1MA 05. RECTES EN EL PLA/1MA.05.1 Equacions de la recta/1MA.05.1.3 InterconversióEq 1MA.05.1.3.10DT CART/EXPL→PARAM  

De cartesiana/explícita a paramètriques
Passa, si cal, la cartesiana a explícita: y = mx + n
Ja tens les equacions paramètriques: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»mk«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»
]]> 0.0000000 0.0000000 0 1MA.05.1.3.11Q Cartesiana→Paramètriques Troba les equacions paramètriques de la recta que té per equació cartesiana 

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«/mrow»«/mstyle»«/math»

 

Paràmetre: k

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]]> 1.0000000 0.5000000 0 0 x=#x1y=#y1]]> <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>C</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</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></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><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></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>A</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>B</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>C</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>A</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>B</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>C</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mo>-</mo><mfrac><mi>A</mi><mi>B</mi></mfrac><mo>*</mo><mi>k</mi><mo>-</mo><mfrac><mi>C</mi><mi>B</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>9</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>2</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</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>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><mi>k</mi><mo>+</mo><mfrac><mn>2</mn><mn>9</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>x</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</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> Substituïm: x = k 

Si es substitueix x per k en #e, trobem l'equació #e1. A partir de #e1, si aïllem la y, trobem l'equació paramètrica que correspon a y.

]]> 1MA.05.1.3.12Q Cartesiana→Paramètriques Troba les equacions paramètriques de  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«/mstyle»«/math»

 

Paràmetre: k

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]]> 1.0000000 0.5000000 0 0 x=#x1y=#y1]]> <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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>C</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><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>B</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/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo><mo>≠</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>C</mi><mo>,</mo><mi>B</mi><mo>)</mo><mo>≠</mo><mn>1</mn></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"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>A</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>B</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>C</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mi>A</mi><mi>B</mi></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mi>C</mi><mi>B</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mo>-</mo><mfrac><mi>A</mi><mi>B</mi></mfrac><mo>*</mo><mi>k</mi><mo>-</mo><mfrac><mi>C</mi><mi>B</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</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>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>*</mo><mi>k</mi><mo>-</mo><mfrac><mn>2</mn><mn>3</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>x</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></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> Transforma l'equació cartesiana a explícita: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«/mrow»«/mstyle»«/math»

x = k és la primera equació paramètrica.

Substitueix x  per k en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«/mstyle»«/math», i tens  la segona equació paramètrica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»y«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«/mrow»«/mstyle»«/math»

]]> 1MA.05.1.3.15Q Explícita→Paramètriques Troba les equacions paramètriques de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«/mstyle»«/math»

Paràmetre: k

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]]> 1.0000000 0.5000000 0 0 x=#x1y=#y1]]> <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>m</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></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>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></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>y</mi><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>e1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</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>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>1</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>x</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</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> x = k és la primera equació paramètrica.

Substitueix  x per k en l'equació  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»e«/mi»«/mrow»«/mstyle»«/math», i ja tens  la segona equació paramètrica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«/mrow»«/mstyle»«/math»

