de estado

]]> Es falsa. Cuando un compuesto covalente molecular cambia de estado no se rompen los enlaces

]]> Puede ser cierta, pero hay que tener en cuenta la energía reticular

]]> Es falsa. Los cambios de estado no tienen nada que ver con la fuerza de un enlace

]]> Los compuestos covalentes son poco solubles en los disolventes polares porque: Los compuestos covalentes son poco solubles en los disolventes polares porque:

]]> 1.0000000 0.1000000 0 true true abc La moléculas de disolvente están más atraidas por ellas mismas que por el soluto Las molećulas de soluto están muy atraidas entre sí y poco por las de disolvente Esto sería verdad si la electronegatividad del soluto es mayor que la del disolvente Ninguna de las otras Los compuestos iónicos no son conductores en estado sólido porque Los compuestos iónicos son malos conductores eléctricos en estado sólido porque

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Los electrones no caben entre los iones

]]> Los electrones están muy atraidos por los aniones y repelidos por los cationes

]]> Los electrones están muy atraidos por los cationes y repelidos por los aniones

]]> Son buenos conductores eléctricos en estado sólido

]]> Los compuestos iónicos son aislantes en estado sólido Los compuestos iónicos son aislantes en estado sólido porque:

]]> 1.0000000 0.1000000 0 true true abc Los electrones no caben entre los iones que ocupan el maximo de espacio

]]> Los electrones no se pueden mover porque los iones están muy atraidos entre sí

]]> Los compuestos iónicos son conductores en estado sólido

]]> Ninguna de las otras

]]> Los compuestos iónicos son frágiles porque Los compuestos iónicos son frágiles porque

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Es su naturaleza

]]> Si desplazamos una capa de iones los iones del mismo signo se repelen entre sí

]]> No son frágiles

]]> Los cationes crean huecos entre los aniones

]]> Los sólidos iónicos son... Los sólidos iónicos son...

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Frágiles

]]> Resistentes

]]> Maleables

]]> Ninguna de las tres cosas

]]> 1º BACHILLERATO/QUÍMICA/ESTADOS DE LA MATERIA Temperatura y cambio de estado ¿Es posible hervir agua a 20ºC? ¿cómo lo harías? 1.0000000 0.5000000 0 true true abc Si. Disminuyendo la presión No. Es imposible Si. Aumentando la presión 1º BACHILLERATO/QUÍMICA/ESTADOS DE LA MATERIA/CAMBIOS DE ESTADO ¡Cómo se llama el cambio de estado que se representa en cada tramo horizontal? ¡Cómo se llama el cambio de estado que se representa en cada tramo horizontal?

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UklGRpYhAABXRUJQVlA4IIohAADQkgCdASrCATMBPpFEnEulo6KhpDF6GLASCWVu/FuYief+jZFF5m8f87zmrS/qfTlsvPYnxv9t/0PaV95fuF/qz03PMb/Of8d+xPvIekj/LeoB/aP7v1q/oAfsZ6bv7M/Dd/Zf+B+13s5f+XWlvIX9s9F3gD+U8R/I1709yuW11b5mfyf79/sf8H6Hf6bxN+OH+R6hH5L/Of9J6Z78PmX+F/m/UF9s/pf+o/wv5MejV/jeiX2I/3vuA/z7+0f6z19/4PhM/bv83+wnwAfxP+hf57/A/u9/s/kA/6v8t59/pz/0/57/TfIX/Pv7R/0vXJ9hf7if/X3PP18/+BEUv2n15tXm7wrOhEXXf+x7Pr8kXLBD/ipNYOYL8Db6L3r1Cp51rmCccMBIaN4v2n14Thwpgl0wR7aNZLqd27eiMjM4ANiXVfSZNOwQH6oGjeL9p9ebV5u8Fo6IElMOuu2RFottmrWD+Vr7CTJUFmcD6I3oNwwEho3i/afU60ns2brQspXdL8OodLFNrN3k1YQRq4igvlnb9p/zGG7i/W+VFJF+0+vNq83eFZEOruIyNDrJ/f3N60VmXllrGVifgRsIFtrOcXff61Sl7IZfWskVx57ogI46IT/3UXuZycLB1A8kk7pwGAsj71g6kd7fUkLRvF+0+u59/KQg/Y9BRAB5dm0QfdednqIWOz4EPtgiwoFgLwZYoXm1ebvCs6APbJhol9teIEf7sFjiTqn8xk/yfZcKulFHf0LmtzNXgsy/khXNHcv2n15s4/q3v9ij8v4mceDBCAxItdIjhgAwHDLMSSBszrENJLTuKZCtPdh3eFZ0I/oNJXnPgsJVEl658Ge5TdoElRYE3wNq42pXDJJ7z3Yd3hWdCP4xWLLi+xo1EMpF2sjYGq7C6GwGx2CpqUGtz35B6QNwwEgvDRkKx3SmPTo79Vvj9nKPXGnaMzECK5h/4GYpftPa02iVeOW92cvdb/n13VR26I4+TmKOd6Q2cTYOc6GYp5iMxyZb4KTP+X2bwuSN2HG5X5TbeNtp9qjjzPNP1oELnyE3A9TjR/Zl2FQjrTQzACDEW06DcbNet+oPMStDqTEFUc1lF5IjmcNN75Mkouuig7MS5V2WSS/5WHeeuyozqNhj4aP195886oTu3zC8jA5wX8sPSyeTOmpM7OjRuqM7PFjcwiDArUiNLR8l8gV7UUscM3+p9wgJ7zBh91m9+PtG9H+oDq0YHZVkYuOqqRCqPtPipFaI8+sH578iZd+pmSCzODpXKEiQLxgSvPUUuqHmwcn/7f53Iud+EcNpEfWunqcYmZ0PrkAB/3KEQsGzqA//8O3qUr/3cLauLy0dd7Eo8/tKn0d0vzKWNaYwybmEW4dG5Kr6BBvWPg34WIyNOTqfa5Mydv70YdO32RVXgbI1l5qq8ZYFOzn2qtXm7qhy/996RVGXBlQaoApFBIhLqcGDdMGJ0A1XpP+Dhv7O7SoEcwvGhv2rWuqrtl4h7TuCIDk/2XyjB4CFelQGjJw92Qf04AaFiFtj82s7LHbjXrsRrEWRftPrzavN3hWdCQZ1XiP6UOKZ/LhsWuFAAP7+1iAHaryrmoiMu9QGdbhjP0yLVzG0hiSYLtg3O4AJPdquB79JMQzE3DkoO1DrfsC+ExokRKPvhGrwV0a0iE2VtLvpg4xj4dX3YbXjRY2YdGEJwsaLHE/yEIQKMQ6xGR3g7nNFl1eCWchd0UYUrSABhJRr71zByhahYyHLKAiOgFW2xyGkuogsoAXDjgk3AMB0ApWT8luvuG6EZ6oQgOckw6WqpN+cAmWFfJjJzjs3wdd4lmKSfZIohmttf2pRN2F590s9UomwN4pZOcYQY4asdTp9KPmzHAChn79hyBNi07VS7zAhEe8O74I96RZXb0nmH3YsojWPFrn0FxwmSbGLM96zbPJgCx6wJy01frdgG3XQ7O5Y0+fxSIje/07MJ1PqmdixsdlTKqB2MWb/Z9KrRQmc87wh7CZ90EomCKg9PqEUUrXUjCiiqfIr2iJAADH/DT2kOkwl7PeYn3RTevnxVuKjDcNriER9afaw4N73285T8ueAjaAneP07htQFS0hidEXREHg7PFBMKJn5a+8G0qmdQc4ZD3gGEyIDrhfvTKMR3HBRKy9WXfPRLcSgFtIC1BjKVfe8cfRA4TBoQA70ajFd5Heq1e/1ohaOLZgbSSujb5bDc+uqoVgC6auUrqYS5PSzbq+Lps/hB/QkFTJDKZCEPIiJWeSeFWdRIB6zy9B6N9p0v5pDDAARlT+dnGr2BWXB0ELw4feKYWfo/fwNPvBiyZSYg1E3oHjw0AHzpbQ6dn3SUKm/QjU7NOeFUbLzVNMQRwHH0vefjBl3f6hiIZwykQ5HGuE6w4zjnlx1Th63DcEbixNOiz2aVMthWSb4XC/yv5+33J3fShPS8Ed7SXhFNLNJBZJ6kCLkt1jZL6ryahad04Wefo451K3fhp9jLLI5pSPpw1IMjFTdFtr5y1xzYLSEDLfHZ2KePVYOrf/0AFi6m2kqTEz1fezfp4ekX7iz6iEQHxXr9WrcmIE0Kje8qgxgcfxJvpIq/DrboXh3NkhMXwxupWWHcqAZAZpMFpWOO3qmCbSmp10Ycv0p0cKFEl0eGk7zgQYV9Vb+4Yu5Fv0f7pkvziIhfTWsEzS1qZzZcuQjx0oxl1hMtXnx2g9KnjdwWHiVaGwTexdopKvELbhMmd7HuqHdyfAxk+RLmMMZ9SmcmXZkJCd3MpoCF/C/j1R6ynS4FoucgqTIMiBY2wIKcZByrAwmblfSdFkk7vVT+dPcz4ybbcPVdZzBUDzPVSgVXitSV70LaGCHSBKmbPb+vYPOQ69LKls14KVc01hIimZqHThwAlB8bZvtViUsfHH5yG9i3aNYKFTiri0xJIenKIqplvPVioN/N/YjU2xTSM/AacbdCOq42HlQBidvgBvZ241JZ/qbwEi7vr5vuXuUuxNyunOifpDb0B5pFoB8GOzUC2esrTsOka3OtFramnB6o2BCLiCKexH4a7yR99k8Z33xNftv2GY5V48/lUqR6vj1fZx7eFp9QdHjKMjdFRFfJyGFpaHUWI3P+U3Kw42XFcG2bXpSxzMzcCqf9IItCQvSMvok4avk9S5EObmEMpNq3VQ3HN2tUiGvEb+12jgHHGrr6J1j85fvsbIQiiVDhR8rd5YkUYP2Yb8c9+eSV4d7BBbBtyQiQNYRhBxYN1dnWzd0JEpxOKxedPEu+4DhmvOFUAPcerKjBnNwIVHG+LGqUWmP9QuYrbmxFv6om2CvMih5oU3KxseY9b03f1dAOPFOrzyrTlwQilr2tB2I6OfYdCPXH972oM+dBWPcEATFm1v2FX8oh1R/fn+GlVgpFaZyzP+FG3PxEzx51KfcIhkzaow3RiY/CnfEI3d0v/qzGH/+SkIqCBtRRJneB6i1lpuJH6eG8Kzduu2nKFOiFuGi3QoL6Twcleu+6H/Zf3HrOaKESLiNtznxrspFIaluBBdX1siUVc0VPaqBgPviiKcJp7IZngbrDeNMvsuATb2XEH0LgU3E9n5/KWOEO6/l5+P2vNh/h0s+eOZhwGXng4Nit9LqGBP5pKsdE/PrbN791g/hAGU6Ndw7Mob71mxLF5t6qZMt5cIeXori7mwAa/bOZ9MAz3/Bjihr7b0ql1rrbmToAkDWHHnp66QY5lqolXLsRBUzdOsz198wK09qa4x1NxcLoLdzUfW1iPbsc+dcO9vevb4+ikUZpDcfAGWg4dh6UEVw7VCHwMpNcdms2VH3T3aXAHYBR3YBCo/kZXr8d+JqD1AbsUpNSzDmiQ6YxqHvcJwGl37PxP4FtIFLtezepfenszrOmg7RvFQ0fgS0mZdcvyWYQVSpiTyaT90yHIeT2EpJmNjidfvuiXs/nRHHmUbIJgj9ZHsgtfwIm7Em/YjB/SQ8PBq6U4qAxkzKKdj+dWSrEcXzmhBeZ7P7WvHAkEy0ysa0IGmsu1zjfAcCwlIe6oz3hO7p0BZqfadV4kSmmzGJoPHN8YM/d4tVAgsjfSWgab8zLC7OsrthixJ2R69nfMfwTkRC8wI2x/98BbQu+Z/FfKJh3j5clYgjmZwJOwIeB7fCULYJyl7nHyi7alenoiY23x9ZCAcCPzNihmHLP9FgSznxK+IUDMAt+Ei8gqzuZT/mZrMtRz6hrRDR8PS2DFNSMpskWd1EancVqJIHfQiAYXJYr1ggO96ivYAKeRzxECgnu1i2pAZ5daeaG0BJ0+Nzeu45b/AvFshZgYotdDHh731dXz40kE5sY1eibe90pagZi/ygkhFBmfE9V2dQAEOPB2OSxoPm8EVbiuTsbyFw/2v2vbj29wwJQSRgS42YyGUPppVArV5pR350vd6pUAGux3urxKJ1RzvRcyx4281Cg0H08Fkl+soP5qx5FiCgKf4Yw0537tZKY5NEPEGBGAoSLB2HbCiPCC1cV9qo0WpdO74FZhmEuFQ9Fvtgh/9a74Yk/6Ax6fHTrNqRB8y9HjtU6et49Q8q9/VYpyu5x9PJbHW3XJY6CRCXfa944h59upgroewmOKoUctC+AY2t0cQltDZwUqAugE+q73WXZXHlaW4c/ZbNt1qJh80FIpmC/XQS7o9MyqHgftp2qqd5SXuJPDCU3VKi+MFYp4rGyv3oZ7egH8Pwbjjxhd1YA3wJl+hu2H3Ai0fDlg0OKE0/cuH/K4wZ8N8hgF35WZXNuObX3r0V8020An3vkj04kBbPZGRBN/awBByAgp6Uqjc02BlrhL0oNINaBLFOz26oah+J/FaCaCZEdKGUMY7BjQB0ZchJx+8WA9vh5Bwi9iCcKG69B06kpX6G/DwAxH4U76UMc0vkBUSsVrizSNU4KAIPU4n5wTgN4NIWUg61oLNHFl/Vds7TZptj3HvUPpXJyZja6ADnZP6KWav7yDaaWvJIe1n/bi3RSa4YXTvfgU9NC0DLEHf+om/3OWTGHXG6vcDNQzaoWuwuwH7FocOziNvgVmu+UxwPqAvnU4UfIJTvST3mWiw0IFAXQgMcP+fSBYPt9o7+EVzVcwl4wWUrp/1/tfJ/99dxlA74rUm50YlFIpDLpI3+JKb3ekknSV/oLLDyW/LWikSRgzHACsxM1UaFeXT9K8MyEiDL9AlAIJv9ByNOD6CBU2IeIcJMJ7jX6U1BXuxkVjTlm3ENC5RfSXkE66ERf/FXmoDcnyWtkwZi9ncpZ8RME8bK4fsHGX+ys5SjyBsdzsEKthVa8/lsvjkM5bi2JGECY5NnbfeWHIo+9w3+sXxa8p/ubw05WH7ieSQNmxmiiU11HBrwk42amwScaFP0ALI2vqun1pDZlZNTfCa9fx6E8m4TMRWTPUkNzbug0I6mATw1ziWUo3ImWfnSQeXG322R8wwGTq0K3lLmraL9P5YBjpHro/WxLrVSay7ZVt6vXUQUpUnOP8Ko5mg3Fxk8Y5KfkJVSxei8//jR9FCZtFkU1WWN9IR1JR8NWQsCbl+BHgH6bZTpUMdg9xTD+yBvM6QRTwOylozYIU+5iqxGMDlROzPPBxfEIScI9Pt0HZWE7EOMkv4UoJCK6+uKbyFiBIzYIyhwnA8e3qLXBGxCRHuaZp/YXbVxjRhs9G2WInOpSGB+Dp6TBPKpAXmB6xejYz1bAH/amnBuVqXEDYt51Sf+rihEKloRADPqoYyHghRRypYfXOOmRnlvIvTx/Y/Vi+fItckmKsBaanjOkeqpOb3TfpoE3iJYHEBEHn4m/H6RGznzVTnWnON4K/NWAqAr9pz+S/KROtprxm/f248yTSuISDwwt5x0lq+QAqJpXx8SoTanX2yYGE3HwCzn4QNXT9ePlugB5vSFXg/R6koASHXmmjEI8eLCJMmnGaO8nlPVt6W/3fwC8nUIQK32MmvgHhkmmSRM8rbcACBdSytT4OHn/Ylnoa3qr0XS1cNltgw7gs14944WyeccF1mfIKz0lnwuX3slPccqtLoqz8pQD6DX7xUuntZOLAZvcWpv6kpnmsuXhkDXmiSHZpquqovbCBlvyT0igTpl80V+4ImRr96DRfJHHnuJ65n12heCGs0JyMA5A0mYc6sYNwceQIvN0PE+2AF8FQMIW+ZDM4uWzKfMg4/VAARYNa5sfu6K8zQS6dmxYK7Fc18g/jGt2n2EjFZv8E9UPvzEaQGk7R2lmZq7hVVgaiCJpnFj0UEG34DaSZNuHje87NjKv3+fMNoaJOhYeylEuCR3mcde9jjxGbkTF23ucIwPVLFSspZgMRR85nkzJvd6jwj3lN8Bs1znXz2U8DAnt1DZCFojiLlMbClIjs5NMsknW4NCdjpiGKjSH3enee3f/K+GXa/lnMjkbhncQYfpc7bgG7DEeIbMBTpqYjJs5FxCWp3bgBLVN+O6/998Tqvvynt/yktWqkWVw0OVY/aMwME2r8Cs0umYUAnhzWAhvc/gjNdIm7Z0hk3iiVcigPCYq+Sb3otDF3YRPLWWHPbqFd4SJOpbIrb9TsEZzcHrIoXRk25eADsMdqr4QyNYKxpBoKF7MaSezfachd+WdePjdwxd/MCmM8ekNxEsJguoAW6iwBuZfyD9VDU7u++wAITzoFgp0D7ypU6ficCLCJEaSjLpbHg3Bqq2m8hobYGcCwV23E00icFd5rxQ4pzYzHe9/gnqh9/LBMiLuUpyoKq0JX/LHrOKYuMXkLkoiNzY5sj3Sp9Kvp1veT8TiXGKUqKQK1yap/8bUMvNuD1BTy1YrP/5Qp/rAf2RtskGfxEYjPmcapoo8CM8FhT4jQXmN9RoQeuxW1BKdpFmgH44GoUVh/76G++tVrwgAVByL5MVaTeNkPAvwsk2l9bGPscjCtArUTsjBLcFrmfvQ+jHWgqVDmnIktDJvCL5bhGGgvT2go0pN/CqsX7cxHERiO+Gbh1bzyYfaDLqfn9AIPzwqbKe9I3LMeMuAO9Sf1HAPorWaHa5iOK/5Akb87E2fCuo/F2DYPsXJvkbphVcstO+owOy5gQRIyCKneOQizIujLnjtXOwEQUlEGtqi2XbipfqeZtPhiLJeeBDa9rI7y5JFsk+mEsX2Z1mP9I6avqVsZGdBYiBEAaFsDeUEdl3ecKrHpv0/x2cobytDp56/MtcMJFbx5J6ZHWmPuwKnv/YLYP5vcn+zSkdrWpXPT3zrh2gHoCmAP2aE2cELuk9bD4x4QPgTTb7+xcDzxdeTsbPPsyzysASjYOr8JmRFqOg6xjfNd7vngyW8HYsm5avvPFZQUsSPxmjLoPUHVltOlJmDoCGAdPv3CFVhIoIrZ/SIPTwNyiFC2AXO4boju7xHcidav/TahD4oYC5Ct5B3smLy1FytFfjT0UGssKAYJzBD933aR/DfVSyYvRyOJ9BSEo77buljJFUh1ejUf9xO45eMiphveOIg4/ipYhWg2W1gANqIUtkmqmafPcmGPf5Q5YirkWNtLARl2JbpzgWTtEda64G0RZep19VGg3xIvNoX8bWKbugFGTFsvi6IQsLXIn/zyDX8XkE96eExKck/8v4Z26jeFdks1toVWpUjaVudbRII5rm8oqGdfFGC7POUhiRWyWjWAYSy7faL+f9Ke+UnVSMStgLFP+lL428NXxgA2RNO6KjsnuVlJBiHinwjdsGGxNNPR6vESQVBx6ch+EVs46obD1hSY3oEJSLZYYUD5AAdp1cTPkZ2BD4B0lM28hrd9r84aCxlaZHVpOLms4db6HXyqaYdcsRtScvjTv+CujiT1MUO1VElR77kUNEI2ZlobdkjgS0SBy4uRyqfVdc2qOUdta9D4rSjbZSZRVEIkmuRi23Zp2rW12/sujwJ21a2A8Th4MPEiWs0NlrRo9olotJ5y37OQCBngJnHWFCjW/qDZ8MaDBAotAd4d0SVhOyaiABa7FIjDDGij04vTiXA7WpBczWmk0VAo3xc3gzDt851623IATaXIv2eXzadb3mssOvP5uohxE4jiDvDau069nFct33/bEDQK8eDfhWfMiKQxT3tbzhHmyRuj92s34RzwFG2wSxGfZR2aAGAqF+tXWpnSRBAvEmQmrdW1JyqG7sLGy3zCfh/t6msDJ/SCzj5Lg7lD8iLgfpvAxf/vYhV/bo9FhBZj0//LjDIeqj4GteUXF5RLNarJZpo/G3t0vRZtrP/odH1vwQ1w1auvGvq1WsCwPiVqRU69h/uroQLf9ligrK1L/gd5OxGkiMeT4crzxJRb+1FH4A5TQE+0dtJhHaaCtHpwgM0cDabzHDWwPxo/Gyt5+aVTsDOZ8IJ3oEk1DWtC9PQkMfO1kJGVjp8kS7oUkXNlss21XSHis8GzN3xCcUZQ3bKNVCbz0vRqaBhulI56+VDDzXKoqdoib5Y9MWygEWgnZKHqOq1QusfeWOjQ2AFNhBDH5ZhPuiBxyKeAqwoUZX8wF0Cue3msXwyCKCFganu19Nwmaihi6sEYaRAHPM4nY6mHuk5IjIUlqjl46UG/R2azpzjzcgPTJNBQcxtY2b6HddxpKkdGFTpSm9jVFNU1OpwUqo2xNnucmGUtzjI6+5qxliUydtmh1SCD3eVs/dvqjGk3riiI82WJwEvHznz6QdEP9oHNn+lIKDuZYpTDpbWAqW19YJXhse0h/72pmL2vgYiRCacwBmPE4Iaxp4ww9dSSOmEqixHzJsWX8lACfxFWXg6UN6jTK0cPhWkEM5cSoxz9ShiSGgNT4wC41Wm+ZF3ELGieQy7Wiw32Z5bwny991GkU3dnHJbw6U+hgpRlvtH3lqfLfJ7kZ6S0xtyvnurbmX4J0jfNRnwjswPChkI5FMXHTF/7MGmDOEivCnxz6w6cXjQxR7Nh6xYThz9h0LFE1u7VdcsY0pLBgz1aT4Bsg+MyTApxkddlpZHSmYMMN+QswGVsLlUrrRgXjp6ZJ2QuAc9X9apFXs4TBN2IWpu7yP7pGoQsLujZjANLih1rQMLF+akdaG2US54roIRUua3Iz6eH9BjrtkF1I/45mUjJu8nH6g/x5+d9Yv+gjyxWVgAX2smrbV0ZVFFHaNHZyWzAWdddFohjdEq0UtDslqod0mq71HfqjR9tmdxC8wKFsPOcSNm0Mye1U/n81O8kcMIo1oD3tx12r4HR60CKZTS9c2Vq6yTIR0m8S9oXQ0cpjmMjbS6MnHUzCOui2ktsljRlz3Y3lCe3lWkIaDZWKNHG3Ru2doC79qDVVxtRzqtHQZ64/n1rT+AciURlnDWILcynGgVsqGcD7NCFlwHgQ6ty+7+bpPNRPMoFQE73zi/z9meM0q7PHPah0UadFL2oXoGUE+hKugqmR3QAd2C0dABFvpifBrmi4hPDn6vlqfqxcEMo8FCLSVY4iIZpiuhyV4blzQydbIZkTfVBw5Ckt3DIWT5Sik9V0jjmmaNBP9ZOr63FbS++hDzE8WVVEXYYeMcLV2n9eGH73bMEKx588rPhHiTNOBjhpwwXk742toHj1ku1vWbLMm35fMO7ziRW5QUTWc2Xl69uYAhr90WUr3bmC+lmqdVcleIOkyXnBEKmYRChWOpNOgm6EKT5GsAF1lzuY699yvC5ptEUaCtjh8KTGHu8k/it8rGusyBjuC9qVukw2o+4hvel1tyazysB1Va4hlHzGwqp6PrSSfbNkvxs1WB14u8M0/F0IOrYe91xdCcBsQBy4NCVuDP7RcVwhA1QNUftt+mBHb2MfFKK54VGvrpNWtoRIwCb+7jSnmU2c/mZDsk0MU9yY4sDpBrGob3HlWy8I59ZhF+g2xteKkDmg1DRcCc9L6rGv915OriZypOuotoD4rMYhJhlhktFzqpfchCdyE7JlS0H3ZW/fY2hW4h5YKZf0tPuAfZi7PIkbZEDNxRXWPfCzc5auPZwx5F/WoiRFXUw/YyyrKapwMj5ZDZpRSxWo1j11WFd0X68TRI+taoiaEknkzpoGcjrcjW+98OvyPHa2Y5M2CDWzogulb0vCYXS9zhek8LM3ZDGkZafs3DP5GmxRd2YZZ3asCX02mRrjhRvjxyBf48jVYAnirSClYfAPdCXn9NJtWfAKFRXU6QnFoTCgvbjeohqMtYXfOe+QVFeAb2/XeU0mZcgopTqLSNUg9KP38yzr2OGFglLbLfBVWkjUDVFjhc4yQx/amk724scEjv75lknTjgK842VvHAMQtK/BBtVVFBa/DvG5E0AfgBgahz11UiAo/BReqA8e/1yE98Ic3RAgryMIDQ1qfnzctHow/P8NBgX9h53ZbA8zvQeLxT2UK+6VgJ19OBVANEIdoKgEwPIbCtknJqlFhl8mGZOrubwIoiX3/Hv1Er3PTdN1qtIJzI1uMnPVRZtlSD9HpWBX3btuRJwKFjiwRJD3WN807HY+RvVEba86QG4uDt1Xx9oJrYNyXVYg+inuFlpXmltUSufNc7ihRKydUZQuACFJ5ePwkayiP+vyEQfWhmN54hRmoiF7Tyj6yn0m1SBlgvBrFevqRlg1sqcvGU+gh9ZfCvfcBGvr5LBzpuqspaOd0Fz7iFJFpcf+YDN+r5UBmx1frYlUiCnQb319h5+vY2Lt3dxRykM/PYUuJvVXuPv62UZK3FFGHxY0Kw5GeDgSENEjem4i7Pw7GxafcB9NHOy2bd8iusJ51Y30pSQVU7mObXdPc+gPv7sAYrbQXEFy5F3IWAxCCN1GDBZSBpcNCbfycwLNTLoEJelC2xX+t0TMiV0A8Zk+D7q1BFbJ2vcyWhcMi0KTh9N4/7ZD2e7kf0GBa8VmyNA5DNy5PU7Sd6fVLUtDvYyJ777BakaBDwDpjU/L3lctREKzaGuTgw5NBurCqzwMAM6Gdj+Ni8rBUODZE/GTrEGUAiJ/YFVZXWVMSo2z+wIgfTF6W4cC4JI+zZJal1X0lozdtu+sZN3mj5lqgjQCr2HSMHi+7nwWdDyd54cZrCTRH05uz/H8HZsN3rmmD6oCNO0gQgIUpJO2OkKLnLqx9BsAuX69u/mpaUEkG79vv+bgSBkdCXqbLsA3jimPVTgi1kJI1+CDm/qCzGoAY2XjhgAZcF9DIsC6ADUAzqsMDlyuIHLqEteEMd86scfN76YtHQISeFXLC44TC0lgYswZglSCCLP7JTpREJTgtKIOcSDnxa8gIAIK1GuXkvKYNKVw5rWy1vR1onTDvqLQ0Sf/rxYgAMhtNiovN51BxKNomVhvQlIlDr9VzjGX73DmA/jOxtwxfwYVL+itIxkXLpIEveBvh5iz+w9JO3TuzVp1S3mbTmEhRFN/aRg4EeGyzI/5Cz37qjiDaHrUXxjXEMzD1QvsHHtEQ2b2oox3+exK+opdHfLnq816Ay1aeZiRLTipY/V58068fshKfEVc/94h6DyYdtI87efWlAWGIg+EArL87XWgQHs4xYz0HOboAGIucQvJO8COweeZK0K8N2qv+pW2Kj1o7ZtaYgy1XVeFcJlkDYTeupj3fmoEih5T+tlLqTCWIAAAA= 1.0000000 0.1000000 0 true true abc condensación y fusión

