1MA 04. VECTORS/1MA.04.5 Problemes amb vectors 1MA.04.5.11Q TrobarParàmetreAmbMòdul Quins són els valors de m que fan que el vector d'origen (#a1,#a2) i d'extrem (#b1,m) tingui mòdul #r?

Format de la resposta: {-2,4}

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]]> 1.0000000 0.5000000 0 0 #sol1]]> #sol2 <question><wirisCasSession><![CDATA[<session lang="ca" 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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>b1</mi><mo>-</mo><mi>a1</mi><mo>,</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mfenced close="‖" open="‖"><mi>v</mi></mfenced></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mo>-</mo><mn>2</mn><mo>*</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><msup><mi>a2</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b1</mi><mn>2</mn></msup><mo>-</mo><mn>2</mn><mo>*</mo><mi>a1</mi><mo>*</mo><mi>b1</mi><mo>-</mo><msup><mi>r</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>c</mi><mo>></mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>b1</mi><mo>-</mo><mi>a1</mi><mo>,</mo><mi>m</mi><mo>-</mo><mi>a2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mfenced close="‖" open="‖"><mi>v2</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>r2</mi><mo>=</mo><mi>r</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mo>{</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>R</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mo>{</mo><msub><mi>R</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>}</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>9</mn><mo>,</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>2</mn><mo>,</mo><mn>8</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>8</mn><mo>,</mo><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>m</mi><mo>=</mo><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>m</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></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><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn></math>]]></correctAnswer><correctAnswer id="1">#sol2</correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic" correctAnswer="1"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></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">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">50 50</data><data name="casSession"/></localData></question> Es calculen els components del vector, el seu mòdul i s'iguala al mòdul de l'enunciat.

Per treure l'arrel, s'eleva al quadrat.

]]> 1MA.04.5.12Q TrobarComponentsmbMòdulArgument Quins són els components cartesians del vectors de mòdul «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«/mrow»«/mstyle»«/math» i d'argument en radians «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math» ?

Format de la resposta: {[-2,4],[1,5]}

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]]> 1.0000000 0.5000000 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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"><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x1</mi><mo>,</mo><mi>x2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mfenced close="‖" open="‖"><mi>v</mi></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>atan</mi><mfenced><mfrac><mi>x2</mi><mi>x1</mi></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>tan</mi><mo>(</mo><mi>a1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><msup><mi>r</mi><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><msup><mi>x</mi><mn>2</mn></msup><mo>+</mo><msup><mi>y</mi><mn>2</mn></msup><mo>=</mo><msup><mi>r</mi><mn>2</mn></msup></mtd></mtr><mtr><mtd><mfrac><mi>y</mi><mi>x</mi></mfrac><mo>=</mo><mi>tan</mi><mo>(</mo><mi>a1</mi><mo>)</mo></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mfenced close="]" open="["><mrow><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mfenced close="]" open="["><mrow><msub><mi>R</mi><mrow><mn>2</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub><mo>,</mo><msub><mi>R</mi><mrow><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn></mrow></msub></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</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"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>89</mn></msqrt><mo>,</mo><mn>89</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>,</mo><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.5586</mn><mo>,</mo><mn>0.625</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>8.</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>5.</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>8.</mn><mo>,</mo><mi>y</mi><mo>=</mo><mn>5.</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>,</mo><mi>v2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>8.</mn><mo>,</mo><mo>-</mo><mn>5.</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mn>8.</mn><mo>,</mo><mn>5.</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="]" open="["><mrow><mo>-</mo><mn>8.</mn><mo>,</mo><mo>-</mo><mn>5.</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mn>8.</mn><mo>,</mo><mn>5.</mn></mrow></mfenced></mtd></mtr></mtable></mfenced></math></output></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><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></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">popupEditor</data><data name="gradeCompound">distribute</data><data name="gradeCompoundDistribution">50 50</data><data name="casSession"/></localData></question> Si x i y són els components dels vectors solució, has de resoldre el sistema:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mfrac»«mi mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»x«/mi»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»tg«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]> 1MA.04.5.15Q VectorPosició_Polars→cartesianes Quines són les coordenades cartesianes del punt associat al vector posició de mòdul #m i d'argument #a º?

Format de la resposta: [2.42,-3.24] arrodonides als centèsims amb punt, separades per coma. Les coordenades poden ser positives o negatives.

