1MA 05. RECTES EN EL PLA/1MA.05.0 Preguntes teòriques 1MA.05.0.11 PT Equacions paramètriques Escriu les equacions paramètriques d'una recta que passa pel punt [a,b] i que té per vector director [v,w], si el paràmetre és k.
Format de la resposta: {x=a-k,y=a+k} (les dues equacions entre claus, separades per coma)

]]> 1.0000000 0.5000000 0 0 #r_1 <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>r_1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>v</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>w</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>a</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>v</mi><mo>,</mo><mi>y</mi><mo>=</mo><mi>b</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>w</mi></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"> #r_1 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> 1MA.05.0.12 PT Equació contínua Escriu l'equació contínua d'una recta que passa pel punt [a,b] i que té per vector director [v,w].

]]> 1.0000000 0.5000000 0 0 #r_1 <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>r_1</mi><mo>=</mo><mfrac><mrow><mi>x</mi><mo>-</mo><mi>a</mi></mrow><mi>v</mi></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mi>b</mi></mrow><mi>w</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mo>-</mo><mi>a</mi><mo>+</mo><mi>x</mi></mrow><mi>v</mi></mfrac><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>+</mo><mi>y</mi></mrow><mi>w</mi></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"> #r_1 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> 1MA.05.0.13 PT Pas de contínua a cartesiana Per passar de l'equació contínua a l'equació cartesiana, cal

]]> 1.0000000 0.5000000 0 false true abc treure denominadors amb el mcm

]]> aïllar la y

]]> multiplicar en creu

]]> transposar tots els termes a l'esquerra del signe igual

]]> 1MA.05.0.14 PT Vector a partir de les equacions Un vector director de la recta (x,y) = (a,b) + k·(v,w) és ({1:SA: ~=v}, {1:SA: ~=w})

Un vector director de la recta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced close=¨¨ open=¨{¨»«mtable»«mtr»«mtd»«mi»x«/mi»«mo»=«/mo»«mi»k«/mi»«mi»z«/mi»«mo»+«/mo»«mi»m«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi»y«/mi»«mo»=«/mo»«mi»k«/mi»«mi»t«/mi»«mo»+«/mo»«mi»n«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»és ({1:SA: ~=z}, {1:SA: ~=t})
Un vector director de la recta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mi»e«/mi»«/mrow»«mi»p«/mi»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»-«/mo»«mi»f«/mi»«/mrow»«mi»q«/mi»«/mfrac»«/math» és ({1:SA: ~=p}, {1:SA: ~=q})

Un vector director de la recta Gx + Hy + I és ({1:SA: ~=-H}, {1:SA: ~=G})

Un vector director de la recta y= rx + s és ({1:SA: ~=1}, {1:SA: ~=r})

]]> 0.3333333 0 1MA.05.0.15 PT Punt a partir de les equacions Un punt de la recta (x,y) = (a,b) + k·(v,w) és ({1:SA: ~=a}, {1:SA: ~=b})

Un punt de la recta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfenced mathcolor=¨#007F00¨ open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»k«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»z«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mi mathvariant=¨bold¨»k«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»t«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»és ({1:SA: ~=m}, {1:SA: ~=n})
Un punt de la recta «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#007F00¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«mi mathvariant=¨bold¨»p«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mfrac mathcolor=¨#007F00¨»«mrow»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«mi mathvariant=¨bold¨»q«/mi»«/mfrac»«/math» és ({1:SA: ~=e}, {1:SA: ~=f})

Per trobar un punt de la recta Gx + Hy + I podem substituir y per k i {1:MC: ~aïllar y~=aïllar x}

Per trobar un punt de la recta y= rx + s, substituïm x per k i {1:MC: ~aïllem x~=aïllem y})

]]> 0.3333333 0 1MA.05.0.21 PT paral·lelisme i vectors Si dues rectes són paral·leles, el {1:MC: ~producte escalar ~=determinant} dels seus vectors directors és nul.

]]> 1.0000000 0 1MA.05.0.22 PT paral·lelisme i sistema Si dues rectes són paral·leles,
el sistema d'equacions és {1:MC: ~compatible ~=incompatible}.

]]> 1.0000000 0 1MA.05.0.51 PT RectesPerpendicularsProdEscalar Si dues rectes són perpendiculars, el {1:MC: ~determinant ~=producte escalar} dels seus vectors directors és zero.