]]> solidificación y fusión

]]> fusión y vaporización

]]> fusión y sublimación

]]> Diagrama de Fase Para el diagrama de fases del agua mostrado en la figura, indica cuáles de las siguientes afirmaciones son correctas:

]]> 1.0000000 0.1000000 0 false true abc A 100 ºC sólo puede haber agua líquida y gaseosa A 0 ºC puede haber agua en los tres estados a 0.003 atm no puede haber agua líquida La presión no tiene nada que ver con el estado del agua A 0.006 atm y 0.01 ºC están los tres estados a la vez Diagrama de fase carbón El diagrama de fases que se indica es el del carbono. Indica en qué forma se encontrará sí:

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Su temperatura es #t1 K y la presión es de #p1 Kbares

]]> Diamante Su temperatura es #t2 K y la presión es de #p2 Kbares

]]> Líquido Su temperatura es #t3 K y la presión es de #p3 Kbares

]]> grafito Su temperatura es #t4 K y la presión es de #p4 Kbares

]]> Líquido Su temperatura es #t5 K y la presión es de #p5 Kbares

]]> Carbono II Su temperatura es #t6 K y la presión es de #p6 Kbares

]]> Vapor <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2000</mn><mo>,</mo><mn>3000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2500</mn><mo>,</mo><mn>3000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>550</mn><mo>,</mo><mn>650</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3500</mn><mo>,</mo><mn>4000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3500</mn><mo>,</mo><mn>5000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>450</mn><mo>,</mo><mn>600</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>2000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>650</mn><mo>,</mo><mn>700</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t6</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4500</mn><mo>,</mo><mn>5000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p6</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Dilatación y estado Para que un cuerpo dilate al aumentar su temperatura

]]> 1.0000000 0.1000000 0 true true abc Debe ser sólido, los líquidos y gases no dilatan No puede ser líquido, los líquidos no dilatan Los cuerpos dilatan en todos los estados de la materia Su cambio de temperatura debe ser mayor que 20ºC Ninguna de las otras respuestas es correcta El paso de sólido a gas El paso de sólido a gas se llama

]]> 1.0000000 0.1000000 0 true true abc Sublimación Evaporación Fluidificación Concatenación Ninguno de los otros nombres Estados de la materia Los estados de la materia son (marca las opciones correctas):

]]> 1.0000000 0.1000000 0 false true abc Sólido Líquido Gaseoso Plasma Bose-Einstein Born-Openheiner Estelar Vacío Bose-plasmatico Indica el orden de los estados de la materia Indica el orden de los estados de la materia de menor a mayor temperatura 1.0000000 0.1000000 0 true Bose-Einstein 1 Sólido 2 Líquido 3 Gas 4 Plasma 5 La siguiente gráfica representa el enfriamiento de un gas. ¿Cuánto vale la temperatura de condensación? La siguiente gráfica representa el enfriamiento de un gas. ¿Cuánto vale la temperatura de condensación?