]]> 1.0000000 0.5000000 0 0 #v <question><wirisCasSession><![CDATA[<session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msqrt><mrow><msup><mi>a_1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a_2</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>85</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mn>100</mn><mo>*</mo><mi>m</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>a</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></mrow></mfenced></mrow><mn>100</mn></mfrac><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>v_2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mn>100</mn><mo>*</mo><mi>m</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>a</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></mrow></mfenced></mrow><mn>100</mn></mfrac><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>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v_1</mi><mo>,</mo><mi>v_2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>89</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>v_1</mi><mo>,</mo><mi>v_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7.63</mn><mo>,</mo><mn>5.55</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>7.63</mn><mo>,</mo><mn>5.55</mn></mrow></mfenced></math></output></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>v</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> x = #m · cos(#aº)
y = #m · sin(#aº)

]]> 1MA.04.5.16Q TrobarVectorSiC.L.Nul·laAmbAltre Calcula les components del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»u«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mstyle»«/math» si:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mover mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»u«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mover mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»v_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»
amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»v_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math»

Format de la resposta: [-3/5,6/5] (enters o fraccions simplificades)

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfenced close="|" open="|"><mi>n</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>c</mi><mo>,</mo><mi>d</mi></mrow></mfenced></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>n</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>v_1</mi><mo>-</mo><mi>n</mi><mo>*</mo><mi>v_2</mi></mrow><mi>m</mi></mfrac></mrow><mrow><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>v_1</mi><mo>+</mo><mfenced close="|" open="|"><mi>n</mi></mfenced><mo>*</mo><mi>v_2</mi></mrow><mi>m</mi></mfrac></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>n</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>s</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>s</mi><mo>=</mo><mo>"</mo><mo>-</mo><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>n</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>t</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow><mrow><mi>t</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_3</mi><mo>=</mo><mi>k</mi><mo>*</mo><mi>v_2</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>n</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>v_4</mi><mo>=</mo><mi>v_1</mi><mo>-</mo><mi>v_3</mi></mrow><mrow><mi>v_4</mi><mo>=</mo><mi>v_1</mi><mo>+</mo><mi>v_3</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></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>v_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>3</mn><mo>,</mo><mo>-</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>9</mn><mo>,</mo><mo>-</mo><mn>12</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>5</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Aïlla «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mover mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»u«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mstyle»«/math»:
a) Suma o resta #k · «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math» als dos membres: #m · «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math» = #v_1 #t #k · «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math»
b) Substitueix «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math» per #v_2: #m · «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math» = #v_1 #t #k · #v_2
fes la multiplicació: #m · «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math» = #v_1 #t #v_3
i després la suma/resta: #m · «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math» = #v_4
c) Divideix tot per #m

]]> 1MA.04.5.17Q TrobarVectorSabentC.L.AmbAltre Calcula les components del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»u«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/math» si:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mover mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»u«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mover mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»v_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»
amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»v_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math»

Format: [-3/5,6/5] (enters o fraccions simplificades)

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mfenced close="|" open="|"><mi>n</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a</mi><mo>,</mo><mi>b</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>c</mi><mo>,</mo><mi>d</mi></mrow></mfenced></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>n</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>v_1</mi><mo>-</mo><mi>n</mi><mo>*</mo><mi>v_2</mi></mrow><mi>m</mi></mfrac></mrow><mrow><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>v_1</mi><mo>+</mo><mfenced close="|" open="|"><mi>n</mi></mfenced><mo>*</mo><mi>v_2</mi></mrow><mi>m</mi></mfrac></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>n</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>s</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>s</mi><mo>=</mo><mo>"</mo><mo>-</mo><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>n</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>t</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow><mrow><mi>t</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_3</mi><mo>=</mo><mi>k</mi><mo>*</mo><mi>v_2</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>n</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>v_4</mi><mo>=</mo><mi>v_1</mi><mo>-</mo><mi>v_3</mi></mrow><mrow><mi>v_4</mi><mo>=</mo><mi>v_1</mi><mo>+</mo><mi>v_3</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>17</mn><mo>,</mo><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>16</mn><mo>,</mo><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>17</mn><mo>,</mo><mo>-</mo><mn>10</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>16</mn><mo>,</mo><mo>-</mo><mn>9</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>16</mn><mo>,</mo><mo>-</mo><mn>9</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mo>-</mo><mn>19</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><mn>1</mn><mn>9</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>19</mn><mn>9</mn></mfrac></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></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="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Aïlla «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mover mathcolor=¨#007F00¨»«mrow»«mi mathvariant=¨bold¨»u«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mstyle»«/math»:
a) Suma o resta #k · «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math» als dos membres: #m · «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math» = #v_1 #t #k · «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math»
b) Substitueix «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math» per #v_2: #m · «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math» = #v_1 #t #k · #v_2
fes la multiplicació: #m ·«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math» = #v_1 #t #v_3
i després la suma/resta: #m · «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«/math» = #v_4
c) Divideix tot per #m