]]> 1MA.05.1.3.50DT PARAM ↔ CONT  

De paramètriques a contínua i viceversa
Per passar de paramètriques a contínua, s'identifica el punt (xA,yA) i el vector (xV,yV) i s'escriu la contínua
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub mathcolor=¨#FF0000¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»x«/mi»«mi mathvariant=¨bold¨»V«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub mathcolor=¨#FF0000¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»y«/mi»«mi mathvariant=¨bold¨»V«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8658;«/mo»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Punt«/mi»«mfenced mathcolor=¨#0000FF¨»«mrow»«msub»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mo mathvariant=¨bold¨»,«/mo»«msub»«mi mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«/mrow»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»Vector«/mi»«mfenced mathcolor=¨#FF0000¨»«mrow»«msub»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»v«/mi»«/msub»«mo mathvariant=¨bold¨»,«/mo»«msub»«mi mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»v«/mi»«/msub»«/mrow»«/mfenced»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8658;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»Cont§#237;nua«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»:«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«/mrow»«msub mathcolor=¨#FF0000¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»x«/mi»«mi mathvariant=¨bold¨»V«/mi»«/msub»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»-«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«/mrow»«msub mathcolor=¨#FF0000¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»y«/mi»«mi mathvariant=¨bold¨»V«/mi»«/msub»«/mfrac»«mspace linebreak=¨newline¨/»«mrow mathcolor=¨#191919¨»«mfenced open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»9«/mn»«mi mathvariant=¨bold-italic¨»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨»§#8658;«/mo»«mfenced open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi mathvariant=¨bold¨»P«/mi»«mi mathvariant=¨bold¨»u«/mi»«mi mathvariant=¨bold¨»n«/mi»«mi mathvariant=¨bold¨»t«/mi»«mfenced»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»V«/mi»«mi mathvariant=¨bold¨»e«/mi»«mi mathvariant=¨bold¨»c«/mi»«mi mathvariant=¨bold¨»t«/mi»«mi mathvariant=¨bold¨»o«/mi»«mi mathvariant=¨bold¨»r«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/mfenced»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨»§#8658;«/mo»«mi mathvariant=¨bold¨»C«/mi»«mi mathvariant=¨bold¨»o«/mi»«mi mathvariant=¨bold¨»n«/mi»«mi mathvariant=¨bold¨»t«/mi»«mi mathvariant=¨bold¨»§#237;«/mi»«mi mathvariant=¨bold¨»n«/mi»«mi mathvariant=¨bold¨»u«/mi»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»:«/mo»«mfrac»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«mn mathvariant=¨bold¨»9«/mn»«/mfrac»«/mrow»«/mstyle»«/math»
Per passar de contínua a paramètriques, s'identifica el punt (xA,yA) i el vector (xV,yV) i s'escriuen les paramètriques
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#00007F¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«/mrow»«msub mathcolor=¨#FF0000¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»x«/mi»«mi mathvariant=¨bold¨»V«/mi»«/msub»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»-«/mo»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«/mrow»«msub mathcolor=¨#FF0000¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»y«/mi»«mi mathvariant=¨bold¨»V«/mi»«/msub»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8658;«/mo»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi mathcolor=¨#0000FF¨ mathvariant=¨bold¨»Punt«/mi»«mfenced mathcolor=¨#0000FF¨»«mrow»«msub»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mo mathvariant=¨bold¨»,«/mo»«msub»«mi mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«/mrow»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mi mathcolor=¨#FF0000¨ mathvariant=¨bold¨»Vector«/mi»«mfenced mathcolor=¨#FF0000¨»«mrow»«msub»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»v«/mi»«/msub»«mo mathvariant=¨bold¨»,«/mo»«msub»«mi mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»v«/mi»«/msub»«/mrow»«/mfenced»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8658;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»P«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»r«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»a«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»m«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»§#232;«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»t«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»r«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»i«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»q«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»u«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»e«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»s«/mi»«mfenced mathcolor=¨#00007F¨ open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«msub mathcolor=¨#0000FF¨»«mi mathcolor=¨#0000FF¨ mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub mathcolor=¨#FF0000¨»«mi mathcolor=¨#FF0000¨ mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»V«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«msub mathcolor=¨#0000FF¨»«mi mathcolor=¨#0000FF¨ mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub mathcolor=¨#FF0000¨»«mi mathcolor=¨#FF0000¨ mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»V«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mspace linebreak=¨newline¨/»«mfrac mathcolor=¨#191919¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#191919¨»=«/mo»«mfrac mathcolor=¨#191919¨»«mrow»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«mn mathvariant=¨bold¨»9«/mn»«/mfrac»«mo»§#8658;«/mo»«mtable mathcolor=¨#191919¨ columnalign=¨left¨»«mtr»«mtd»«mi mathvariant=¨bold¨»Punt«/mi»«mfenced»«mrow»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/mfenced»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»Vector«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»,«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mrow»«/mfenced»«/mtd»«/mtr»«/mtable»«mo»§#8658;«/mo»«mi»P«/mi»«mi»a«/mi»«mi»r«/mi»«mi»a«/mi»«mi»m«/mi»«mi»§#232;«/mi»«mi»t«/mi»«mi»r«/mi»«mi»i«/mi»«mi»q«/mi»«mi»u«/mi»«mi»e«/mi»«mi»s«/mi»«mfenced mathcolor=¨#191919¨ open=¨{¨ close=¨¨»«mrow»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»9«/mn»«/mtd»«/mtr»«/mtable»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«/mrow»«/mfenced»«/mstyle»«/math»
]]> 0.0000000 0.0000000 0 1MA.05.1.3.51Q Paramètriques→Contínua Escriu l'equació contínua de  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

]]>  La resposta correcta és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #sol1 <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>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</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>v2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</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>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>v2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow><mi>v1</mi></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mi>a2</mi></mrow><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>1</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"><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>1</mn><mn>5</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>#sol1</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></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> Has d'escriure l'equació contínua «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mfrac»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«/mrow»«msub»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»v«/mi»«/msub»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»-«/mo»«msub»«mi mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«/mrow»«msub»«mi mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»v«/mi»«/msub»«/mfrac»«/mrow»«/mfenced»«/mstyle»«/math» d'una recta sabent-ne un punt A i el seu vector director: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»A«/mi»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»i«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mover»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨»=«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

 

]]> 1MA.05.1.3.52Q Explícita→Paramètriques Troba les equacions paramètriques de la recta que té per equació explícita, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«/mrow»«/mstyle»«/math»

Paràmetre: k

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]]> 1.0000000 0.5000000 0 0 x=#x1y=#y1]]> <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>m</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></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>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></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>y</mi><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>e1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>k</mi><mo>+</mo><mi>n</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</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>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>8</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>1</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>x</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</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> x = k és la primera equació paramètrica.

Si substituïm x per k en l'equació explícita #e, trobem l'equació #e1 que és la segona equació paramètrica.

]]> 1MA.05.1.3.53Q Contínua→Paramètriques Escriu les equacions paramètriques de  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

Paràmetre: k

]]> 1.0000000 0.5000000 0 0 x=#x1y=#y1]]> <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>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</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>v2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</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>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>v2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow><mi>v1</mi></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mi>a2</mi></mrow><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>1</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"><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>2</mn><mn>3</mn></mfrac><mo>=</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>1</mn><mn>5</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>x</mi><mo>=</mo><mo>#</mo><mi>x</mi><mn>1</mn><mspace linebreak="newline"/><mi>y</mi><mo>=</mo><mo>#</mo><mi>y</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_equations"/></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> Has d'escriure les equacions paramètriques «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨{¨ close=¨¨»«mtable columnalign=¨left¨»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«msub»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»v«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«msub»«mi mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub»«mi mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»v«/mi»«/msub»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» d'una recta sabent-ne un punt A i el seu vector director: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»A«/mi»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»i«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mover»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨»=«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

 

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