geometria plana/vectors
angle entre vectors (graus)
Caluleu l'angle que formen els vectors «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«mo»#«/mo»«mi»u«/mi»«/math» i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«mo»#«/mo»«mi»v«/mi»«/math», arrodonint el resultat al primer decimal.]]>
1.0000000
0.3333333
0
0
#a
<question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Angle</mi><mo> </mo><mi>entre</mi><mo> </mo><mi>vectors</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r0</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mo> </mo><mi>aleatori</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mrow><mrow><mfenced close="‖" open="‖"><mi>u</mi></mfenced><mo>!</mo><mo>=</mo><mn>0</mn></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">repeat</csymbol><mrow><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mrow><mrow><mfenced close="‖" open="‖"><mi>v</mi></mfenced><mo>!</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mi>acos</mi><mo>(</mo><mi>u</mi><mo>*</mo><mi>v</mi><mo>/</mo><mo>(</mo><mfenced close="‖" open="‖"><mi>u</mi></mfenced><mo>*</mo><mfenced close="‖" open="‖"><mi>v</mi></mfenced><mo>)</mo><mo>)</mo><mo>*</mo><mn>180</mn><mo>/</mo><pi/><mo>*</mo><mn>10</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn><mo>)</mo></mrow></mfenced><mo>/</mo><mn>10</mn><mo>.</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>a</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>
Operacions amb vectors
Siguin els vectors «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«mo»#«/mo»«mi»u«/mi»«/math», «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«mo»#«/mo»«mi»v«/mi»«/math», «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»w«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«mo»#«/mo»«mi»w«/mi»«/math» . Calculeu: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»#«/mo»«mi»a«/mi»«mo»§#160;«/mo»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»b«/mi»«mo»§#160;«/mo»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«mo»)«/mo»«mo»+«/mo»«mo»(«/mo»«mo»#«/mo»«mi»c«/mi»«mo»§#160;«/mo»«mover»«mi»w«/mi»«mo»§#8594;«/mo»«/mover»«mo»)«/mo»«/math»]]>
1.0000000
0.3333333
0
0
#resul]]>
<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>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r0</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mo> </mo><mi>aleatori</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mrow><mrow><mfenced close="‖" open="‖"><mi>u</mi></mfenced><mo>!</mo><mo>=</mo><mn>0</mn></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">repeat</csymbol><mrow><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mrow><mrow><mfenced close="‖" open="‖"><mi>v</mi></mfenced><mo>!</mo><mo>=</mo><mn>0</mn></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">repeat</csymbol><mrow><mi>w</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mrow><mrow><mfenced close="‖" open="‖"><mi>w</mi></mfenced><mo>!</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>r0</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>r0</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>r0</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resul</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>u</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>v</mi><mo>+</mo><mi>c</mi><mo>*</mo><mi>w</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>u</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></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"></data></localData></question>
Perímetre d'un triangle
Calculeu el perímetre del triangle de vèrtex: #A, #B i #C, arrodonint el resultat al primer decimal.]]>
1.0000000
0.3333333
0
0
#peri]]>
<question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Perímetre</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>un</mi><mo> </mo><mi>triangle</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mrow><mrow><mfenced close="‖" open="‖"><mi>u</mi></mfenced><mo>!</mo><mo>=</mo><mn>0</mn></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">repeat</csymbol><mrow><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mrow><mrow><mfenced close="‖" open="‖"><mi>v</mi></mfenced><mo>!</mo><mo>=</mo><mn>0</mn><mo>∧</mo><mo>(</mo><mi>v</mi><mo>.</mo><mn>1</mn><mo>/</mo><mi>u</mi><mo>.</mo><mn>1</mn><mo>!</mo><mo>=</mo><mi>v</mi><mo>.</mo><mn>2</mn><mo>/</mo><mi>u</mi><mo>.</mo><mn>2</mn><mo>)</mo></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>P</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>P</mi><mo>+</mo><mi>u</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mi>P</mi><mo>+</mo><mi>v</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>peri</mi><mo>=</mo><mfenced close="⌋" open="⌊"><mrow><mo>(</mo><mfenced close="‖" open="‖"><mrow><mi>B</mi><mo>-</mo><mi>A</mi></mrow></mfenced><mo>+</mo><mfenced close="‖" open="‖"><mrow><mi>C</mi><mo>-</mo><mi>B</mi></mrow></mfenced><mo>+</mo><mfenced close="‖" open="‖"><mrow><mi>C</mi><mo>-</mo><mi>A</mi></mrow></mfenced><mo>)</mo><mo>*</mo><mn>10</mn><mo>.</mo><mo>+</mo><mn>0</mn><mo>.</mo><mn>5</mn></mrow></mfenced><mo>/</mo><mn>10</mn><mo>.</mo></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>p</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi mathvariant="normal">i</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>