]]> 1MA.04.5.21Q Valor de m per 3 punts alineats Per quin valor de m, els punts A (#x1,#y1), B(#x2,#y2) i C (m,#y3) estan alineats

Format de la resposta: nombre enter o fracció simplificada.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>x1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>y1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>y2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>x3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>y3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x2</mi><mo>-</mo><mi>x1</mi></mtd><mtd><mi>x3</mi><mo>-</mo><mi>x1</mi></mtd></mtr><mtr><mtd><mi>y2</mi><mo>-</mo><mi>y1</mi></mtd><mtd><mi>y3</mi><mo>-</mo><mi>y1</mi></mtd></mtr></mtable></mfenced></mtd></mtr></mtable><mrow><mfenced><mrow><mi>rang</mi><mo>(</mo><mi>A</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>x2</mi><mo>≠</mo><mi>x1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>y2</mi><mo>≠</mo><mi>y1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>x3</mi><mo>≠</mo><mi>x1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>y3</mi><mo>≠</mo><mi>y1</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mfenced><mtable><mtr><mtd><mi>x2</mi><mo>-</mo><mi>x1</mi></mtd><mtd><mi>m</mi><mo>-</mo><mi>x1</mi></mtd></mtr><mtr><mtd><mi>y2</mi><mo>-</mo><mi>y1</mi></mtd><mtd><mi>y3</mi><mo>-</mo><mi>y1</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi><mo>=</mo><mfenced close="|" open="|"><mi>M</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>x3</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>,</mo><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x2</mi><mo>,</mo><mi>y2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x3</mi><mo>,</mo><mi>y3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mtable><mtr><mtd><mo>-</mo><mn>3</mn></mtd><mtd><mi>m</mi><mo>+</mo><mn>3</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>6</mn></mtd><mtd><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>m</mi><mo>+</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></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="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Si estan alineats, els vectors «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mover mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»AB«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mover mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»AC«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mrow»«/mstyle»«/math» són dependents ja que tenen la mateixa direcció.

Cal doncs que el determinant de la matriu #M sigui igual a zero.

]]> 1MA.04.5.21Q VectorUnitariDependent Determina els components d’un vector unitari sabent que és perpendicular al vector (#a1,#a2).

Es recorda que el mòdul d'un vector unitari és 1.

Format de la resposta: [2,3] Simplificat

]]> 1.0000000 0.5000000 0 0 #sol2 #sol3 <question><wirisCasSession><![CDATA[<session lang="ca" 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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr></mtable><mrow><mfrac><mi>a1</mi><mi>a2</mi></mfrac><mo>∉</mo><integers/></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a1</mi><mo>,</mo><mi>a2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mfrac><mi>a3</mi><mi>a2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>=</mo><msup><mfenced><mi>a4</mi></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a6</mi><mo>=</mo><mn>1</mn><mo>+</mo><mi>a5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a7</mi><mo>=</mo><msqrt><mi>a6</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x</mi><mo>,</mo><mi>a4</mi><mo>*</mo><mi>x</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mi>a4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfenced close="‖" open="‖"><mi>v1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><msqrt><mrow><mn>1</mn><mo>+</mo><msup><mfenced><mi>a4</mi></mfenced><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mi>v1</mi><mi>m1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mi>v2</mi><mi>m2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mo>-</mo><mi>sol2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>6</mn><mo>,</mo><mo>-</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mi>x</mi><mo>,</mo><mfrac><mn>6</mn><mn>7</mn></mfrac><mo>*</mo><mi>x</mi></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>,</mo><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mrow><mn>85</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></msqrt><mn>7</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>85</mn></msqrt><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>,</mo><mi>sol2</mi><mo>,</mo><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><mrow><mn>7</mn><mo>*</mo><mi>x</mi></mrow><msqrt><mrow><mn>85</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></msqrt></mfrac><mo>,</mo><mfrac><mrow><mn>6</mn><mo>*</mo><mi>x</mi></mrow><msqrt><mrow><mn>85</mn><mo>*</mo><msup><mi>x</mi><mn>2</mn></msup></mrow></msqrt></mfrac></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mfrac><mrow><mn>7</mn><mo>*</mo><msqrt><mn>85</mn></msqrt></mrow><mn>85</mn></mfrac><mo>,</mo><mfrac><mrow><mn>6</mn><mo>*</mo><msqrt><mn>85</mn></msqrt></mrow><mn>85</mn></mfrac></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mrow><mn>7</mn><mo>*</mo><msqrt><mn>85</mn></msqrt></mrow><mn>85</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mrow><mn>6</mn><mo>*</mo><msqrt><mn>85</mn></msqrt></mrow><mn>85</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>6</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>,</mo><mi>a6</mi><mo>,</mo><mi>a7</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>36</mn><mn>49</mn></mfrac><mo>,</mo><mfrac><mn>85</mn><mn>49</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>85</mn></msqrt><mn>7</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol2</correctAnswer><correctAnswer id="1">#sol3</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="equivalent_symbolic"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic" correctAnswer="1"/></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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Sigui (x,y) el vector perpendicular.