]]> 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1.0000000 0.1000000 0 true true abc -15 ºC

]]> 75ºc

]]> 100 ºC

]]> 0 ºC

]]> La siguiente gráfica representa el enfriamiento de un gas. ¿Cuánto vale la temperatura de condensación? La siguiente gráfica representa el enfriamiento de un gas. ¿Cuánto vale la temperatura de solidificación?

]]> 75ºc

]]> 100 ºC

]]> 0 ºC

]]> Mientras que un cuerpo está cambiando de estado Mientras que un cuerpo está cambiando de estado..

]]> 1.0000000 0.1000000 0 true true abc Su temperatura no cambia Su volumen no cambia su estructura interna no cambia Cambia todo No hay ningún tipo de cambio interno Nombra los cambios de estado Nombra los cambios de estado 1.0000000 0.1000000 0 true De sólido a gas Sublimación De sólido a líquido Fusión De líquido a sólido Solidificación De líquido a gas Vaporización De gas a líquido Condensación Enfriamiento Calcificación Crionización Temperatura y cambio de estado ¿Es posible hervir agua a 20ºC? ¿cómo lo harías?

]]> 1.0000000 0.5000000 0 true true abc Si. Disminuyendo la presión No. Es imposible Si. Aumentando la presión 1º BACHILLERATO/QUÍMICA/ESTADOS DE LA MATERIA/ESCALAS DE TEMPERATURA Convierte K en ºC ¿Qué temperatura absoluta correspondería a #tc ºC?

]]> 1.0000000 0.3333333 0 0 #tk <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>200</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>tk</mi></mrow></mfenced><mo>/</mo><mi>tk</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tk</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Convierte K en ºC ¿Qué temperatura absoluta correspondería a #tc ºC?

]]> 1.0000000 0.3333333 0 0 #tk <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>200</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>tk</mi></mrow></mfenced><mo>/</mo><mi>tk</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tk</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Convierte K en ºF ¿Qué temperatura Fahrenheit correspondería a #tk K?

]]> 1.0000000 0.3333333 0 0 #tf <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>tk</mi><mo>-</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tf</mi><mo>=</mo><mo>(</mo><mn>9</mn><mo>*</mo><mi>tc</mi><mo>/</mo><mn>5</mn><mo>)</mo><mo>+</mo><mn>32</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>tf</mi></mrow></mfenced><mo>/</mo><mi>tf</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tf</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Convierte K en ºF ¿Qué temperatura Fahrenheit correspondería a #tk K?

]]> 1.0000000 0.3333333 0 0 #tf <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>tk</mi><mo>-</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tf</mi><mo>=</mo><mo>(</mo><mn>9</mn><mo>*</mo><mi>tc</mi><mo>/</mo><mn>5</mn><mo>)</mo><mo>+</mo><mn>32</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>tf</mi></mrow></mfenced><mo>/</mo><mi>tf</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tf</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Convierte ºC en K ¿Qué temperatura centígrada correspondería a #tk K?

]]> 1.0000000 0.3333333 0 0 #tc <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>tk</mi><mo>-</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>tc</mi></mrow></mfenced><mo>/</mo><mi>tc</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tc</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Convierte ºC en K ¿Qué temperatura centígrada correspondería a #tk K?

]]> 1.0000000 0.3333333 0 0 #tc <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>tk</mi><mo>-</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>tc</mi></mrow></mfenced><mo>/</mo><mi>tc</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tc</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Convierte ºC en ºF ¿Qué temperatura Fahrenheit correspondería a #tc ºC?

]]> 1.0000000 0.3333333 0 0 #tf <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>200</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tf</mi><mo>=</mo><mo>(</mo><mn>9</mn><mo>*</mo><mi>tc</mi><mo>/</mo><mn>5</mn><mo>)</mo><mo>+</mo><mn>32</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>tf</mi></mrow></mfenced><mo>/</mo><mi>tf</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tf</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Convierte ºC en ºF ¿Qué temperatura Fahrenheit correspondería a #tc ºC?

]]> 1.0000000 0.3333333 0 0 #tf <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>200</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tf</mi><mo>=</mo><mo>(</mo><mn>9</mn><mo>*</mo><mi>tc</mi><mo>/</mo><mn>5</mn><mo>)</mo><mo>+</mo><mn>32</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>tf</mi></mrow></mfenced><mo>/</mo><mi>tf</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tf</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Convierte ºF en K ¿Qué temperatura absoluta correspondería a #tf ºF?

]]> 1.0000000 0.3333333 0 0 #tk <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tf</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>200</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mn>5</mn><mo>*</mo><mo>(</mo><mi>tf</mi><mo>-</mo><mn>32</mn><mo>)</mo><mo>/</mo><mn>9</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>tk</mi></mrow></mfenced><mo>/</mo><mi>tk</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tk</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Convierte ºF en K ¿Qué temperatura absoluta correspondería a #tf ºF?

]]> 1.0000000 0.3333333 0 0 #tk <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tf</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>200</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mn>5</mn><mo>*</mo><mo>(</mo><mi>tf</mi><mo>-</mo><mn>32</mn><mo>)</mo><mo>/</mo><mn>9</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>tk</mi></mrow></mfenced><mo>/</mo><mi>tk</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tk</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Convierte ºF en ºC ¿Qué temperatura centígrada correspondería a #tf ºF?

]]> 1.0000000 0.3333333 0 0 #tc <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tf</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>200</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mn>5</mn><mo>*</mo><mo>(</mo><mi>tf</mi><mo>-</mo><mn>32</mn><mo>)</mo><mo>/</mo><mn>9</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>tc</mi></mrow></mfenced><mo>/</mo><mi>tc</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tc</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Convierte ºF en ºC ¿Qué temperatura centígrada correspondería a #tf ºF?

]]> 1.0000000 0.3333333 0 0 #tc <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tf</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>100</mn><mo>,</mo><mn>200</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mn>5</mn><mo>*</mo><mo>(</mo><mi>tf</mi><mo>-</mo><mn>32</mn><mo>)</mo><mo>/</mo><mn>9</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mi>x</mi><mo>-</mo><mi>tc</mi></mrow></mfenced><mo>/</mo><mi>tc</mi><mo>)</mo><mo><</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tc</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El agua a 270 K El agua a 270 K y presión atmosférica

]]> 1.0000000 0.1000000 0 true true abc Estaría estupenda para tomar un baño caliente Sería demasiado caliente para bañarse Sería demasiado fría para bañarse El agua a esa temperatura es hielo normalmente Sería un baño de vapor hirviendo, a esa temperatura el agua es gas El agua a 35 F sería El agua a 35 F de temperatura sería

]]> 1.0000000 0.1000000 0 true true abc Estupenda para tomar un baño caliente Muy fría para bañarse Demasiado caliente para tomar un baño El agua a esa temperatura es hielo normalmente El agua a esa temperatura es un gas normalmente 1º BACHILLERATO/QUÍMICA/ESTADOS DE LA MATERIA/MOLES Y GRAMOS ¿Cuál es la masa en gramos de un átomo de ¿Cuál es la masa en gramos de un átomo de #comp?

]]> 1.0000000 0.3333333 0 0 #masa]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>come</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>Ca</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>H</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>O</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>K</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masae</mi><mo>=</mo><mo>(</mo><mn>40</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>16</mn><mo>,</mo><mn>39</mn><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>avog</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>*</mo><msup><mn>10</mn><mn>23</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>come</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><msub><mi>masae</mi><mi>ind</mi></msub><mo>/</mo><mi>avog</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ¿Cuál es la masa en gramos de un átomo de ¿Cuál es la masa en gramos de un átomo de #comp?

]]> 1.0000000 0.3333333 0 0 #masa]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>come</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>Cl</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>S</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>N</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>Na</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masae</mi><mo>=</mo><mo>(</mo><mn>35</mn><mo>.</mo><mn>5</mn><mo>,</mo><mn>32</mn><mo>,</mo><mn>14</mn><mo>,</mo><mn>23</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>avog</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>*</mo><msup><mn>10</mn><mn>23</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>come</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><msub><mi>masae</mi><mi>ind</mi></msub><mo>/</mo><mi>avog</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ¿Cuál es la masa en gramos de un mol de ¿Cuál es la masa en gramos de un mol de #comp?

]]> 1.0000000 0.3333333 0 0 #masa]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>come</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>HCl</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>H2SO4</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>HNO3</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>NaCl</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masae</mi><mo>=</mo><mo>(</mo><mn>36</mn><mo>.</mo><mn>5</mn><mo>,</mo><mn>98</mn><mo>,</mo><mn>63</mn><mo>,</mo><mn>58</mn><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>come</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><msub><mi>masae</mi><mi>ind</mi></msub></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ¿Cuál es la masa en gramos de una molécula de ¿Cuál es la masa en gramos de una molécula de #comp?

]]> 1.0000000 0.3333333 0 0 #masa]]> Recuerda que el oxígeno en su estado natural es O₂

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>come</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>Cloro</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>Oxígeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>Nitrógeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>HCl</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masae</mi><mo>=</mo><mo>(</mo><mn>71</mn><mo>,</mo><mn>32</mn><mo>,</mo><mn>28</mn><mo>,</mo><mn>36</mn><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>avog</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>*</mo><msup><mn>10</mn><mn>23</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>come</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><msub><mi>masae</mi><mi>ind</mi></msub><mo>/</mo><mi>avog</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ¿Cuál es la masa en gramos de una molécula de ¿Cuál es la masa en gramos de una molécula de #comp?

]]> 1.0000000 0.3333333 0 0 #masa]]> Recuerda que, en su estado natural, los elementos forman moléculas diatómicas

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>come</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>Cloro</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>Oxígeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>Nitrógeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>HCl</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masae</mi><mo>=</mo><mo>(</mo><mn>71</mn><mo>,</mo><mn>32</mn><mo>,</mo><mn>28</mn><mo>,</mo><mn>36</mn><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>avog</mi><mo>=</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>*</mo><msup><mn>10</mn><mn>23</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>come</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><msub><mi>masae</mi><mi>ind</mi></msub><mo>/</mo><mi>avog</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ¿Cuántas moléculas hay en ¿Cuántas moléculas hay en #m gramos de #comp?

]]> 1.0000000 0.3333333 0 0 #molec]]> Recuerda que en su estado natural forma moléculas diatómicas

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>come</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>hidrógeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>cloro</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>oxígeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>nitrógeno</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masae</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>71</mn><mo>,</mo><mn>32</mn><mo>,</mo><mn>28</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>come</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><msub><mi>masae</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>moles</mi><mo>=</mo><mi>m</mi><mo>/</mo><mi>masa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molec</mi><mo>=</mo><mi>moles</mi><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>*</mo><msup><mn>10</mn><mn>23</mn></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>mol</mi><mi mathvariant="normal">e</mi><mi>c</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ¿Cuántos átomos de hay en gramos de ¿Cuántos átomos de #el hay en #m gramos de #comp?

]]> 1.0000000 0.3333333 0 0 #atom]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ele</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>hidrógeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>oxígeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>azufre</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nume</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>el</mi><mo>=</mo><msub><mi>ele</mi><mi>ind1</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mul</mi><mo>=</mo><msub><mi>nume</mi><mi>ind1</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><mo>"</mo><msub><mi>H</mi><mn>2</mn></msub><msub><mi>SO</mi><mn>4</mn></msub><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>moles</mi><mo>=</mo><mi>m</mi><mo>/</mo><mn>98</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>atom</mi><mo>=</mo><mi>mul</mi><mo>*</mo><mi>moles</mi><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>*</mo><msup><mn>10</mn><mn>23</mn></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>t</mi><mi>o</mi><mi mathvariant="normal">m</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ¿Cuántos átomos de hay en gramos de ¿Cuántos átomos de #el hay en #m gramos de #comp?

]]> 1.0000000 0.3333333 0 0 #atom]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ele</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>hidrógeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>oxígeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>azufre</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nume</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>el</mi><mo>=</mo><msub><mi>ele</mi><mi>ind1</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mul</mi><mo>=</mo><msub><mi>nume</mi><mi>ind1</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><mo>"</mo><msub><mi>H</mi><mn>2</mn></msub><msub><mi>S</mi><mn>2</mn></msub><msub><mi>O</mi><mn>3</mn></msub><mo>"</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>moles</mi><mo>=</mo><mi>m</mi><mo>/</mo><mn>114</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>atom</mi><mo>=</mo><mi>mul</mi><mo>*</mo><mi>moles</mi><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>*</mo><msup><mn>10</mn><mn>23</mn></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>t</mi><mi>o</mi><mi mathvariant="normal">m</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ¿Cuántos átomos hay en ¿Cuántos átomoss hay en #m gramos de #comp?

]]> 1.0000000 0.3333333 0 0 #atom]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>come</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>sodio</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>carbono</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>helio</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>cobre</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masae</mi><mo>=</mo><mo>(</mo><mn>23</mn><mo>,</mo><mn>12</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>63</mn><mo>.</mo><mn>54</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>come</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><msub><mi>masae</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>moles</mi><mo>=</mo><mi>m</mi><mo>/</mo><mi>masa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>atom</mi><mo>=</mo><mi>moles</mi><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>*</mo><msup><mn>10</mn><mn>23</mn></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>t</mi><mi>o</mi><mi mathvariant="normal">m</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ¿Cuántos átomos hay en ¿Cuántos átomoss hay en #m gramos de #comp?

]]> 1.0000000 0.3333333 0 0 #atom]]> Recuerda que en su estado natural forma moléculas diatómícas

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>come</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>hidrógeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>cloro</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>oxígeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>nitrógeno</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masae</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>71</mn><mo>,</mo><mn>32</mn><mo>,</mo><mn>28</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>come</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><msub><mi>masae</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>moles</mi><mo>=</mo><mi>m</mi><mo>/</mo><mi>masa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>atom</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>moles</mi><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>*</mo><msup><mn>10</mn><mn>23</mn></msup></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</mi><mi>t</mi><mi>o</mi><mi mathvariant="normal">m</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ¿Cuántos moles hay en ¿Cuántos moles hay en #m gramos de #comp?

]]> 1.0000000 0.3333333 0 0 #moles]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>come</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>HCl</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>H2SO4</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>HNO3</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>NaCl</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masae</mi><mo>=</mo><mo>(</mo><mn>36</mn><mo>.</mo><mn>5</mn><mo>,</mo><mn>98</mn><mo>,</mo><mn>63</mn><mo>,</mo><mn>58</mn><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>come</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><msub><mi>masae</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>moles</mi><mo>=</mo><mi>m</mi><mo>/</mo><mi>masa</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>mol</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> ¿Cuántos moles hay en ¿Cuántos moles hay en #m gramos de #comp?

]]> 1.0000000 0.3333333 0 0 #moles]]> Recuerda que en su estado natural forma moléculas diatómicas

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>come</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>hidrógeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>cloro</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>oxígeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>nitrógeno</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masae</mi><mo>=</mo><mo>(</mo><mn>2</mn><mo>,</mo><mn>71</mn><mo>,</mo><mn>32</mn><mo>,</mo><mn>28</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>come</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><msub><mi>masae</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>moles</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mi>m</mi><mo>/</mo><mi>masa</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>mol</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Composición de un elemento #m gramos de oligisto (Fe₂O₃) tienen un #por % de impurezas. Calcula la masa de hierro (g) presente en la misma.