producte escalar de vectors
Siguin els vectors «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«mo»#«/mo»«mi»u«/mi»«/math» i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«mo»#«/mo»«mi»v«/mi»«/math». Calculeu «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«mo»§#183;«/mo»«mover»«mi»v«/mi»«mo»§#8594;«/mo»«/mover»«/math»]]>
1.0000000
0.3333333
0
0
#resul]]>
<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>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r0</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mo> </mo><mi>aleatori</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mrow><mrow><mfenced close="‖" open="‖"><mi>u</mi></mfenced><mo>!</mo><mo>=</mo><mn>0</mn></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">repeat</csymbol><mrow><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mrow><mrow><mfenced close="‖" open="‖"><mi>v</mi></mfenced><mo>!</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>resul</mi><mo>=</mo><mi>v</mi><mo>*</mo><mi>u</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>s</mi><mi>u</mi><mi>l</mi></math>]]></correctAnswer><correctAnswer id="1"></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"></data></localData></question>
Punt d'un segment
EL segment determinat pels punts #A i #B el dividim en #a segments de la mateixa llargada. Quin és el punt de separació entre el #s segments?]]>
1.0000000
0.3333333
0
0
#C
<question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Punt</mi><mo> </mo><mi>d</mi><mo>'</mo><mi>un</mi><mo> </mo><mi>segment</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tros</mi><mo>=</mo><mo>{</mo><mo>"</mo><mi>dos</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>tres</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>quatre</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>cinc</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>sis</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>set</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>vuit</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>nou</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>deu</mi><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>separa</mi><mo>=</mo><mo>{</mo><mo>"</mo><mi>primer</mi><mo> </mo><mi>i</mi><mo> </mo><mi>segon</mi><mo> </mo><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>segon</mi><mo> </mo><mi>i</mi><mo> </mo><mi>tercer</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>tercer</mi><mo> </mo><mi>i</mi><mo> </mo><mi>quart</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>quart</mi><mo> </mo><mi>i</mi><mo> </mo><mi>cinquè</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>cinquè</mi><mo> </mo><mi>i</mi><mo> </mo><mi>sisè</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>sisè</mi><mo> </mo><mi>i</mi><mo> </mo><mi>setè</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>setè</mi><mo> </mo><mi>i</mi><mo> </mo><mi>vuitè</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>vuitè</mi><mo> </mo><mi>i</mi><mo> </mo><mi>novè</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>novè</mi><mo> </mo><mi>i</mi><mo> </mo><mi>desè</mi><mo>"</mo><mo>}</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo> </mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>10</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><mn>1</mn><mo>.</mo><mo>.</mo><mo>(</mo><mi>a</mi><mo>-</mo><mn>1</mn><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>separa</mi><mo>.</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mo>[</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mo>[</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mo>(</mo><mo>(</mo><mi>a</mi><mo>-</mo><mi>b</mi><mo>)</mo><mo>*</mo><mi>A</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>B</mi><mo>)</mo><mo>/</mo><mi>a</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#C</correctAnswer><correctAnswer id="1"></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"></data></localData></question>
Punts alineats
Decidiu si els punts #A, #B i #C estan alineats.]]>
1.0000000
0.3333333
0
true
true
abc
#sol]]>
#solo]]>