El producte escalar ha de ser nul:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#8658;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»x«/mi»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»el«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»vector«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»`«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»escriu«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨»x«/mi»«/mrow»«/mfenced»«/mstyle»«/math»

]]> Ara cal que el mòdul del vector, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold-italic¨»x«/mi»«/mrow»«/mfenced»«/mstyle»«/math» , sigui 1.

Dividim pel mòdul: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#000066¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»x«/mi»«msqrt mathcolor=¨#000066¨»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»5«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»x«/mi»«msqrt mathcolor=¨#000066¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»6«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»7«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»x«/mi»«/mstyle»«/math»

El vector demanat és doncs:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mfrac»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»7«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»,«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»4«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»7«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»x«/mi»«/mrow»«/mfrac»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mfrac»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»7«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»,«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»7«/mn»«/mrow»«/mfrac»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

i es racionalitza, si cal!

]]> 1MA.04.5.50DT VECTORS EQUIPOL·LENTS

Vectors equipol·lents

Es diu que dos vectors són equipol·lents si tenen les mateixes components.
La relació d'equipol·lència R és una relació d'equivalència, ja que és:

simètrica (aRa),
reflexiva (si aRb, bRa)
transitiva (si aRb i bRc, aleshores bRc).

El conjunt de vectors equipol·lents a un vector donat constitueix una classe d'equivalència.

]]> 0.0000000 0.0000000 0 1MA.04.5.51 ExtremEquipol·lentOrigenDiferent Determina l'extrem d'un vector que té per origen A (#a_1,#a_2) i que és equipol·lent al vector (#b_1,#b_2).

Format de la resposta: [-5,3]

]]> 1.0000000 0.5000000 0 0 #v_42 <question><wirisCasSession><session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mi>b_1</mi><mo>+</mo><mi>a_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mi>b_2</mi><mo>+</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v_1</mi><mo>,</mo><mi>v_2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>v_1</mi><mo>,</mo><mi>v_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>9</mn><mo>,</mo><mn>8</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #v_42 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Com que són equipol·lents, tenen els mateixos components. Aleshores, cal aplicar: extrem = origen + vector: (#a_1 + #b_1, #a_2 + #b_2)

]]> 1MA.04.5.52 OrigenEquipol·lentExtremDiferent Determina l'origen d'un vector que té per extrem B (#a_1,#a_2) i que és equipol·lent al vector de components (#b_1,#b_2).

Format de la resposta: [-5,3]

]]> 1.0000000 0.5000000 0 0 #v_42 <question><wirisCasSession><session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mi>a_1</mi><mo>-</mo><mi>b_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mi>a_2</mi><mo>-</mo><mi>b_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v_1</mi><mo>,</mo><mi>v_2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>v_1</mi><mo>,</mo><mi>v_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>9</mn><mo>,</mo><mn>8</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #v_42 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Com que són equipol·lents tenen els mateixos components, aleshores només cal aplicar: origen = extrem - vector: (#a_1 - #b_1, #a_2 - #b_2)

]]> 1MA.04.5.60DT APLICACIÓ EQUIPOL·LÈNCIA

Aplicacions de l'equipol·lència

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0.0000000 0.0000000 0 1MA.04.5.61Q Punt mitjà Determina les coordenades del punt mitjà del segment AB amb A(#a_1,#a_2) i B(#b_1,#b_2).

Format de la resposta: [-5/2,3]

]]> Si no es demana de justificar-ho, les coordenades del punt mitjà també es poden calcular amb la semi-suma de les coordenades dels dos punts.

]]> 1.0000000 0.5000000 0 0 #v_42 <question><wirisCasSession><session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mfrac><mrow><mi>a_1</mi><mo>+</mo><mi>b_1</mi></mrow><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mfrac><mrow><mi>a_2</mi><mo>+</mo><mi>b_2</mi></mrow><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v_1</mi><mo>,</mo><mi>v_2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>v_1</mi><mo>,</mo><mi>v_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mfrac><mn>13</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>5</mn><mo>,</mo><mfrac><mn>13</mn><mn>2</mn></mfrac></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #v_42 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Si M és el punt mitjà, es compleix que AM = 1/2 AB
Un cop calculat el vector AM, el punt M és l'extrem del vector AM:
coneixes les seves components i el seu origen

]]> 1MA.04.5.62Q PuntSimètric Determina les coordenades del punt simètric de A respecte a B amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math» i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨»B«/mi»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math».