Masas atómicas : Fe = 55.8; O=16

]]> 1.0000000 0.3333333 0 0 #mhi]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>80</mn><mo>,</mo><mn>250</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>por</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>25</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mhi</mi><mo>=</mo><mi>m</mi><mo>*</mo><mo>(</mo><mn>100</mn><mo>-</mo><mi>por</mi><mo>)</mo><mo>*</mo><mn>111</mn><mo>.</mo><mn>6</mn><mo>/</mo><mo>(</mo><mn>100</mn><mo>*</mo><mn>159</mn><mo>.</mo><mn>6</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>m</mi><mi>h</mi><mi mathvariant="normal">i</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Empareja cantidades equivalentes Empareja cantidades equivalentes

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #m1 g de O₂

]]> #mol1 moles de oxígeno #ato2 ·10²³ átomos de O

]]> #mol2 moles de oxígeno #molec3 ·10²³moléculas de O₂

]]> #mol3 moles de oxígeno #m4 g de O₂

]]> #mol4 moles de oxígeno #ato5 ·10²³ átomos de O

]]> #mol5 moles de oxígeno #molec6 ·10²³moléculas de O₂

]]> #mol6 moles de oxígeno #mol7 moles de oxígeno #mol8 moles de oxígeno <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ato2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molec3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ato5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molec6</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol1</mi><mo>=</mo><mi>m1</mi><mo>/</mo><mn>32</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol2</mi><mo>=</mo><mi>ato2</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol3</mi><mo>=</mo><mi>molec3</mi><mo>/</mo><mn>6</mn><mo>.</mo><mn>022</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol4</mi><mo>=</mo><mi>m4</mi><mo>/</mo><mn>32</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol5</mi><mo>=</mo><mi>ato5</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol6</mi><mo>=</mo><mi>molec6</mi><mo>/</mo><mn>6</mn><mo>.</mo><mn>022</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol7</mi><mo>=</mo><mi>mol2</mi><mo>*</mo><mn>2</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol8</mi><mo>=</mo><mi>mol5</mi><mo>*</mo><mn>2</mn></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Empareja cantidades equivalentes Empareja cantidades equivalentes

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #m1 g de N₂

]]> #mol1 moles de nitrógeno #ato2 ·10²³ átomos de N

]]> #mol2 moles de nitrógeno #molec3 ·10²³moléculas de N₂

]]> #mol3 moles de Nitrógeno #m4 g de N₂

]]> #mol4 moles de nitrógeno #ato5 ·10²³ átomos de N

]]> #mol5 moles de nitrógeno #molec6 ·10²³moléculas de N₂

]]> #mol6 moles de Nitrógeno #mol7 moles de nitrógeno #mol8 moles de nitrógeno <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ato2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molec3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ato5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molec6</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol1</mi><mo>=</mo><mi>m1</mi><mo>/</mo><mn>28</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol2</mi><mo>=</mo><mi>ato2</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol3</mi><mo>=</mo><mi>molec3</mi><mo>/</mo><mn>6</mn><mo>.</mo><mn>022</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol4</mi><mo>=</mo><mi>m4</mi><mo>/</mo><mn>28</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol5</mi><mo>=</mo><mi>ato5</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol6</mi><mo>=</mo><mi>molec6</mi><mo>/</mo><mn>6</mn><mo>.</mo><mn>022</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol7</mi><mo>=</mo><mi>mol2</mi><mo>*</mo><mn>2</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol8</mi><mo>=</mo><mi>mol5</mi><mo>*</mo><mn>2</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Empareja cantidades equivalentes (gramos) Empareja cantidades equivalentes

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #mol1 moles de Cl₂

]]> #masa1 gramos de cloro #ato2 ·10²³ átomos de Cl

]]> #masa2 gramos de cloro #molec3 ·10²³moléculas de Cl₂

]]> #masa3 gramos de cloro #mol4 moles de Cl₂

]]> #masa4 gramos de cloro #ato5 ·10²³ átomos de Cl

]]> #masa5 gramos de cloro #molec6 ·10²³moléculas de Cl₂

]]> #masa6 gramos de cloro #masa7 gramos de cloro #masa8 gramos de cloro <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ato2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molec3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ato5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molec6</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa1</mi><mo>=</mo><mi>mol1</mi><mo>*</mo><mn>71</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa2</mi><mo>=</mo><mo>(</mo><mi>ato2</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo><mo>)</mo><mo>*</mo><mn>71</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa3</mi><mo>=</mo><mo>(</mo><mi>molec3</mi><mo>/</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo><mo>*</mo><mn>71</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa4</mi><mo>=</mo><mi>mol4</mi><mo>*</mo><mn>71</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa5</mi><mo>=</mo><mo>(</mo><mi>ato5</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo><mo>)</mo><mo>*</mo><mn>71</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa6</mi><mo>=</mo><mo>(</mo><mi>molec6</mi><mo>/</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo><mo>*</mo><mn>71</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa7</mi><mo>=</mo><mi>masa4</mi><mo>*</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa8</mi><mo>=</mo><mi>masa5</mi><mo>*</mo><mn>2</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"></data></localData></question> Empareja cantidades equivalentes (gramos) Empareja cantidades equivalentes

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> #mol1 moles de H₂

]]> #masa1 gramos de hidrógeno #ato2 ·10²³ átomos de H

]]> #masa2 gramos de hidrógeno #molec3 ·10²³moléculas de H₂

]]> #masa3 gramos de hidrógeno #mol4 moles de H₂

]]> #masa4 gramos de hidrógeno #ato5 ·10²³ átomos de H

]]> #masa5 gramos de hidrógeno #molec6 ·10²³moléculas de H₂

]]> #masa6 gramos de hidrógeno #masa7 gramos de hidrógeno #masa8 gramos de hidrógeno <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ato2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molec3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ato5</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molec6</mi><mo>=</mo><mi>aleatorio72</mi><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa1</mi><mo>=</mo><mi>mol1</mi><mo>*</mo><mn>2</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa2</mi><mo>=</mo><mo>(</mo><mi>ato2</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo><mo>)</mo><mo>*</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa3</mi><mo>=</mo><mo>(</mo><mi>molec3</mi><mo>/</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo><mo>*</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa4</mi><mo>=</mo><mi>mol4</mi><mo>*</mo><mn>2</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa5</mi><mo>=</mo><mo>(</mo><mi>ato5</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo><mo>)</mo><mo>*</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa6</mi><mo>=</mo><mo>(</mo><mi>molec6</mi><mo>/</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo><mo>*</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa7</mi><mo>=</mo><mi>masa2</mi><mo>*</mo><mn>2</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa8</mi><mo>=</mo><mi>masa5</mi><mo>*</mo><mn>2</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">2</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> En un recipiente átomos moleculas En #ato • 10²³ atomos de #comp hay más cantidad que en #molec • 10²³ moléculas del mismo compuesto

]]> Recuerda que, en su estado natural, forma moléculas diatómicas

]]> 1.0000000 1.0000000 0 verdadero falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>compe</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>Hidrógeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>Oxígeno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>Cloro</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>Nitrógeno</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>compe</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ato</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molec</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>18</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molecu</mi><mo>=</mo><mi>ato</mi><mo>/</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resul</mi><mo>=</mo><mo>(</mo><mo>(</mo><mi>molecu</mi><mo>></mo><mi>molec</mi><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="casSession"/></localData></question> En un recipiente gramos moleculas En #masa gramos de #comp hay más cantidad que en #molec • 10²³ moléculas del mismo compuesto

]]> 1.0000000 1.0000000 0 verdadero falso <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>compe</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>HNO3</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>HCl</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>H2O2</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>H2O</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ind</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mole</mi><mo>=</mo><mo>(</mo><mn>63</mn><mo>,</mo><mn>36</mn><mo>.</mo><mn>5</mn><mo>,</mo><mn>34</mn><mo>,</mo><mn>18</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol</mi><mo>=</mo><msub><mi>mole</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>compe</mi><mi>ind</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molec</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>18</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molec</mi><mo>=</mo><mi>molec</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masac</mi><mo>=</mo><mo>(</mo><mi>molec</mi><mo>/</mo><mn>6</mn><mo>.</mo><mn>022</mn><mo>)</mo><mo>*</mo><mi>mol</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resul</mi><mo>=</mo><mo>(</mo><mo>(</mo><mi>masa</mi><mo>></mo><mo>=</mo><mi>masac</mi><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 1º BACHILLERATO/QUÍMICA/REACCIONES QUÍMICAS cicn para el hidrógeno Hemos de llenar de hidrógeno un recipiente ce #vo litros a una temperatura de #tc ºC y con una presión de #pre mm de Hg. Calcula cuántos gramos de cinc tendremos que hacer reaccionar con HCl para obtenerlo

HCl + Zn --> ZnCl₂ + H₂

Datos : masas atómicas Zn = 65.4; 1 atm = 760 mm de Hg

]]> 1.0000000 0.3333333 0 0 #mc]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>740</mn><mo>,</mo><mn>800</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pa</mi><mo>=</mo><mi>pre</mi><mo>/</mo><mn>760</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>nm</mi><mo>=</mo><mi>pa</mi><mo>*</mo><mi>vo</mi><mo>/</mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>082</mn><mo>*</mo><mi>tk</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mc</mi><mo>=</mo><mi>nm</mi><mo>*</mo><mn>65</mn><mo>.</mo><mn>4</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>c</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Composición aleación Se quiere conocer la composición de una mezcla se cinc y aluminio. Para ello se trata una mezcla de #mmez g de muestra con un exceso de ácido sulfúrico para dar las sales correspondientes e hidrógeno. Tras la disolución se obtienen #vol cm³ de H₂ medidos a #tc ºC y #pres atm. Calcula la composición de la muestra.

Al +H₂SO₄ --> Al ₂(SO ₄)₃ + H₂

Zn + H₂SO₄ --> ZnSO₄ + H₂

Datos (A) : Al = 27; Zn = 65.3

]]> 1.0000000 0.3333333 0 0 % Zn =#pci% Al =#pal]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mmez</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>6</mn><mo>,</mo><mn>1</mn><mo>.</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pci</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pres</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>250</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pres</mi><mo>=</mo><mo>(</mo><mi>pres</mi><mo>/</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mci</mi><mo> </mo><mo>=</mo><mo> </mo><mi>mmez</mi><mo>*</mo><mi>pci</mi><mo>/</mo><mn>100</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mal</mi><mo>=</mo><mi>mmez</mi><mo>-</mo><mi>mci</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molh</mi><mo>=</mo><mo>(</mo><mi>mci</mi><mo>/</mo><mn>65</mn><mo>.</mo><mn>3</mn><mo>)</mo><mo>+</mo><mo>(</mo><mi>mal</mi><mo>*</mo><mn>3</mn><mo>/</mo><mn>54</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vol</mi><mo>=</mo><mn>1000</mn><mo>*</mo><mi>molh</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>082</mn><mo>*</mo><mi>tk</mi><mo>/</mo><mi>pres</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pal</mi><mo>=</mo><mo> </mo><mn>100</mn><mo>-</mo><mi>pci</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>%</mo><mo> </mo><mi>Z</mi><mi>n</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi>c</mi><mi mathvariant="normal">i</mi><mspace linebreak="newline"/><mo>%</mo><mo> </mo><mi>A</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi>a</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> reacción con disolución Se tratan #mal g. de Al con #vd cm³. de disolución acuosa de ácido sulfúrico #ms M, para dar sulfato de aluminio e hidrógeno gaseoso. Determina: a) El volumen, en litros, de hidrógeno que se obtendrá en la reacción, medido a #tc ºC y #pre mm de Hg. b) Los gramos de sal obtenidos.

Al + H₂SO₄ -> Al₂(SO₄)₃ + H₂

Datos (A): Al=27; O=16; S=32

]]> 1.0000000 0.3333333 0 0 volumen = #vhMasa sal= #msal]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mal</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vd</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ms</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ms</mi><mo>=</mo><mi>ms</mi><mo>/</mo><mn>10</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>70</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>740</mn><mo>,</mo><mn>780</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msa1</mi><mo>=</mo><mi>mal</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mn>342</mn><mo>/</mo><mn>54</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msa2</mi><mo>=</mo><mo>(</mo><mi>ms</mi><mo>*</mo><mi>vd</mi><mo>/</mo><mn>1000</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>*</mo><mn>342</mn><mo>/</mo><mn>3</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>msa1</mi><mo>></mo><mi>msa2</mi></mrow><mtable><mtr><mtd><mi>msal</mi><mo>=</mo><mi>msa2</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>vh</mi><mo>=</mo><mo>(</mo><mi>ms</mi><mo>*</mo><mi>vd</mi><mo>/</mo><mn>1000</mn><mo>)</mo><mo>*</mo><mn>0</mn><mo>.</mo><mn>082</mn><mo>*</mo><mi>tk</mi><mo>*</mo><mn>760</mn><mo>/</mo><mi>pre</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>msal</mi><mo>=</mo><mi>msa1</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>vh</mi><mo>=</mo><mo>(</mo><mi>mal</mi><mo>*</mo><mn>3</mn><mo>/</mo><mn>54</mn><mo>)</mo><mo>*</mo><mn>0</mn><mo>.</mo><mn>082</mn><mo>*</mo><mi>tk</mi><mo>*</mo><mn>760</mn><mo>/</mo><mi>pre</mi></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi>o</mi><mi mathvariant="normal">l</mi><mi>u</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mi mathvariant="normal">h</mi><mspace linebreak="newline"/><mi>M</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi><mo> </mo><mi mathvariant="normal">s</mi><mi>a</mi><mi mathvariant="normal">l</mi><mo>=</mo><mo> </mo><mo>#</mo><mi>ms</mi><mi>a</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.03))</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> reaccion con disoluciones Una forma de obtener HCl es calentando NaCl con ácido sulfúrico concentrado dando también sulfato de sodio. ¿Cuántos gramos ácido sulfúrico del #pors % en masa se necesita para obtener #mhcl Kg de HCl con el #porc % en masa?

NaCl + H₂SO₄ --> Na₂SO₄ + HCl

]]> 1.0000000 0.3333333 0 0 #mas]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pors</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>porc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mhcl</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mcp</mi><mo>=</mo><mi>mhcl</mi><mo>*</mo><mi>porc</mi><mo>*</mo><mn>1000</mn><mo>/</mo><mn>100</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msp</mi><mo>=</mo><mi>mcp</mi><mo>*</mo><mn>98</mn><mo>/</mo><mn>73</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mas</mi><mo>=</mo><mi>msp</mi><mo>*</mo><mn>100</mn><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>/</mo><mi>pors</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>a</mi><mi mathvariant="normal">s</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> reaccion con gas Calcula el volumen de hidrógeno, en litros, obtenido a #tc ºC y #pres mm de Hg si se hacen reaccionar #mal g de Al con HNO₃ en exceso.

Al + HNO₃ -> Al(NO₃)₃ + H₂

Datos A: Al = 27; H = 1; N = 14; O = 16

]]> 1.0000000 0.3333333 0 0 #volu]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pres</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>700</mn><mo>,</mo><mn>800</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pat</mi><mo>=</mo><mi>pres</mi><mo>/</mo><mn>760</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mal</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molhid</mi><mo>=</mo><mi>mal</mi><mo>*</mo><mn>3</mn><mo>/</mo><mn>54</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>volu</mi><mo>=</mo><mi>molhid</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>082</mn><mo>*</mo><mi>tk</mi><mo>/</mo><mi>pat</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>v</mi><mi>o</mi><mi mathvariant="normal">l</mi><mi>u</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> reacción gases La hidracina (N₂H₄) es un combustible usado en la propulsión de vehículos espaciales. Se combina con oxígeno para obtener nitrógeno y agua. Calcula el volumen, en litros, de nitrógeno generado en condiciones normales y la masa, en gramos, de agua formada si quemamos #mh gramos de hidracina.