<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>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mn>0</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rrr</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>r</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>rr</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>aa</mi><mo>=</mo><mi>rrr</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mo>[</mo><mi>a</mi><mo>,</mo><mi>f</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>+</mo><mi>aa</mi><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><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mi>a</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>bb</mi><mo>=</mo><mi>rrr</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mo>[</mo><mi>b</mi><mo>,</mo><mi>f</mi><mo>(</mo><mi>b</mi><mo>)</mo><mo>+</mo><mi>bb</mi><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><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo><mo>/</mo><mo>{</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>cc</mi><mo>=</mo><mi>rrr</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>=</mo><mo>[</mo><mi>c</mi><mo>,</mo><mi>f</mi><mo>(</mo><mi>c</mi><mo>)</mo><mo>+</mo><mi>cc</mi><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mi>B</mi><mo>-</mo><mi>A</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mi>C</mi><mo>-</mo><mi>A</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><mo>(</mo><mi>u</mi><mo>.</mo><mn>1</mn><mo>/</mo><mi>v</mi><mo>.</mo><mn>1</mn><mo>)</mo><mo>=</mo><mo>=</mo><mo>(</mo><mi>u</mi><mo>.</mo><mn>2</mn><mo>/</mo><mi>v</mi><mo>.</mo><mn>2</mn><mo>)</mo></mrow><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>SI</mi></mtd></mtr><mtr><mtd><mi>solo</mi><mo>=</mo><mi>NO</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol</mi><mo>=</mo><mi>NO</mi></mtd></mtr><mtr><mtd><mi>solo</mi><mo>=</mo><mi>SI</mi></mtd></mtr></mtable></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer></correctAnswer></correctAnswers><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question>
vector paral·lel amb mòdul determinat
Quin seria un vector paral·lel a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«mo»#«/mo»«mi»u«/mi»«/math» amb mòdul #m?]]>
1.0000000
0.3333333
0
0
#w
<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>nota</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>v</mi><mo>=</mo><mo>=</mo><mo>[</mo><mi>w</mi><mo>]</mo><mo>)</mo><mo> </mo><mo>∨</mo><mo> </mo><mo>(</mo><mi>v</mi><mo>=</mo><mo>=</mo><mo>-</mo><mo>[</mo><mi>w</mi><mo>]</mo><mo>)</mo></mrow><mrow><mi>tornar</mi><mo> </mo><mn>1</mn></mrow><mrow><mi>tornar</mi><mo> </mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rm</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mo> </mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>defineixo</mi><mo> </mo><mi>un</mi><mo> </mo><mi>vector</mi><mo> </mo><mi>no</mi><mo> </mo><mi>nul</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mrow><mrow><mfenced close="‖" open="‖"><mi>u</mi></mfenced><mo>!</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>defineixo</mi><mo> </mo><mi>el</mi><mo> </mo><mi>mòdul</mi><mo> </mo><mi>del</mi><mo> </mo><mi>vector</mi><mo> </mo><mi>demanat</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>rm</mi><mo>(</mo><mo>)</mo></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>calculo</mi><mo> </mo><mi>el</mi><mo> </mo><mi>vector</mi><mo> </mo><mi>demanat</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mi>u</mi><mo>/</mo><mfenced close="‖" open="‖"><mi>u</mi></mfenced><mo>*</mo><mi>m</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>w</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer><correctAnswer id="2"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">nota</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>
vector perpendicular amb mòdul determinat
Calcula un vector perpendicaular a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover»«mi»u«/mi»«mo»§#8594;«/mo»«/mover»«mo»=«/mo»«mo»#«/mo»«mi»u«/mi»«/math» que tingui mòdul #m]]>
1.0000000
0.3333333
0
0
#w
<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>nota</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>:</mo><mo>=</mo><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">begin</csymbol><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mo>(</mo><mi>v</mi><mo>=</mo><mo>=</mo><mo>[</mo><mi>w</mi><mo>]</mo><mo>)</mo><mo> </mo><mo>∨</mo><mo> </mo><mo>(</mo><mi>v</mi><mo>=</mo><mo>=</mo><mo>-</mo><mo>[</mo><mi>w</mi><mo>]</mo><mo>)</mo></mrow><mrow><mi>tornar</mi><mo> </mo><mn>1</mn></mrow><mrow><mi>tornar</mi><mo> </mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>rm</mi><mo>(</mo><mo>)</mo><mo>:</mo><mo>=</mo><mo> </mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>r</mi><mo>(</mo><mo>)</mo><mo>,</mo><mi>r</mi><mo>(</mo><mo>)</mo></mrow></mfenced></mrow><mrow><mfenced close="‖" open="‖"><mi>u</mi></mfenced><mo>!</mo><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>rm</mi><mo>(</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>uu</mi><mo>=</mo><mo>[</mo><mi>u</mi><mo>.</mo><mn>2</mn><mo>,</mo><mo>-</mo><mi>u</mi><mo>.</mo><mn>1</mn><mo>]</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w</mi><mo>=</mo><mi>uu</mi><mo>/</mo><mfenced close="‖" open="‖"><mi>uu</mi></mfenced><mo>*</mo><mi>m</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>w</mi></math>]]></correctAnswer><correctAnswer id="1"></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_function"><param name="name">nota</param></assertion></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question>