Format de la resposta: [-5,3]

]]> 1.0000000 0.5000000 0 0 #v_42 <question><wirisCasSession><session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>b_1</mi><mo>-</mo><mi>a_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>b_2</mi><mo>-</mo><mi>a_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>v_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi><mo>=</mo><mi>a_2</mi><mo>+</mo><mi>v_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>m_1</mi><mo>,</mo><mi>m_2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>v_1</mi><mo>,</mo><mi>v_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>,</mo><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m_1</mi><mo>,</mo><mi>m_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>,</mo><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>16</mn><mo>,</mo><mn>32</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #v_42 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Si M és el punt simètric, es compleix que AM = 2 AB = (#v_1, #v_2)
Un cop calculat el vector AM, el punt M és l'extrem del vector AM; coneixem les seves components (#v_1, #v_2) i el seu origen (#a_1, #a_2)

]]> 1MA.04.5.63Q PuntSimètricEnunciatDiferent Si el vector que uneix A i B és la meitat del vector que uneix A i C, quines són les coordenades de C amb A(#a_1,#a_2) i B(#b_1,#b_2)?

Format de la resposta: [-5,3]

]]> 1.0000000 0.5000000 0 0 #v_42 <question><wirisCasSession><session lang="ca" 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_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>b_1</mi><mo>-</mo><mi>a_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>b_2</mi><mo>-</mo><mi>a_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>v_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi><mo>=</mo><mi>a_2</mi><mo>+</mo><mi>v_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>m_1</mi><mo>,</mo><mi>m_2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>v_1</mi><mo>,</mo><mi>v_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>,</mo><mn>36</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m_1</mi><mo>,</mo><mi>m_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>,</mo><mn>32</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>16</mn><mo>,</mo><mn>32</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #v_42 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Es calculen les components del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»AC«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mover mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»AB«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/math».

Es calculen les coordenades de C fent servir que C és l'extrem del vector AC

]]> 1MA.04.5.64Q 4tVèrtexParal·lelogram Determina les coordenades de D en el paral·lelogram ABCD amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»C«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»

Format de la resposta: [-5,3]

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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"><apply><csymbol 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>30</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>30</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>,</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>v1</mi><mo>,</mo><mi>v2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>,</mo><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>0</mn><mo>,</mo><mo>-</mo><mn>8</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></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="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Si D és el quart vèrtex,
primer calculem les components del vector BA (#v1, #v2) que és equipol·lent a CD;
El vector CD és doncs (#v1, #v2), i D és l'extrem d'un vector (#v1, #v2) que té per origen (#c1,#c2)

#W

]]> 1MA.04.5.71Q Centre i radi d'una circumferència Quin és el centre i el radi d'una circumferència de diàmetre AB amb A(#a1,#a2) i B(#b1,#b2)?

Format de la resposta: centre: [-5,3] radi: 3/5

]]> 1.0000000 0.5000000 0 0 Centre=#sol1Radi=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mfenced><mrow><mi>a1</mi><mo>,</mo><mi>a2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mfrac><mrow><mi>a1</mi><mo>+</mo><mi>b1</mi></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mfrac><mrow><mi>a2</mi><mo>+</mo><mi>b2</mi></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mi>C</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mfrac><mrow><mi>b1</mi><mo>-</mo><mi>a1</mi></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mfrac><mrow><mi>b2</mi><mo>-</mo><mi>a2</mi></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mfenced close="‖" open="‖"><mi>u</mi></mfenced></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>r</mi><mo>></mo><mn>2</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>c1</mi><mo>,</mo><mi>c2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>20</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>20</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S1</mi><mo>,</mo><mi>B</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S1</mi><mo>,</mo><mi>C</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S1</mi><mo>,</mo><mi>circumferència</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>r</mi><mo>)</mo><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"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>5</mn><mn>2</mn></mfrac></math></output></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"><mi>C</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">e</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>R</mi><mi>a</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> El centre és el punt mitjà de AB.

El radi és la meitat del mòdul del vector AB.

]]> 1MA.04.5.72Q DividirSegmentEn4 Troba les coordenades dels punts que divideixen el segment AB en 4 segments iguals amb A(#a1,#a2), B(#b1,#b2)?