N₂H₄ + O₂ -> N₂ + H₂O

]]> 1.0000000 0.3333333 0 0 Volumen de nitrógeno = #vnMasa de agua =#mag]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mh</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>300</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vn</mi><mo>=</mo><mn>22</mn><mo>.</mo><mn>4</mn><mo>*</mo><mi>mh</mi><mo>/</mo><mn>32</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mag</mi><mo>=</mo><mi>mh</mi><mo>*</mo><mn>36</mn><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>/</mo><mn>32</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>n</mi><mi mathvariant="normal">i</mi><mi>t</mi><mi>r</mi><mi>ó</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mi>n</mi><mspace linebreak="newline"/><mi>M</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>a</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>a</mi><mi mathvariant="normal">g</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> reaccion simple Zn y sulf El Zn se disuelve en ácido sulfúrico dando sulfato de cinc e hidrógeno gas. Suponiendo que el rendimiento de la reacción es del 100 %, calcule los gramos de Zn que podrían reaccionar con #volu cm³ de ácido sulfúrico #molar M

Datos (A) : H = 1; O = 16; S = 32; Zn = 65.4

]]> 1.0000000 0.3333333 0 0 #maci]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>volu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molar</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>2</mn><mo>,</mo><mn>0</mn><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molci</mi><mo>=</mo><mi>volu</mi><mo>*</mo><mi>molar</mi><mo>/</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>maci</mi><mo>=</mo><mi>molci</mi><mo>*</mo><mn>65</mn><mo>.</mo><mn>4</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/QUÍMICA/REACCIONES QUÍMICAS/RENDIMIENTO Y RIQUEZA HCl y Al con rendimiento Se hace reaccionar ácido clorhídrico con una muestra de #mal g de aluminio. ¿Cuántos litros de hidrógeno, medidos en condiciones normales, que se obtiene si la reacción tiene un rendimiento del #por %?

Al + HCl --> AlCl₃ + H₂

Datos (A): Al = 27; Cl= 35.5; H=1

]]> 1.0000000 0.3333333 0 0 #volh]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mal</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>por</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>70</mn><mo>,</mo><mn>95</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>volh</mi><mo>=</mo><mi>mal</mi><mo>*</mo><mn>3</mn><mo>*</mo><mn>22</mn><mo>.</mo><mn>4</mn><mo>*</mo><mi>por</mi><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mn>27</mn><mo>*</mo><mn>100</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>v</mi><mi>o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">h</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="relative_tolerance">true</option><option name="tolerance">10^(--log(0.02))</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Reacción con riqueza El amoniaco se puede obtener calentando cloruro amónico con hidróxido de sodio. Calcula cuántos gramos de una muestra de cloruro de amonio que tiene un #riq % de riqueza, se necesitan para obtener #volu litros de amoniaco medidos a #tc ºC y #pres atm.

NH₄Cl + NaOH -> NH₃ + H₂O + NaCl

Datos (A): Cl = 35.5; H = 1; N = 14; O = 16

]]> 1.0000000 0.3333333 0 0 #masclo]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>riq</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>95</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>volu</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mo> </mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pres</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molam</mi><mo>=</mo><mi>pres</mi><mo>*</mo><mi>volu</mi><mo>/</mo><mo>(</mo><mn>0</mn><mo>.</mo><mn>082</mn><mo>*</mo><mi>tk</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masclo</mi><mo>=</mo><mn>53</mn><mo>.</mo><mn>5</mn><mo>*</mo><mi>molam</mi><mo>*</mo><mn>100</mn><mo>/</mo><mi>riq</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>cl</mi><mi>o</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> reaccion gases y riqueza ¿Cuántos litros de oxígeno a #tc ºC y #pres mm de Hg se obtienen de la descomposición de #maclo g de clorato de potasio del #riq % de pureza? ¿Cuántos gramos de cloruro potásico se obtendrá?

KClO₃ --> O₂ + KCl

Masas atómicas: Cl = 35.5; K = 39.1; O = 16

]]> 1.0000000 0.3333333 0 0 Volumen de oxígeno = #voloxmasa cloruro = #mafi]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pres</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>700</mn><mo>,</mo><mn>800</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pat</mi><mo>=</mo><mi>pres</mi><mo>/</mo><mn>760</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>maclo</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>riq</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>95</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molclo</mi><mo>=</mo><mi>maclo</mi><mo>*</mo><mi>riq</mi><mo>/</mo><mo>(</mo><mn>122</mn><mo>.</mo><mn>6</mn><mo>*</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molox</mi><mo>=</mo><mi>molclo</mi><mo>*</mo><mn>3</mn><mo>/</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>volox</mi><mo>=</mo><mi>molox</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>082</mn><mo>*</mo><mi>tk</mi><mo>/</mo><mi>pat</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mafi</mi><mo>=</mo><mi>molclo</mi><mo>*</mo><mn>74</mn><mo>.</mo><mn>6</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">V</mi><mi>o</mi><mi mathvariant="normal">l</mi><mi>u</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>o</mi><mi>x</mi><mi>í</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>v</mi><mi>o</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>x</mi><mspace linebreak="newline"/><mi mathvariant="normal">m</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi><mo> </mo><mi>cl</mi><mi>o</mi><mi>r</mi><mi>u</mi><mi>r</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>a</mi><mi>f</mi><mi mathvariant="normal">i</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Rendimiento El hidruro de calcio reacciona energéticamente con agua desprendiendo hidrógeno según la reacción:

CaH₂ + H₂O -> Ca(OH)₂ + H₂

Responde a las siguientes cuestiones:

A partir de #mh gramos de hidruro de calcio se han obtenido #vh litros de hidrógeno a #pres atm y #tk K. Determina el rendimiento de la reacción.
¿Cuántos gramos de agua serán necesarios en el proceso anterior?

Datos (A): Ca =40; H=1; O=16

]]> 1.0000000 0.3333333 0 0 Rendimiento=#rendMasa de agua= #magu]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mh</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>12</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pres</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>400</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>95</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molh</mi><mo>=</mo><mi>r</mi><mo>*</mo><mi>mh</mi><mo>*</mo><mn>2</mn><mo>/</mo><mn>4200</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vh</mi><mo>=</mo><mi>molh</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>082</mn><mo>*</mo><mi>tk</mi><mo>/</mo><mi>pres</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>magu</mi><mo>=</mo><mi>mh</mi><mo>*</mo><mn>36</mn><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn><mo>/</mo><mn>42</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rend</mi><mo>=</mo><mi>r</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>o</mi><mo>=</mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>d</mi><mspace linebreak="newline"/><mi>M</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>a</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi>a</mi><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>a</mi><mi mathvariant="normal">g</mi><mi>u</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Rendimiento En un soplete oxiacetilénico se quema acetileno (etino) en presencia de oxígeno. Se queman #mac gramos de acetileno del #rac % de pureza. Se pide: a) Gramos de oxígeno necesarios para la combustión, si el rendimiento de la misma es del #rre %. b) Número de moles de oxígeno necesario.

C₂H₂ + O₂ --> CO₂ + H₂O

]]> 1.0000000 0.3333333 0 0 Masa de oxígeno = #moxMoles de oxígeno =#molox]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mac</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rac</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>70</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mox</mi><mo>=</mo><mi>mac</mi><mo>*</mo><mi>rac</mi><mo>*</mo><mn>32</mn><mo>*</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>/</mo><mo>(</mo><mn>26</mn><mo>*</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molox</mi><mo>=</mo><mi>mox</mi><mo>/</mo><mn>32</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>o</mi><mi>x</mi><mi>í</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mi>x</mi><mspace linebreak="newline"/><mi>M</mi><mi>o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>o</mi><mi>x</mi><mi>í</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>o</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>mol</mi><mi>o</mi><mi>x</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Rendimiento En un soplete oxiacetilénico se quema acetileno (etino) en presencia de oxígeno. Se queman #mac gramos de acetileno del #rac % de pureza. Se pide: a) Gramos de oxígeno necesarios para la combustión, si el rendimiento de la misma es del #rre %. b) Número de moles de oxígeno necesario.

C₂H₂ + O₂ --> CO₂ + H₂O

]]> 1.0000000 0.3333333 0 0 Masa de oxígeno = #moxMoles de oxígeno =#molox]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mac</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rac</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>70</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mox</mi><mo>=</mo><mi>mac</mi><mo>*</mo><mi>rac</mi><mo>*</mo><mn>32</mn><mo>*</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>/</mo><mo>(</mo><mn>26</mn><mo>*</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molox</mi><mo>=</mo><mi>mox</mi><mo>/</mo><mn>32</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>o</mi><mi>x</mi><mi>í</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi>o</mi><mi>x</mi><mspace linebreak="newline"/><mi>M</mi><mi>o</mi><mi mathvariant="normal">l</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">s</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>o</mi><mi>x</mi><mi>í</mi><mi mathvariant="normal">g</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>o</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>mol</mi><mi>o</mi><mi>x</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Rendimiento En la oxidación de #ghi g de Fe con exceso de oxígeno se obtienen #mob gramos de óxido de hierro(III). Determina: a) El rendimiento de la reacción. b) Los gramos de Fe que no se han oxidado.

Fe + O₂ --> Fe₂O₃

Datos (A) :Fe = 55.8; O= 16

]]> 1.0000000 0.3333333 0 0 Rendimiento = #rendMasa de hierro no oxidada = #mhn]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ghi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>moxi</mi><mo>=</mo><mi>ghi</mi><mo>*</mo><mn>2</mn><mo>*</mo><mn>159</mn><mo>.</mo><mn>6</mn><mo>/</mo><mo>(</mo><mn>4</mn><mo>*</mo><mn>55</mn><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rend</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mob</mi><mo>=</mo><mi>moxi</mi><mo>*</mo><mi>rend</mi><mo>/</mo><mn>100</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mhn</mi><mo>=</mo><mi>ghi</mi><mo>-</mo><mo>(</mo><mi>mob</mi><mo>*</mo><mn>4</mn><mo>*</mo><mn>55</mn><mo>.</mo><mn>8</mn><mo>/</mo><mo>(</mo><mn>2</mn><mo>*</mo><mn>159</mn><mo>.</mo><mn>6</mn><mo>)</mo><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>d</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>d</mi><mspace linebreak="newline"/><mi>M</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi><mo> </mo><mi>d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi mathvariant="normal">h</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>r</mi><mi>o</mi><mo> </mo><mi>n</mi><mi>o</mi><mo> </mo><mi>o</mi><mi>x</mi><mi mathvariant="normal">i</mi><mi>d</mi><mi>a</mi><mi>d</mi><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">m</mi><mi mathvariant="normal">h</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Riqueza y gases La descomposición térmica del carbonato de calcio produce óxido de calcio y dióxido de carbono gas. ¿Cuántos litros de dióxido de carbono medido a #tc ºC y #pre mm de Hg se obtendrán al descomponer #mca Kg de caliza del #riq % de riqueza en carbonato de calcio.

CaCO₃ --> CaO + CO₂

]]> 1.0000000 0.3333333 0 0 #voldi]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>700</mn><mo>,</mo><mn>800</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mca</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>riq</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pres</mi><mo>=</mo><mi>pre</mi><mo>/</mo><mn>760</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>moldi</mi><mo>=</mo><mi>mca</mi><mo>*</mo><mn>1000</mn><mo>*</mo><mi>riq</mi><mo>/</mo><mo>(</mo><mn>100</mn><mo>*</mo><mn>100</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>voldi</mi><mo>=</mo><mi>moldi</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>082</mn><mo>*</mo><mi>tk</mi><mo>/</mo><mi>pres</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>fc</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>:</mo><mo>=</mo><mo>(</mo><mo>(</mo><mfenced close="|" open="|"><mrow><mo>(</mo><mi>x</mi><mo>-</mo><mi>voldi</mi><mo>)</mo><mo>/</mo><mi>voldi</mi></mrow></mfenced><mo><</mo><mn>0</mn><mo>.</mo><mn>02</mn><mo>)</mo><mo>?</mo><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>v</mi><mi>o</mi><mi mathvariant="normal">l</mi><mi>d</mi><mi mathvariant="normal">i</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_function"><param name="name">fc</param><param name="notevaluate">false</param></assertion></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/QUÍMICA/TERMOQUÍMICA/ENTALPÍAS DE ENLACE Combustión dos isómeros ¿Cuál será el calor liberado por la combustión #ma gramos de C₄H₁₀ si usamos:

El isómero butano
El isómero metilpropano

Datos: energías de enlace (KJ/mol): C-H= 415 ; C-C = 347 KJ/mol; C=O = 743; H-O= 460; O=O = 494

]]> 1.0000000 0.3333333 0 0 Butano (KJ)= #cabMetil propano (KJ)=#cam]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol</mi><mo>=</mo><mi>ma</mi><mo>/</mo><mn>58</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cmbu</mi><mo>=</mo><mn>10</mn><mo>*</mo><mn>415</mn><mo>+</mo><mn>3</mn><mo>*</mo><mn>347</mn><mo>+</mo><mn>6</mn><mo>.</mo><mn>5</mn><mo>*</mo><mn>494</mn><mo>-</mo><mn>8</mn><mo>*</mo><mn>743</mn><mo>-</mo><mn>10</mn><mo>*</mo><mn>460</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cab</mi><mo>=</mo><mo>-</mo><mi>cmbu</mi><mo>*</mo><mi>mol</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cam</mi><mo>=</mo><mi>cab</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mi>u</mi><mi>t</mi><mi>a</mi><mi>n</mi><mi>o</mi><mo> </mo><mo>(</mo><mi mathvariant="normal">K</mi><mi mathvariant="normal">J</mi><mo>)</mo><mo>=</mo><mo> </mo><mo>#</mo><mi>c</mi><mi>a</mi><mi mathvariant="normal">b</mi><mspace linebreak="newline"/><mi>M</mi><mi mathvariant="normal">e</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi mathvariant="normal">l</mi><mo> </mo><mi>p</mi><mi>r</mi><mi>o</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>o</mi><mo> </mo><mo>(</mo><mi mathvariant="normal">K</mi><mi mathvariant="normal">J</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>a</mi><mi mathvariant="normal">m</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Combustión dos isómeros (II) ¿Cuál será el calor liberado por la combustión #ma gramos de C₃H₆O si usamos:

El isómero propanona
El isómero prop2-en,1-ol

Datos: energías de enlace (KJ/mol): C-H= 415 ; C-C = 347 ; C=C = 610; C-O = 352; C=O = 743; H-O= 460; O=O = 494

]]> 1.0000000 0.3333333 0 0 Propanona (KJ)= #cabProp-2-en-1-ol (KJ)=#cam]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol</mi><mo>=</mo><mi>ma</mi><mo>/</mo><mn>58</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cmbu</mi><mo>=</mo><mn>6</mn><mo>*</mo><mn>415</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>347</mn><mo>+</mo><mo>+</mo><mn>743</mn><mo>+</mo><mn>4</mn><mo>*</mo><mn>494</mn><mo>-</mo><mn>6</mn><mo>*</mo><mn>743</mn><mo>-</mo><mn>6</mn><mo>*</mo><mn>460</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cmpr</mi><mo>=</mo><mn>5</mn><mo>*</mo><mn>415</mn><mo>+</mo><mn>347</mn><mo>+</mo><mn>610</mn><mo>+</mo><mn>460</mn><mo>+</mo><mn>352</mn><mo>+</mo><mn>4</mn><mo>*</mo><mn>494</mn><mo>-</mo><mn>6</mn><mo>*</mo><mn>743</mn><mo>-</mo><mn>6</mn><mo>*</mo><mn>460</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cab</mi><mo>=</mo><mo>-</mo><mi>cmbu</mi><mo>*</mo><mi>mol</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cam</mi><mo>=</mo><mo>-</mo><mi>cmpr</mi><mo>*</mo><mi>mol</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>r</mi><mi>o</mi><mi>p</mi><mi>a</mi><mi>n</mi><mi>o</mi><mi>n</mi><mi>a</mi><mo> </mo><mo>(</mo><mi mathvariant="normal">K</mi><mi mathvariant="normal">J</mi><mo>)</mo><mo>=</mo><mo> </mo><mo>#</mo><mi>c</mi><mi>a</mi><mi mathvariant="normal">b</mi><mspace linebreak="newline"/><mi>P</mi><mi>r</mi><mi>o</mi><mi>p</mi><mo>-</mo><mn>2</mn><mo>-</mo><mi mathvariant="normal">e</mi><mi>n</mi><mo>-</mo><mn>1</mn><mo>-</mo><mi>o</mi><mi mathvariant="normal">l</mi><mo> </mo><mo>(</mo><mi mathvariant="normal">K</mi><mi mathvariant="normal">J</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>a</mi><mi mathvariant="normal">m</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> en enlace H-X Calcule la energía de enlace H−X sabiendo que la entalpía de formación del HX(g) es - #enhi kJ/mol y las de disociación del H₂ y X₂son 436 kJ/mol y #endi kJ/mol, respectivamente.]]> 1.0000000 0.3333333 0 0 #enel]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enhi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>130</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>endi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>200</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enel</mi><mo>=</mo><mo>(</mo><mi>endi</mi><mo>+</mo><mn>436</mn><mo>)</mo><mo>/</mo><mn>2</mn><mo>.</mo><mn>0</mn><mo>+</mo><mi>enhi</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> En enlace XH3 Sabiendo que ΔHº_f (XH₃) = -#entf KJ/mol y las energías de enlace X-H es #enthi kJ/mol y H-H es 390 kJ/mol, determina la energía de enlace X-X en KJ/mol

]]> 1.0000000 0.3333333 0 0 #entel]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>entf</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>500</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enthi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>300</mn><mo>,</mo><mn>600</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>entel</mi><mo>=</mo><mn>2</mn><mo>*</mo><mo>(</mo><mo>-</mo><mi>entf</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>enthi</mi><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>*</mo><mn>390</mn><mo>.</mo><mn>0</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Formación de amoniaco

Calcule, en la reacción de formación del amoniaco, la energía desprendida al formarse #vol litros de amoniaco en condiciones normales.:

N_{2 (g)} + 3 H_{2 (g)} --> 2 NH_{3 (g)}

Datos: Energías medias de enlace en kJ/mol: (N≡N) = 946; (H−H) = 436;(N-H) = 390.

]]> 1.0000000 0.3333333 0 0 #cre]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vol</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enta</mi><mo>=</mo><mo>(</mo><mn>946</mn><mo>+</mo><mn>3</mn><mo>*</mo><mn>436</mn><mo>-</mo><mn>6</mn><mo>*</mo><mn>390</mn><mo>)</mo><mo>/</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol</mi><mo>=</mo><mi>vol</mi><mo>/</mo><mn>22</mn><mo>.</mo><mn>4</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cre</mi><mo>=</mo><mo>-</mo><mi>mol</mi><mo>*</mo><mi>enta</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>r</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Formación de clorometano Teniendo en cuenta las energías de enlace , en KJ/mol, en condiciones standard de (Cl-Cl)= 243.8; (C-Cl)=327.8; (Cl-H)=432.4; (C-H)=415.3. Determina la energía intercambiada, en KJ, en condiciones standard, por #ma gramos de metano al clorarse según la reacción:

CH_{4 (g)} + Cl_{2 (g)} --> CH₃Cl _(g) + HCl_(g)

]]> 1.0000000 0.3333333 0 0 #cre]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>entr</mi><mo>=</mo><mo> </mo><mn>4</mn><mo>*</mo><mn>415</mn><mo>.</mo><mn>3</mn><mo>+</mo><mn>243</mn><mo>.</mo><mn>8</mn><mo>-</mo><mn>432</mn><mo>.</mo><mn>4</mn><mo>-</mo><mn>3</mn><mo>*</mo><mn>415</mn><mo>.</mo><mn>3</mn><mo>-</mo><mn>327</mn><mo>.</mo><mn>8</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cre</mi><mo>=</mo><mi>entr</mi><mo>*</mo><mi>ma</mi><mo>/</mo><mn>16</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>r</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Hidrogenación (entalpías de enlace) Considere la reacción de hidrogenación del propino:

CH₃C≡CH + 2 H₂ → CH₃CH₂CH₃

Calcule el calor de reacción (en KJ) de #ma gramos de propino, a partir de las entalpías medias de enlace.

Datos: Entalpías de enlace en kJ/mol: (C−C) = 347; (C≡C) = 830; (C−H) = 415; (H−H) = 436. Masa atómica: H = 1.

]]> 1.0000000 0.3333333 0 0 #cre]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol</mi><mo>=</mo><mi>ma</mi><mo>/</mo><mn>40</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enta</mi><mo>=</mo><mn>4</mn><mo>*</mo><mn>415</mn><mo>+</mo><mn>830</mn><mo>+</mo><mn>347</mn><mo>+</mo><mn>872</mn><mo>-</mo><mn>8</mn><mo>*</mo><mn>415</mn><mo>-</mo><mn>2</mn><mo>*</mo><mn>347</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cre</mi><mo>=</mo><mi>mol</mi><mo>*</mo><mi>enta</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>r</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> hidrogenación butadieno La reacción de hidrogenación del but-1,3-dieno para dar butano es:

$C_4H_6(g) + 2\ H_2(g)\ \to\ C_4H_{10}(g)$

Calcula la entalpía de la reacción a 25 ºC:

a) A partir de la entalpía de formación del agua y de las entalpías de combustión del buta-1,3-dieno y del butano.

b) A partir de las entalpías de enlace.

Datos: ΔHº_c (KJ/mol): (C₄H₆ _(g))= -2540.2; C₄H_{10 (g)} = -2877.6 ; ΔHºf (H₂O) =-285.6 KJ/mol ;

Entalpías de enlace (kJ/mol): (C-C) = 348,2 ; (C=C) = 612,9 ; (C-H) = 415,3 ; (H-H) = 436,4.

]]> 1.0000000 0.3333333 0 0 ΔHº (reacciones) (KJ/mol)= #entrΔHº (enlace) (KJ/mol)=#ente]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>entr</mi><mo>=</mo><mo>-</mo><mn>2540</mn><mo>.</mo><mn>2</mn><mo>+</mo><mn>2877</mn><mo>.</mo><mn>6</mn><mo>-</mo><mn>2</mn><mo>*</mo><mn>285</mn><mo>.</mo><mn>6</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ente</mi><mo>=</mo><mn>6</mn><mo>*</mo><mn>415</mn><mo>.</mo><mn>3</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>612</mn><mo>.</mo><mn>9</mn><mo>+</mo><mn>348</mn><mo>.</mo><mn>2</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>436</mn><mo>.</mo><mn>4</mn><mo>-</mo><mn>3</mn><mo>*</mo><mn>348</mn><mo>.</mo><mn>2</mn><mo>-</mo><mn>10</mn><mo>*</mo><mn>415</mn><mo>.</mo><mn>3</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Δ</mi><mi>H</mi><mo>º</mo><mo> </mo><mo>(</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>a</mi><mi>c</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>o</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>s</mi><mo>)</mo><mo> </mo><mo>(</mo><mi>K</mi><mi>J</mi><mo>/</mo><mi>m</mi><mi>o</mi><mi>l</mi><mo>)</mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>r</mi><mspace linebreak="newline"/><mi>Δ</mi><mi>H</mi><mo>º</mo><mo> </mo><mo>(</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi>l</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">e</mi><mo>)</mo><mo> </mo><mo>(</mo><mi>K</mi><mi>J</mi><mo>/</mo><mi>m</mi><mi>o</mi><mi>l</mi><mo>)</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> 1º BACHILLERATO/QUÍMICA/TERMOQUÍMICA/ENTALPÍAS DE REACCIÓN Calcule el calor de formación de #ma gramos de acetileno Calcule el calor de formación de #ma gramos de acetileno (etino) conocidos los calores de formación del H₂O _(l) y del CO₂, así como el calor de combustión del acetileno. (Datos: ΔH°(agua)= -285 KJ/mol; ΔH°(CO₂)= -393.13 KJ/m; ΔH°(combustión C₂H₂) = -1297 KJ/mol)

]]> 1.0000000 0.3333333 0 0 #calf]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mol</mi><mo>=</mo><mi>ma</mi><mo>/</mo><mn>26</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>calf</mi><mo>=</mo><mi>mol</mi><mo>*</mo><mo>(</mo><mn>1297</mn><mo>-</mo><mn>285</mn><mo>-</mo><mn>2</mn><mo>*</mo><mn>393</mn><mo>.</mo><mn>13</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>a</mi><mi mathvariant="normal">l</mi><mi>f</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calor carbonato cálcico Una muestra de carbonato cálcico se descompone térmicamente dando #mox g de óxido de calcio (s) y dióxido decarbono (g). Calcular el calor absorbido o desprendido en el proceso. (Datos: ΔH⁰_f CaO (s) = -633 KJ/mol; ΔH⁰_f CO₂ (g) = -393.5 KJ/mol; ΔH⁰_f CaCO₃ (s) = -1207.6 KJ/mol; A(Ca)=40; A(C)=12; A(O)=16)

]]> 1.0000000 0.3333333 0 0 #calcom]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cmol</mi><mo>=</mo><mi>masc</mi><mo>/</mo><mn>58</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>calcom</mi><mo>=</mo><mi>cmol</mi><mo>*</mo><mo>(</mo><mo>-</mo><mn>4</mn><mo>*</mo><mn>393</mn><mo>.</mo><mn>5</mn><mo>-</mo><mn>5</mn><mo>*</mo><mn>285</mn><mo>.</mo><mn>5</mn><mo>+</mo><mn>124</mn><mo>.</mo><mn>7</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>a</mi><mi mathvariant="normal">l</mi><mi>c</mi><mi>o</mi><mi mathvariant="normal">m</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calor combustion etanol Considera la reacción de combustión del etanol. Determina la cantidad de calor, en KJ, que se libera a presión constante, en la combustión completa de #masa g de etanol en las mismas condiciones de presión y temperatura.

DATOS: ΔHº_f [C₂H₅OH_(l)] = −277,7 kJ/mol, ∆Hº_f [ CO₂ (g)] = -393,5 kJ/mol, ∆Hº_f [ H₂O (l)] = -285,8 kJ/mol.

MASAS ATÓMICAS C-12; O-16; H-1

]]> 1.0000000 0.3333333 0 0 #calor <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>care</mi><mo>=</mo><mn>3</mn><mo>*</mo><mo>(</mo><mo>-</mo><mn>285</mn><mo>.</mo><mn>8</mn><mo>)</mo><mo>+</mo><mn>2</mn><mo>*</mo><mo>(</mo><mo>-</mo><mn>393</mn><mo>.</mo><mn>5</mn><mo>)</mo><mo>+</mo><mn>277</mn><mo>.</mo><mn>7</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>calor</mi><mo>=</mo><mo>-</mo><mi>care</mi><mo>*</mo><mi>masa</mi><mo>/</mo><mn>46</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#calor</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m, y, z, a, f, p, n, µ, d, da, h, G, T, P, E, Z, Y</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calor formación e hidrogenación Al quemar completamente #mbe g de un hidrocarburo C₄H₈ (g) en condiciones estándar, se desprenden #enbe KJ; al quemar #mbu g de otro hidrocarburo C₄H₁₀(g) en condiciones estándar, se desprenden #enbu KJ. Si los calores de formación del agua (l) y del CO₂ (g) son, respectivamente, -285.6 KJ/mol y–393.5 KJ/mol, calcula (en KJ/mol) el calor absorbido o desprendido en condiciones estándar en la reacción:

C₄H₈ (g) +H₂ (g) --> C₄H₁₀ (g)

]]> 1.0000000 0.3333333 0 0 #cre]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mbe</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mbu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enbe</mi><mo>=</mo><mi>mbe</mi><mo>*</mo><mn>48</mn><mo>.</mo><mn>26</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enbu</mi><mo>=</mo><mi>mbu</mi><mo>*</mo><mn>49</mn><mo>.</mo><mn>63</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ccbe</mi><mo>=</mo><mo>-</mo><mi>enbe</mi><mo>*</mo><mn>56</mn><mo>/</mo><mi>mbe</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ccbu</mi><mo>=</mo><mo>-</mo><mi>enbu</mi><mo>*</mo><mn>58</mn><mo>/</mo><mi>mbu</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cre</mi><mo>=</mo><mi>ccbe</mi><mo>-</mo><mi>ccbu</mi><mo>-</mo><mn>285</mn><mo>.</mo><mn>6</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>r</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calor reacción amoniaco Para la fabricación industrial del ácido nítrico, se parte de la oxidación catalítica del amoniaco, según:

4 NH_3(g) + 5 O_{2 (g)} → 6 H₂O_(l) + 4 NO _(g)

Calcule el calor intercambiado por #ma g de amoniaco en esta reacción a 25 ºC y 1 atm de presión contante.

Datos:∆Hº_f [H₂O (l)] = −285’8 kJ/mol, ∆Hº_f [NH₃(g)] = −46’1 kJ/mol, ∆Hº_f [NO(g)] = 90’25 kJ/mol. Masas atómicas: H=1; N=14;O=16

]]> 1.0000000 0.3333333 0 0 #cre]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enta</mi><mo>=</mo><mo>-</mo><mn>6</mn><mo>*</mo><mn>285</mn><mo>.</mo><mn>8</mn><mo>+</mo><mn>4</mn><mo>*</mo><mn>90</mn><mo>.</mo><mn>25</mn><mo>+</mo><mn>4</mn><mo>*</mo><mn>46</mn><mo>.</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cre</mi><mo>=</mo><mi>enta</mi><mo>*</mo><mi>ma</mi><mo>/</mo><mo>(</mo><mn>4</mn><mo>*</mo><mn>17</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>r</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> En. interna de reacción Calcular la variación de energía interna, en KJ en condiciones standard para la reacción:

4 NH_{3 (g)} + 5 O_{2 (g)} --> 4 NO _(g) + 6 H₂O _(l)

Entalpías standard de formación: NH_{3 (g)} = -46.15 KJ/mol; NO _(g) = 90.29 KJ/mol; H₂O _(l) = -285.58 KJ/mol

]]> 1.0000000 0.3333333 0 0 #enin]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ent</mi><mo>=</mo><mn>6</mn><mo>*</mo><mo>(</mo><mo>-</mo><mn>285</mn><mo>.</mo><mn>58</mn><mo>)</mo><mo>+</mo><mn>4</mn><mo>*</mo><mn>90</mn><mo>.</mo><mn>29</mn><mo>-</mo><mn>4</mn><mo>*</mo><mo>(</mo><mo>-</mo><mn>46</mn><mo>.</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enin</mi><mo>=</mo><mi>ent</mi><mo>-</mo><mo>(</mo><mo>-</mo><mn>5</mn><mo>)</mo><mo>*</mo><mn>8</mn><mo>.</mo><mn>31</mn><mo>*</mo><mn>298</mn><mo>/</mo><mn>1000</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">i</mi><mi>n</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"></data></localData></question> Hervir agua Queremos calentar agua y convertir en vapor a 100 ºC, #masa Kg de agua que están a 0ºC: hallar los Kg de #comp que necesitaremos quemar suponiendo que se aprovecha el #rend % del calor desprendido en la combustión.