Format de la resposta: {[-5,3],[3,2],[6,3]} de més a prop a més lluny de A

]]> 1.0000000 0.5000000 0 0 #sol]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mfenced><mrow><mi>a1</mi><mo>,</mo><mi>a2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>b1</mi><mo>-</mo><mi>a1</mi><mo>,</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mfrac><mi>v1</mi><mn>4</mn></mfrac></mtd></mtr><mtr><mtd><mi>v3</mi><mo>=</mo><mfrac><mi>v1</mi><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mi>v4</mi><mo>=</mo><mfrac><mrow><mn>3</mn><mo>*</mo><mi>v1</mi></mrow><mn>4</mn></mfrac></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mfrac><mrow><mi>b1</mi><mo>-</mo><mi>a1</mi></mrow><mn>4</mn></mfrac></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mfrac><mrow><mi>b2</mi><mo>-</mo><mi>a2</mi></mrow><mn>4</mn></mfrac></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>D</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>d1</mi><mo>,</mo><mi>d2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mfrac><mrow><mi>b1</mi><mo>-</mo><mi>a1</mi></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mfrac><mrow><mi>b2</mi><mo>-</mo><mi>a2</mi></mrow><mn>2</mn></mfrac></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>E</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>e1</mi><mo>,</mo><mi>e2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>f1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mfrac><mrow><mn>3</mn><mo>*</mo><mfenced><mrow><mi>b1</mi><mo>-</mo><mi>a1</mi></mrow></mfenced></mrow><mn>4</mn></mfrac></mtd></mtr><mtr><mtd><mi>f2</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mfrac><mrow><mn>3</mn><mo>*</mo><mfenced><mrow><mi>b2</mi><mo>-</mo><mi>a2</mi></mrow></mfenced></mrow><mn>4</mn></mfrac></mtd></mtr><mtr><mtd><mi>F</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>f1</mi><mo>,</mo><mi>f2</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>a1</mi><mo>≠</mo><mi>b1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a2</mi><mo>≠</mo><mi>b2</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>f1</mi><mo>∈</mo><integers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>f2</mi><mo>∈</mo><integers/></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="]" open="["><mrow><mi>d1</mi><mo>,</mo><mi>d2</mi></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mi>e1</mi><mo>,</mo><mi>e2</mi></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mi>f1</mi><mo>,</mo><mi>f2</mi></mrow></mfenced></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>centre</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>20</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>20</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S1</mi><mo>,</mo><mi>B</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S1</mi><mo>,</mo><mi>D</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S1</mi><mo>,</mo><mi>E</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>V1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>S1</mi><mo>,</mo><mi>F</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></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"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>D</mi><mo>,</mo><mi>E</mi><mo>,</mo><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced><mo>,</mo><mfenced><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced><mo>,</mo><mfenced><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>1</mn></mrow></mfenced></mtd></mtr></mtable></mfenced></math></output></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>s</mi><mi>o</mi><mi>l</mi><mspace linebreak="newline"/></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> #V1

Si el primer punt és D, D és l'extrem d'un vector d'origen A i de longitud igual a 1/4 del vector AB.

Si el segon punt és E, E és l'extrem d'un vector d'origen A i de longitud igual a 1/2 del vector AB.

Si el tercer punt és F, F és l'extrem d'un vector d'origen A i de longitud igual a 3/4 del vector AB.

]]> 1MA.04.5.73Q ValorDe_m_ 2VecDependents Per quin valor de m, els vectors (#x_1,#y_1) i (m,#y_2) són dependents?

Format de la resposta: nombre enter o fracció simplificada.

]]> 1.0000000 0.5000000 0 0 #r_33]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_33</mi><mo>=</mo><mfrac><mrow><mi>x_1</mi><mo>*</mo><mi>y_2</mi></mrow><mi>y_1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>x_1</mi><mo>*</mo><mi>y_2</mi><mo>-</mo><mi>m</mi><mo>·</mo><mi>y_1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y_2</mi></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>r_33</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></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>r</mi><mo>_</mo><mn>33</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></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="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Si són dependents, cal que el determinant sigui 0.
Es calcula el determinant en funció de m:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»D«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»d«/mi»«/mrow»«/mstyle»«/math»

i es resol Determinant = 0.