DATOS: Calor esp (agua) = 1 Kcal/Kg K; Calor vapor (agua) = 539.5 Kcal/kg; calor de combustión (#comp) = #ccomb KJ/mol

(1 J = 0.24 cal)

]]> 1.0000000 0.3333333 0 0 #masa2]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>500</mn><mo>,</mo><mn>1000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rend</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>70</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>indi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>compl</mi><mo>=</mo><mo>(</mo><mo>"</mo><mi>carbón</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>metano</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>propano</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>butano</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>eteno</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>metanol</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>etanol</mi><mo>"</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ccombl</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>393</mn><mo>.</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>890</mn><mo>.</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>2220</mn><mo>,</mo><mo>-</mo><mn>2878</mn><mo>.</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>1411</mn><mo>.</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>726</mn><mo>.</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1366</mn><mo>.</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molcl</mi><mo>=</mo><mo>(</mo><mn>12</mn><mo>,</mo><mn>16</mn><mo>,</mo><mn>44</mn><mo>,</mo><mn>58</mn><mo>,</mo><mn>28</mn><mo>,</mo><mn>32</mn><mo>,</mo><mn>46</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>comp</mi><mo>=</mo><msub><mi>compl</mi><mi>indi</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ccomb</mi><mo>=</mo><msub><mi>ccombl</mi><mi>indi</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molc</mi><mo>=</mo><msub><mi>molcl</mi><mi>indi</mi></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>calor</mi><mo>=</mo><mi>masa</mi><mo>*</mo><mo>(</mo><mn>100</mn><mo>+</mo><mn>539</mn><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mn>0</mn><mo>.</mo><mn>24</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa2</mi><mo>=</mo><mo>-</mo><mi>calor</mi><mo>*</mo><mo>(</mo><mn>100</mn><mo>.</mo><mn>0</mn><mo>/</mo><mi>rend</mi><mo>)</mo><mo>*</mo><mi>molc</mi><mo>/</mo><mo>(</mo><mi>ccomb</mi><mo>*</mo><mn>1000</mn><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">m</mi><mi>a</mi><mi mathvariant="normal">s</mi><mi>a</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La entalpía de formación del amoniaco es ΔH°= -46.2 KJ/mol. Calcule el calor de reacción cuando se forman {a} litros de amoniaco medidos en condiciones estándar La entalpía de formación del amoniaco es ΔH°= -46.2 KJ/mol. Calcule el calor de reacción, en KJ, cuando se forman #vol litros de amoniaco medidos en condiciones estándar

C₆H₁₂O₆ -->2 C₂H₅OH + 2 CO₂

]]> 1.0000000 0.3333333 0 0 #cre]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enta</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>673</mn><mo>+</mo><mn>2</mn><mo>*</mo><mn>328</mn><mo>)</mo><mo>/</mo><mn>0</mn><mo>.</mo><mn>24</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cre</mi><mo>=</mo><mo>-</mo><mi>enta</mi><mo>*</mo><mi>ma</mi><mo>/</mo><mn>2</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>r</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Oxidación etanol En condiciones estándar, en la combustión de #me1 g de etanol se desprenden #ccet kJ y en la combustión de #mac g de ácido acético se desprenden #ccac kJ. Calcula la variación de entalpía estándar, en KJ, de la siguiente reacción para #me2 g de etanol

CH₃CH₂OH + O₂ → CH₃COOH +H₂O

MASAS ATÓMICAS C-12; H-1; O-16

]]> 1.0000000 0.3333333 0 0 #cre]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mac</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>me2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>40</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ccet</mi><mo>=</mo><mn>29</mn><mo>.</mo><mn>8</mn><mo>*</mo><mi>me1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ccac</mi><mo>=</mo><mn>14</mn><mo>.</mo><mn>59</mn><mo>*</mo><mi>mac</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cre</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>495</mn><mo>.</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>me2</mi><mo>/</mo><mn>46</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>r</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Oxidación SO2 En la oxidación catalítica a #tc ºC del dióxido de azufre se obtiene trióxido de azufre según:

2 SO₂ _(g) + O_2 (g) → 2 SO₃ _(g) ∆H = − 198' 2 kJ

Calcule la cantidad de energía, en KJ, que se desprende en la oxidación de #ma g de dióxido de azufre si la reacción tiene lugar a volumen constante

Datos: R = 8’31 J·K^-1·mol^-1. Masas atómicas: O = 16; S = 32.

]]> 1.0000000 0.3333333 0 0 #qv]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qp</mi><mo>=</mo><mn>198</mn><mo>.</mo><mn>2</mn><mo>*</mo><mi>ma</mi><mo>/</mo><mn>128</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qv1</mi><mo>=</mo><mo>-</mo><mn>198</mn><mo>.</mo><mn>2</mn><mo>+</mo><mn>8</mn><mo>.</mo><mn>31</mn><mo>*</mo><mi>tk</mi><mo>/</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qv</mi><mo>=</mo><mo>-</mo><mi>qv1</mi><mo>*</mo><mi>ma</mi><mo>/</mo><mn>128</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>q</mi><mi>v</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Quemar gasolina La gasolina puede ser considerada como una mezcla de octanos (C₈H₁₈). Sabiendo que los calores de formación de: H₂O _(g) = -242 KJ/mol; CO₂ _(g) = -394 KJ/mol; C₈H₁₈ _(l) = -250 KJ/mol. Calcule la energía, en KJ, liberada en la combustión de #volu litros de gasolina (d= 800 Kg/m³)

]]> 1.0000000 0.3333333 0 0 #cre]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>volu</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>20</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><mi>volu</mi><mo>*</mo><mn>800</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enta</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>*</mo><mn>242</mn><mo>-</mo><mn>8</mn><mo>*</mo><mn>394</mn><mo>+</mo><mn>250</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cre</mi><mo>=</mo><mo>-</mo><mi>enta</mi><mo>*</mo><mi>masa</mi><mo>/</mo><mn>114</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>r</mi><mi mathvariant="normal">e</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Quemar gasolina Un automóvil obtiene energía quemando gasolina (octano) para obtener dióxido de carbono y agua gaseosa. Calcula la energía, en KJ, que necesita un automóvil por cada kilómetro si consume #vol litros de octano por cada 100 km.

DATOS: ∆Hº_f [ H₂O_(g)] = -241,8 kJ/mol; ∆Hº_f [CO₂ _(g)] = -393,5 kJ/mol, ∆Hº_f [C₈H_18 (l)] = -250,0 kJ/mol. Densidad del octano líquido 0,8 kg/L.

MASAS ATÓMICAS C-12; H-1

]]> 1.0000000 0.3333333 0 0 #ener]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vol</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><mn>800</mn><mo>*</mo><mi>vol</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>moles</mi><mo>=</mo><mi>masa</mi><mo>/</mo><mn>114</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>entmol</mi><mo>=</mo><mo>-</mo><mn>8</mn><mo>*</mo><mn>393</mn><mo>.</mo><mn>5</mn><mo>-</mo><mn>9</mn><mo>*</mo><mn>241</mn><mo>.</mo><mn>8</mn><mo>+</mo><mn>250</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ener</mi><mo>=</mo><mo>-</mo><mi>entmol</mi><mo>*</mo><mi>moles</mi><mo>/</mo><mn>100</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">e</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Tostación de pirita La tostación de la pirita se produce según:

4 FeS₂ _(s) +11 O₂ _(g) → 2 Fe₂O₃ _(s) + 8 SO₂ _(g)

Calcule la cantidad de calor, en KJ, a presión constante, desprendida en la combustión de #mpi g de pirita del #riq % de riqueza en peso.

Datos: Masas atómicas: Fe = 55’8; S = 32. ΔHºf[FeS₂(s)] = −177’5 kJ/mol, ΔHºf[Fe₂O₃(s)] = −822’2 kJ/mol, ΔHºf[SO₂(g)]= −296’8 kJ/mol.

]]> 1.0000000 0.3333333 0 0 #calor]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>mpi</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>100</mn><mo>,</mo><mn>600</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>riq</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>60</mn><mo>,</mo><mn>90</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>msul</mi><mo>=</mo><mi>mpi</mi><mo>*</mo><mi>riq</mi><mo>/</mo><mn>100</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>molsu</mi><mo>=</mo><mi>msul</mi><mo>/</mo><mo>(</mo><mn>64</mn><mo>+</mo><mn>55</mn><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enta</mi><mo>=</mo><mo>-</mo><mn>8</mn><mo>*</mo><mn>296</mn><mo>.</mo><mn>8</mn><mo>-</mo><mn>2</mn><mo>*</mo><mn>822</mn><mo>.</mo><mn>2</mn><mo>+</mo><mn>4</mn><mo>*</mo><mn>177</mn><mo>.</mo><mn>5</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>calor</mi><mo>=</mo><mo>-</mo><mi>molsu</mi><mo>*</mo><mi>enta</mi><mo>/</mo><mn>4</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>c</mi><mi>a</mi><mi mathvariant="normal">l</mi><mi>o</mi><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1º BACHILLERATO/QUÍMICA/TERMOQUÍMICA/ENTROPÍA Y ENERGÍA LIBRE Energia libre carbonato Una de las reacciones más importantes de la industria química es la descomposición del carbonato de calcio (sólido) en dióxido de carbono (gas) y óxido de calcio (sólido). Si el ΔS⁰ de la reacción es 159 J/K y las entalpías estándar de formación del carbonato de calcio, dióxido de carbono y óxido de calcio son: ΔH⁰_f CaCO₃ (s) = -1207 KJ/mol; ΔH⁰_f CaO (s) = -633 KJ/mol; Δ H⁰_f CO₂ (g) = -393 KJ/mol. Suponiendo que ΔH⁰ e ΔS⁰ son constantes. Calcula la temperatura centígrada a partir de la cual la reacción será espontánea.

]]> 1.0000000 0.3333333 0 0 #temp]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enta</mi><mo>=</mo><mo>-</mo><mn>393</mn><mo>-</mo><mn>633</mn><mo>+</mo><mn>1207</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>temp</mi><mo>=</mo><mo>(</mo><mi>enta</mi><mo>*</mo><mn>1000</mn><mo>/</mo><mn>159</mn><mo>.</mo><mn>0</mn><mo>)</mo><mo>-</mo><mn>273</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>t</mi><mi mathvariant="normal">e</mi><mi mathvariant="normal">m</mi><mi>p</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Espontaneidad Una reacción química endotérmica con incremento de entropía negativo sera:

]]> 1.0000000 0.1000000 0 true true abc Será espontánea a cualquier temperatura No será espontánea a ninguna temperatura Será espontánea por debajo de una cierta temperatura Será espontánea por encima de una cierta temperatura Espontaneidad reacciones endotérmicas Sea la reacción química endotérmica:

#n1 A _(g) + #n2 B _(l) --> #n3 C _(g) + #n4 D _(g)

Marque las opciones más probables

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> El incremento de entropía será #entrc

]]> El incremento de entropía será #entrf

]]> La reacción #espc

]]> La reacción #espf1

]]> La reacción #espf2

]]> La reacción #espf3

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>7</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n1</mi><mo>></mo><mo>(</mo><mi>n3</mi><mo>+</mo><mi>n4</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>entrc</mi><mo>=</mo><mo>"</mo><mi>negativo</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>entrf</mi><mo>=</mo><mo>"</mo><mi>positivo</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espf3</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>por</mi><mo> </mo><mi>encima</mi><mo> </mo><mi>de</mi><mo> </mo><mi>una</mi><mo> </mo><mi>cierta</mi><mo> </mo><mi>temperatura</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espf1</mi><mo>=</mo><mo>"</mo><mi>siempre</mi><mo> </mo><mi>espontánea</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espf2</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>por</mi><mo> </mo><mi>debajo</mi><mo> </mo><mi>de</mi><mo> </mo><mi>una</mi><mo> </mo><mi>cierta</mi><mo> </mo><mi>temperatura</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espc</mi><mo>=</mo><mo>"</mo><mi>nunca</mi><mo> </mo><mi>será</mi><mo> </mo><mi>espontánea</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>entrf</mi><mo>=</mo><mo>"</mo><mi>negativa</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>entrc</mi><mo>=</mo><mo>"</mo><mi>positiva</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espf1</mi><mo>=</mo><mo>"</mo><mi>siempre</mi><mo> </mo><mi>espontánea</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espc</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>por</mi><mo> </mo><mi>encima</mi><mo> </mo><mi>de</mi><mo> </mo><mi>una</mi><mo> </mo><mi>cierta</mi><mo> </mo><mi>temperatura</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espf2</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>por</mi><mo> </mo><mi>debajo</mi><mo> </mo><mi>de</mi><mo> </mo><mi>una</mi><mo> </mo><mi>cierta</mi><mo> </mo><mi>temperatura</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espf3</mi><mo>=</mo><mo>"</mo><mi>nunca</mi><mo> </mo><mi>será</mi><mo> </mo><mi>espontánea</mi><mo>"</mo></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Espontaneidad reacciones exotérmicas Sea la reacción química exotérmica:

#n1 A _(g) + #n2 B _(l) --> #n3 C _(g) + #n4 D _(g)

Marque las opciones más probables

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> El incremento de entropía será #entrc

]]> El incremento de entropía será #entrf

]]> La reacción #espc

]]> La reacción #espf1

]]> La reacción #espf2

]]> La reacción #espf3

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>3</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>n1</mi><mo>></mo><mo>(</mo><mi>n3</mi><mo>+</mo><mi>n4</mi><mo>)</mo></mrow><mtable><mtr><mtd><mi>entrc</mi><mo>=</mo><mo>"</mo><mi>negativo</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>entrf</mi><mo>=</mo><mo>"</mo><mi>positivo</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espf2</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>por</mi><mo> </mo><mi>encima</mi><mo> </mo><mi>de</mi><mo> </mo><mi>una</mi><mo> </mo><mi>cierta</mi><mo> </mo><mi>temperatura</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espf1</mi><mo>=</mo><mo>"</mo><mi>siempre</mi><mo> </mo><mi>espontánea</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espc</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>por</mi><mo> </mo><mi>debajo</mi><mo> </mo><mi>de</mi><mo> </mo><mi>una</mi><mo> </mo><mi>cierta</mi><mo> </mo><mi>temperatura</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espf3</mi><mo>=</mo><mo>"</mo><mi>nunca</mi><mo> </mo><mi>será</mi><mo> </mo><mi>espontánea</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>entrf</mi><mo>=</mo><mo>"</mo><mi>negativo</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>entrc</mi><mo>=</mo><mo>"</mo><mi>positivo</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espc</mi><mo>=</mo><mo>"</mo><mi>siempre</mi><mo> </mo><mi>espontánea</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espf1</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>por</mi><mo> </mo><mi>encima</mi><mo> </mo><mi>de</mi><mo> </mo><mi>una</mi><mo> </mo><mi>cierta</mi><mo> </mo><mi>temperatura</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espf2</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>por</mi><mo> </mo><mi>debajo</mi><mo> </mo><mi>de</mi><mo> </mo><mi>una</mi><mo> </mo><mi>cierta</mi><mo> </mo><mi>temperatura</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>espf3</mi><mo>=</mo><mo>"</mo><mi>nunca</mi><mo> </mo><mi>será</mi><mo> </mo><mi>espontánea</mi><mo>"</mo></mtd></mtr></mtable></apply></math></input></command></group></library></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Formación de amoniaco Para la reacción de formación de amoniaco a partir de los elementos, marque las opciones correctas (ΔHº=-67.2 KJ/mol)

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> La entropía es positiva porque disminuye el número de moles de gas

]]> La entropía es negativa porque disminuye el número de moles de gas

]]> La entropía no cambia

]]> Es endotérmica

]]> Es exotérmica

]]> Es espontánea a todas las temperaturas

]]> Es espontánea por debajo de una temperatura

]]> Es espontánea por encima de una temperatura

]]> Es espontánea siempre la reacción inversa

]]> Oxidación de SO2 Para la reacción:

2 SO₂ _{( g} ) + O₂ _{( g )} → 2 SO_{3 ( g )} ∆H = − 198' 2 kJ

Marque las opciones correctas

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> La entropía es positiva porque disminuye el número de moles de gas

]]> La entropía es negativa porque disminuye el número de moles de gas

]]> La entropía no cambia

]]> Es endotérmica

]]> Es exotérmica

]]> Es espontánea a todas las temperaturas

]]> Es espontánea por debajo de una temperatura

]]> Es espontánea por encima de una temperatura

]]> Es espontánea siempre la reacción inversa

]]> Sentido de la reacción La reacción:

A _(s) ⇒ 2 B_(s) + C_(g) ΔHº = #enta KJ; ΔSº = #entro J/K

A una temperatura de #tc ºC será:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Será #sentidor