]]> 1MA.04.5.74Q VectorPerpendicularUnitari Troba els components d'un vector unitari (de mòdul 1) perpendicular al vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»x_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»y_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

Format de la resposta: [2/3,-1/3]

]]> 1.0000000 0.3333333 0 0 #sol #sol2 <question><wirisCasSession><![CDATA[<session lang="ca" 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>x_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>x</mi><mo>,</mo><mi>y</mi><mo>)</mo><mo> </mo><mi>és</mi><mo> </mo><mi>perpendicular</mi><mo> </mo><mi>a</mi><mo> </mo><mo>(</mo><mi>x_1</mi><mo>,</mo><mi>y_1</mi><mo>)</mo></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mo>-</mo><mfrac><mi>x_1</mi><mi>y_1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>x</mi><mo>*</mo><msqrt><mrow><mn>1</mn><mo>+</mo><msup><mfenced><mi>k1</mi></mfenced><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="]" open="["><mrow><mfrac><mi>x</mi><mi>m</mi></mfrac><mo>,</mo><mfrac><mrow><mi>k1</mi><mo>*</mo><mi>x</mi></mrow><mi>m</mi></mfrac></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mo>-</mo><mi>sol</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>x_1</mi><mo>,</mo><mi>y_1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt><mo>*</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><msqrt><mn>2</mn></msqrt><mn>2</mn></mfrac></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer><correctAnswer id="1">#sol2</correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="equivalent_symbolic"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic" correctAnswer="1"/></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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Anomenem (x,y) el vector demanat

Si els vectors són perpendiculars, el seu producte escalar és zero.
Cal doncs resoldre: (#x_1) · x + (#y_1) · y = 0

]]> Del producte escalar se'n dedueix que el vector és [x,#k1·x].

Calcula el seu mòdul, i divideix els components pel mòdul per tal que sigui unitari.

CAL SIMPLIFICAR

]]> 1MA.04.5.75Q TriangleRectangle3Punts(paràmetre) Per a quin valor de m, el triangle que determinen els punts «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»C«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math» és rectangle en A?

Format de la resposta: enter o fracció simplificada: -5/2

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>x_1</mi><mo>=</mo><mi>b_1</mi><mo>-</mo><mi>a_1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>b_1</mi><mo>≠</mo><mi>a_1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y_1</mi><mo>=</mo><mi>b_2</mi><mo>-</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_2</mi><mo>=</mo><mi>m</mi><mo>-</mo><mi>a_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y_2</mi><mo>=</mo><mi>c_2</mi><mo>-</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mo>(</mo><mi>x_1</mi><mo>,</mo><mi>y_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mo>(</mo><mi>x_2</mi><mo>,</mo><mi>y_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_2</mi><mo>=</mo><mi>x_1</mi><mo>*</mo><mi>x_2</mi><mo>+</mo><mi>y_1</mi><mo>*</mo><mi>y_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>p_2</mi><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msub><mi>P</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn><mo>,</mo><mn>11</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>-</mo><mn>4</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>12</mn><mo>*</mo><mi>m</mi><mo>+</mo><mn>81</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>m</mi><mo>=</mo><mfrac><mn>27</mn><mn>4</mn></mfrac></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>27</mn><mn>4</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></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="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Si el triangle és rectangle en A els vectors «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mover mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»AB«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»x_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»,«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»y_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mover mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»AC«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»x_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»,«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mi»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»y_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»)«/mo»«/mrow»«/mstyle»«/math» són perpendiculars,
i el seu producte escalar és zero.
Cal doncs resoldre: (#x_1) · (#x_2) + (#y_1) · (#y_2) = 0

]]> 1MA.04.5.81Q PlaInclinatVectors El mòbil blau es troba sobre un pla inclinat que forma un angle de #aº amb la horitzontal:

El mòbil està sotmès al seu propi pes, P = #P N.

El vector P es pot escriure com la suma d'un vector paral·lel al pla, i d'un vector perpendicular al pla.

1. Quin és el mòdul de la força F?

2. Quin és el mòdul de la reacció del suport S₂?

3. Recorda que si una massa m està sotmesa a una força F, pateix una acceleració a tal que F = m·a. Si m = #m kg, quina és la seva acceleració? (arrodonida)

]]> 1.0000000 0.2500000 0 0 a)|F| =#sol1b) |S2| =#sol2c) a = #sol3]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>aleatori</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>a</mi><mo>=</mo><mn>5</mn><mo>*</mo><mi>aleatori</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>F</mi><mo>=</mo><mi>P</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>a</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>F</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S2</mi><mo>=</mo><mi>P</mi><mo>*</mo><mi>cos</mi><mo>(</mo><mi>a</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>S2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mfrac><mrow><mn>100</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></mrow><mn>1000</mn></mfrac><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>a3</mi><mo>=</mo><mfrac><mi>F</mi><mi>m</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>a3</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>70</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>50</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>F</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>53.623</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>54</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>45</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>67</mn></math></output></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"><mi>a</mi><mo>)</mo><mo>|</mo><mi>F</mi><mo>|</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>|</mo><msub><mi>S</mi><mn>2</mn></msub><mo>|</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><mi>a</mi><mo> </mo><mo>=</mo><mo> </mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>3</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question>

Fem descomposició del pes (AB) en dues direccions: una paral·lela al pla inclinat, l'altra perpendicular.

Considerem el triangle rectangle ACB rectangle en C. L'angle BAC és el complementari de l'angle α, i val doncs (180º-α).

És per això que l'angle ABC és igual a l'angle α ja que 180º - (180º -α) = α

Per determinar F (costat oposat a l'angle ABC) sabent la hipotenusa (P) i l'angle, només cal fer servir el sinus:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sin§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8201;«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»F«/mi»«mi mathvariant=¨bold¨»P«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8658;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»sin§#945;«/mi»«/math»

]]>

S₁ i S₂ han de ser iguals ja que el mòbil es manté sobre el suport.

En el triangle ADB, l'angle ABD és 90º-α (complementari de ABC) , i l'angle DAB = α (tercer angle del triangle rectangle ADB).

Si emprem l'angle α, S₁ és el costat adjacent i P la hipotenusa, i per tant:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cos§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mfrac mathcolor=¨#00007F¨»«msub»«mi mathvariant=¨bold¨»S«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mi mathvariant=¨bold¨»P«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8658;«/mo»«msub mathcolor=¨#00007F¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»S«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«msub mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»S«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cos§#945;«/mi»«/mstyle»«/math»

]]> «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»F«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mi mathvariant=¨bold¨»F«/mi»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«/math»

Com que F = #sol1 N, i m = #m, n'hi ha prou amb dividir per calcular a.

]]> 1MA.4.4.71Q Angle entre forces Una força de #n1 N té una direcció que forma un angle de #a1º amb l’eix horitzontal. Per sota l’eix horitzontal tenim una força de #n2 N; quina ha de ser la seva direcció si el cos al qual s’apliquen les dues forces té un moviment horitzontal.

Format: arrodonit

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" 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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>40</mn><mo>,</mo><mn>60</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>n2</mi><mo>></mo><mi>n1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mi>n1</mi><mo>*</mo><mi>sin</mi><mfenced><mrow><mi>a1</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mfenced><mrow><mi>asin</mi><mfrac><mrow><mi>n1</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>a1</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></mrow><mi>n2</mi></mfrac></mrow></mfenced><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>360</mn><mo>-</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi><mo>=</mo><mi>n2</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>a2</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>57</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>n1</mi><mo>,</mo><mi>n2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>30</mn><mo>,</mo><mn>60</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>,</mo><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25.16</mn><mo>,</mo><mn>25.16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25.16</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24.793</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>335</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</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>

Si la suma dels 2 vectors és un vector horitzontal, és que la suma de les components verticals (en verd) dels vectors és nul·la, i que per tant les components verticals són iguals i oposades.

Posa les dades de l'enunciat amb els cursors, i fes que el vector resultant (negre) sigui horitzontal (ordenada =0)

Es poden calcular les components verticals dels dos vectors amb el sinus de l'angle.

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La component vertical del vector vermell és #f1 = #n1 · sin#a1.

La component vertical del vector blau és #n2 pel sinus de l'angle que ens demanen.

]]> 1MA.4.4.72Q Forces làmpada penjada Volem penjar un llum a una certa distància del sostre d’una habitació. Per fer-ho, agafem una corda, hi lliguem el llum i la clavem pels extrems en dos punts del sostre separats per una distància de #d centímetres, de manera que els angles entre la corda i el sostre són de #A1^◦ i #B1^◦ a cada un dels extrems.

Si el pes de la làmpada és de #n N, quina força exerceix cada fil, CA i CB (arrodoneix a la unitat)

]]> 1.0000000 0.5000000 0 0 CA=#sol1CB=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" 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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>24</mn><mo>,</mo><mn>50</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>50</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>B1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>30</mn><mo>,</mo><mn>50</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>15</mn></mrow></mfenced></mtd></mtr></mtable><mrow><mi>B1</mi><mo>></mo><mi>A1</mi><mo>+</mo><mn>5</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>CA</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>A1</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>CB</mi><mo>=</mo><mi>n</mi><mo>*</mo><mi>sin</mi><mo>(</mo><mi>B1</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>CA</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>CB</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A1</mi><mo>,</mo><mi>B1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>36</mn><mo>,</mo><mn>46</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>25</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn></math></output></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"><mi>C</mi><mi>A</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>C</mi><mi>B</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</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>