]]> Será #sentidof1

]]> Será #sentidof2

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>700</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enta</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>50</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>entro</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>60</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enli</mi><mo>=</mo><mi>enta</mi><mo>*</mo><mn>1000</mn><mo>-</mo><mi>tk</mi><mo>*</mo><mi>entro</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>enli</mi><mo><</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>sentidor</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>hacia</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derecha</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sentidof1</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>hacia</mi><mo> </mo><mi>la</mi><mo> </mo><mi>izquierda</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sentidof2</mi><mo>=</mo><mo>"</mo><mi>un</mi><mo> </mo><mi>equilibrio</mi><mo> </mo><mi>perfecto</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>enli</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>sentidof2</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>hacia</mi><mo> </mo><mi>la</mi><mo> </mo><mi>izquierda</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sentidof1</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>hacia</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derecha</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sentidor</mi><mo>=</mo><mo>"</mo><mi>un</mi><mo> </mo><mi>equilibrio</mi><mo> </mo><mi>perfecto</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sentidor</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>hacia</mi><mo> </mo><mi>la</mi><mo> </mo><mi>izquierda</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sentidof1</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>hacia</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derecha</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sentidof2</mi><mo>=</mo><mo>"</mo><mi>un</mi><mo> </mo><mi>equilibrio</mi><mo> </mo><mi>perfecto</mi><mo>"</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Sentido de la reacción La reacción:

Ag₂O _(s) ⇒ 2 Ag_(s) + 1/2 O_{2 (g)} ΔHº = 30.6 KJ; ΔSº = 60.2 J/K

A una temperatura de #tc ºC será:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Será #sentidor

]]> Será #sentidof1

]]> Será #sentidof2

3 A _(s) +2 B _(s)⇒ 3 C_(g) ΔHº = #enta KJ; ΔSº = #entro J/K

A una temperatura de #tc ºC será:

]]> 1.0000000 0.3333333 0 true true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Será #sentidor

]]> Será #sentidof1

]]> Será #sentidof2

]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>200</mn><mo>,</mo><mn>1000</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enta</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>50</mn><mo>,</mo><mn>50</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>entro</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mo>-</mo><mn>60</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enli</mi><mo>=</mo><mi>enta</mi><mo>*</mo><mn>1000</mn><mo>-</mo><mi>tk</mi><mo>*</mo><mi>entro</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>enli</mi><mo><</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>sentidor</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>hacia</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derecha</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sentidof1</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>hacia</mi><mo> </mo><mi>la</mi><mo> </mo><mi>izquierda</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sentidof2</mi><mo>=</mo><mo>"</mo><mi>un</mi><mo> </mo><mi>equilibrio</mi><mo> </mo><mi>perfecto</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>enli</mi><mo>=</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>sentidof2</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>hacia</mi><mo> </mo><mi>la</mi><mo> </mo><mi>izquierda</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sentidof1</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>hacia</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derecha</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sentidor</mi><mo>=</mo><mo>"</mo><mi>un</mi><mo> </mo><mi>equilibrio</mi><mo> </mo><mi>perfecto</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sentidor</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>hacia</mi><mo> </mo><mi>la</mi><mo> </mo><mi>izquierda</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sentidof1</mi><mo>=</mo><mo>"</mo><mi>espontánea</mi><mo> </mo><mi>hacia</mi><mo> </mo><mi>la</mi><mo> </mo><mi>derecha</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>sentidof2</mi><mo>=</mo><mo>"</mo><mi>un</mi><mo> </mo><mi>equilibrio</mi><mo> </mo><mi>perfecto</mi><mo>"</mo></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Un proceso endotérmico (marque las opciones correctas) En un proceso endotérmico (marque las opciones correctas)

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Su incremento de entalpía es positivo

]]> Su incremento de entalpía es negativo

]]> El incremento de entropía es positivo

]]> El incremento de entropía es negativo

]]> La entropía no cambia

]]> Con esos datos no sabemos cómo variará la entropía

]]> Con esos datos no sabemos cómo variará la entalpía

]]> Será espontáneo a todas las temperaturas

]]> No será espontáneo nunca

]]> Será espontáneo por debajo de una cierta temperatura

]]> Será espontáneo por encima de una cierta temperatura

]]> Un proceso exotérmico (marque las opciones correctas) En un proceso exotérmico (marque las opciones correctas)

]]> 1.0000000 0.3333333 0 false true abc Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> Su incremento de entalpía es positivo

]]> Su incremento de entalpía es negativo

]]> El incremento de entropía es positivo

]]> El incremento de entropía es negativo

]]> La entropía no cambia

]]> Con esos datos no sabemos cómo variará la entropía

]]> Con esos datos no sabemos cómo variará la entalpía

]]> Será espontáneo a todas las temperaturas

]]> No será espontáneo nunca

]]> Será espontáneo por debajo de una cierta temperatura

]]> Será espontáneo por encima de una cierta temperatura

]]> 1º BACHILLERATO/QUÍMICA/TERMOQUÍMICA/TRABAJO DE EXPANSIÓN Al calentar cloruro de amonio sólido se Al calentar cloruro de amonio sólido se obtiene HCl_(g) y NH_3(g). Este proceso se hizo bajo una presión constante de #p atm, y los gases desprendidos ocuparon un volumen de #vol litros. La reacción es endotérmica y su calor de la reacción en estas condiciones es de #cre kJ. Hallar (en KJ) : a) ΔH b) Trabajo c) ΔU.

(1 atm= 101325 Pa)

]]> 1.0000000 0.3333333 0 0 ΔH = #entTrabajo = #traΔU = #enint]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vol</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>.</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>3</mn><mo>.</mo><mn>1</mn><mo>,</mo><mn>8</mn><mo>.</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ent</mi><mo>=</mo><mi>cre</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tra</mi><mo>=</mo><mo>-</mo><mi>p</mi><mo>*</mo><mn>101325</mn><mo>*</mo><mi>vol</mi><mo>/</mo><msup><mn>10</mn><mn>6</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enint</mi><mo>=</mo><mi>ent</mi><mo>+</mo><mi>tra</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Δ</mi><mi mathvariant="normal">H</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mspace linebreak="newline"/><mi mathvariant="normal">T</mi><mi>r</mi><mi>a</mi><mi mathvariant="normal">b</mi><mi>a</mi><mi mathvariant="normal">j</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mi>r</mi><mi>a</mi><mspace linebreak="newline"/><mi>Δ</mi><mi>U</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calor a volumen constante a partir de pres constante Al quemar #masa gramos de benceno líquido en una bomba calorimétrica a volumen constante se desprenden dióxido de carbono y agua líquida , a #te ºC, y una energía de #calor Kcal. Calcular el calor de combustión molar del benceno a presión constante y a esa temperatura en KJ/mol

(1 J = 0.24 cal)

]]> 1.0000000 0.3333333 0 0 #qp <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>masa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>10</mn><mo>,</mo><mn>30</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>calor</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>25</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>te</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>te</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qv</mi><mo>=</mo><mi>calor</mi><mo>*</mo><mn>1000</mn><mo>*</mo><mn>78</mn><mo>/</mo><mo>(</mo><mi>masa</mi><mo>*</mo><mn>0</mn><mo>.</mo><mn>24</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qp</mi><mo>=</mo><mo>-</mo><mi>qv</mi><mo>+</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>*</mo><mn>8</mn><mo>.</mo><mn>31</mn><mo>*</mo><mi>tk</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qp</mi><mo>=</mo><mi>qp</mi><mo>/</mo><mn>1000</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#qp</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.03))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option><option name="answer_parameter">true</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calor combustión vol constante En la reacción de combustión del propano (gas) #tc ºC y presión constante de #pre atm se forma dióxido de carbono y agua líquida. Se desprenden 529 Kcal/mol. Calcular el calor de reacción a volumen constante a la misma temperatura en KJ/mol

(1 J = 0.24 cal)

]]> 1.0000000 0.3333333 0 0 #qv <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qv</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>529</mn><mo>/</mo><mn>0</mn><mo>.</mo><mn>24</mn><mo>)</mo><mo>+</mo><mn>3</mn><mo>*</mo><mn>8</mn><mo>.</mo><mn>314</mn><mo>*</mo><mo>(</mo><mn>273</mn><mo>+</mo><mi>tc</mi><mo>)</mo><mo>/</mo><mn>1000</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#qv</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Diferencia entre qv y qp Indica, en cada caso, qué valor es mayor q_p o q_v

]]> 1.0000000 0.3333333 0 true Respuesta correcta

]]> Respuesta parcialmente correcta.

]]> Respuesta incorrecta.

]]> C₃H_{8 (g)} + O_{2 (g)} -> H₂O _(l) + CO_{2 (g)}

]]> qv C₃H_8 (g) + O_{2 (g)} -> H₂O _(g) + CO_{2 (g)}

]]> qp C₄H_10 (g) + O_{2 (g)} -> H₂O _(g) + CO_{2 (g)}

]]> qp C₄H_10 (g) + O_{2 (g)} -> H₂O _(l) + CO_{2 (g)}

]]> qv N_{2 (g)} + H_{2 (g)} -> NH_{3 (g)}

]]> qv H_{2 (g)} + O_{2 (g)} -> H₂O _(g)

]]> qv H_{2 (g)} + O_{2 (g)} -> H₂O _(l)

]]> qv C₆H₁₂O_{6 (s)} + 6 O₂ _(g) --> 6 CO_{2 (g)} + 6 H₂O _(l)

]]> Iguales <question/> En la reacción: N2(g) + 3 H2(g) → 2NH3(g) se desprend En la reacción: N_2(g) + 3 H_2(g) → 2NH_3(g) se desprenden #cre kJ cuando reacciona 1 mol de N_2(g) a volumen constante y a #tc ºC. ¿Cuál será el incremento de entalpía, en KJ, del proceso?

]]> 1.0000000 0.3333333 0 0 #enta]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>80</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tc</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>20</mn><mo>,</mo><mn>60</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tk</mi><mo>=</mo><mi>tc</mi><mo>+</mo><mn>273</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enta</mi><mo>=</mo><mo>-</mo><mi>cre</mi><mo>-</mo><mo>(</mo><mo>(</mo><mn>2</mn><mo>*</mo><mi>tk</mi><mo>*</mo><mn>8</mn><mo>.</mo><mn>31</mn><mo>)</mo><mo>/</mo><mn>1000</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo> </mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Quemar etanol entalpia Si en condiciones estándar se quema #ma gramos de etanol C₂ H₆ O _(l) con O_{2 (g)} para dar CO_{2 (g)} y agua líquida en un recipiente cerrado, se desprenden #ene kJ. Hallar enl incremento de entalpía estándar de combustión del etanol líquido en KJ/mol

DATOS:( A: C=12; O=16 H=1)

]]> 1.0000000 0.3333333 0 0 #enta]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ma</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ene</mi><mo>=</mo><mn>1334</mn><mo>*</mo><mi>ma</mi><mo>/</mo><mn>46</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tra</mi><mo>=</mo><mo>-</mo><mn>8</mn><mo>.</mo><mn>314</mn><mo>*</mo><mn>298</mn><mo>/</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enta</mi><mo>=</mo><mo>-</mo><mn>1334</mn><mo>.</mo><mn>0</mn><mo>+</mo><mi>tra</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Racción ,en int, entalpía y trabajo Al hacer una reacción a volumen constante, se desprendieron #qv kJ. Si la misma reacción se hace a presión constante se desprenden #qp kJ. Determinar para la reacción (en KJ) : a)ΔU b) ΔH c)Trabajo

]]> 1.0000000 0.3333333 0 0 ΔU = #enintΔH = #entaTrabajo = #tra]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qv</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>130</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>qp</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>180</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enint</mi><mo>=</mo><mo>-</mo><mi>qv</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>enta</mi><mo>=</mo><mo>-</mo><mi>qp</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tra</mi><mo>=</mo><mi>enint</mi><mo>-</mo><mi>enta</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Δ</mi><mi>U</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">i</mi><mi>n</mi><mi>t</mi><mspace linebreak="newline"/><mi>Δ</mi><mi mathvariant="normal">H</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>a</mi><mspace linebreak="newline"/><mi mathvariant="normal">T</mi><mi>r</mi><mi>a</mi><mi mathvariant="normal">b</mi><mi>a</mi><mi mathvariant="normal">j</mi><mi>o</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>t</mi><mi>r</mi><mi>a</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units">m, s, g, °, ', "</param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="inputCompound">true</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> trabajo expansión Un gas, que ocupa un volumen de #v1 litros, se expande a temperatura constante hasta ocupar un volumen de #v2 litros. Calcula el trabajo, en J, realizado por el gas cuando se expansiona contra una presión externa de #pre atm

(1 atm= 101325 Pa)

]]> 1.0000000 0.3333333 0 0 #tra <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>7</mn><mo>,</mo><mn>10</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pre</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>1</mn><mo>.</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>.</mo><mn>8</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tra</mi><mo>=</mo><mo>-</mo><mi>pre</mi><mo>*</mo><mn>101</mn><mo>.</mo><mn>325</mn><mo>*</mo><mo>(</mo><mi>v2</mi><mo>-</mo><mi>v1</mi><mo>)</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tra</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Vaporización (entalpía) Al vaporizarse una sustancia, a la temperatura de ebullición (#te ºC) y a la presión constante de #pa atm, se absorben #env Kcal/mol. El sistema realiza trabajo sobre la atmósfera que le rodea, a causa de la variación de volumen que tiene lugar cuando la sustancia pasa de líquido a vapor. Calcula el incremento de energía interna, en KJ, realizado por 1 mol de sustancia (masa molecular =38), sabiendo que su densidad en estado líquido a esa temperatura es de #dens g/cm³

(1 J = 0.24 cal)

]]> 1.0000000 0.3333333 0 0 #eni]]> <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>te</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>8</mn><mo>,</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>env</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dens</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>8</mn><mo>,</mo><mn>1</mn><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>voliq</mi><mo>=</mo><mn>38</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>/</mo><mi>dens</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vgas</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>082</mn><mo>*</mo><mo>(</mo><mi>te</mi><mo>+</mo><mn>273</mn><mo>)</mo><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>/</mo><mi>pa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>difvol</mi><mo>=</mo><mi>vgas</mi><mo>-</mo><mi>voliq</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tra</mi><mo>=</mo><mo>-</mo><mi>pa</mi><mo>*</mo><mi>difvol</mi><mo>*</mo><mn>101325</mn><mo>/</mo><mn>1000</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ental</mi><mo>=</mo><mi>env</mi><mo>/</mo><mn>0</mn><mo>.</mo><mn>24</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>eni</mi><mo>=</mo><mi>ental</mi><mo>+</mo><mi>tra</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">i</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Vaporización (trabajo) Al vaporizarse una sustancia, a la temperatura de ebullición (#te ºC) y a la presión constante de #pa atm, se absorben #env Kcal. El sistema realiza trabajo sobre la atmósfera que le rodea, a causa de la variación de volumen que tiene lugar cuando la sustancia pasa de líquido a vapor. Calcula el trabajo, en KJ, realizado por 1 mol de sustancia (masa molecular =38), sabiendo que su densidad en estado líquido a esa temperatura es de #dens g/cm³

(1 J = 0.24 cal; 1 atm= 101325 Pa)

]]> 1.0000000 0.3333333 0 0 #tra <question><wirisCasSession><![CDATA[<session lang="es" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>te</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>50</mn><mo>,</mo><mn>150</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pa</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>8</mn><mo>,</mo><mn>2</mn><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>env</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>dens</mi><mo>=</mo><mi>aleatorio</mi><mo>(</mo><mn>0</mn><mo>.</mo><mn>8</mn><mo>,</mo><mn>1</mn><mo>.</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>voliq</mi><mo>=</mo><mn>38</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>/</mo><mi>dens</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vgas</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>082</mn><mo>*</mo><mo>(</mo><mi>te</mi><mo>+</mo><mn>273</mn><mo>)</mo><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>3</mn></mrow></msup><mo>/</mo><mi>pa</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>difvol</mi><mo>=</mo><mi>vgas</mi><mo>-</mo><mi>voliq</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tra</mi><mo>=</mo><mo>-</mo><mi>pa</mi><mo>*</mo><mi>difvol</mi><mo>*</mo><mn>101325</mn><mo>/</mo><mn>1000</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer>#tra</correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", sr, E, K, mol, cd, rad, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(--log(0.02))</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>