]]> 0.5000000 0 1MA.05.0.52 PT RectesPerpendicularsac+bd Si dues rectes de vectors directors (a,b) i (c,d) són perpendiculars, {1:MC: ~ad-bc ~=ac+bd} = 0.

]]> 1.0000000 0 1MA.05.0.53 PT Vdir de RectaPerpendicular a una altra Si una recta és perpendicular a una recta de vector director (a,b), el seu vector director pot ser ({1:SA: ~=-b}, {1:SA: ~=a})

]]> 0.5000000 0 1MA.05.0.54 PT pendent de RectaPerpendicular a una altra Si una recta és perpendicular a una recta de pendent m, el seu pendent és {1:SA: ~=-1/m}

]]> 1.0000000 0 1MA.05.0.61 PT Posició relativa i sistema Si dues rectes es tallen en un punt, el sistema d'equacions és {1:MC: ~compatible indeterminat~incompatible~=compatible determinat}.

Si dues rectes són paral·leles, el sistema d'equacions és {1:MC: ~compatible indeterminat~=incompatible~compatible determinat}.

Si dues rectes són coincidents, el sistema d'equacions és {1:MC: ~=compatible indeterminat~incompatible~compatible determinat}.

]]> 0.3333333 0 1MA.05.0.62 PT Posició relativa i vectors Si dues rectes es tallen en un punt, els seus vectors directors són {1:MC: ~dependents~=independents}.

Si dues rectes són paral·leles o coincidents, els seus vectors directors són {1:MC: ~ ~=dependents~independents}.

]]> 0.5000000 0 1MA.05.0.63 PT Posició relativa,vectors i determinant Si dues rectes es tallen en un punt, els seus vectors directors són {1:MC: ~dependents~=independents}. El {1:MC: ~producte escalar~=determinant} dels vectors directors és {1:MC: ~zero~=diferent de zero}

Si dues rectes són paral·leles o coincidents, els seus vectors directors són {1:MC: ~ ~=dependents~independents}. El {1:MC: ~producte escalar~=determinant} dels vectors directors és {1:MC: ~=zero~diferent de zero}

]]> 0.3333333 0 1MA.05.0.71 PT angle entre dues rectes Completa la fórmula per calcular el cosinus de l'angle que formen les dues rectes de vectors directors (a,b) i (c,d):

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨normal¨»cos«/mi»«mo»§nbsp;«/mo»«mi»§#945;«/mi»«mo»§nbsp;«/mo»«mo»=«/mo»«/math»
Utilitza a,b,c, i d per la resposta

]]> 1.0000000 0.5000000 0 0 #r_1 <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>r_1</mi><mo>=</mo><mfrac><mrow><mi>a</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi></mrow><mrow><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt><mo>*</mo><msqrt><mrow><msup><mi>c</mi><mn>2</mn></msup><mo>+</mo><msup><mi>d</mi><mn>2</mn></msup></mrow></msqrt></mrow></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mi>a</mi><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>d</mi></mrow><mrow><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><msup><mi>b</mi><mn>2</mn></msup></mrow></msqrt><mo>*</mo><msqrt><mrow><msup><mi>c</mi><mn>2</mn></msup><mo>+</mo><msup><mi>d</mi><mn>2</mn></msup></mrow></msqrt></mrow></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"> #r_1 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> 1MA.05.0.81 PT Distància entre dos punts Completa la frase:

La distància entre els punts A i B és el {1:SA: ~=mòdul} del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#007F00¨»«mi mathvariant=¨bold¨»AB«/mi»«mo»§#8594;«/mo»«/mover»«/math»

]]> 1.0000000 0 1MA.05.0.83 PT distància entre punt i recta Completa la fórmula per calcular la distància entre el punt P(m,n) i la recta d'equació Ax+By+C=0

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»d«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»,«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«/math»
Utilitza A,B,C, m i n per la resposta

]]> 1.0000000 0.5000000 0 0 #r_1 <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>r_1</mi><mo>=</mo><mfrac><mfenced close="&verbar;" open="&verbar;"><mrow><mi>A</mi><mo>*</mo><mi>m</mi><mo>+</mo><mi>B</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>C</mi></mrow></mfenced><msqrt><mrow><msup><mi>A</mi><mn>2</mn></msup><mo>+</mo><msup><mi>B</mi><mn>2</mn></msup></mrow></msqrt></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced close="&verbar;" open="&verbar;"><mrow><mi>A</mi><mo>*</mo><mi>m</mi><mo>+</mo><mi>B</mi><mo>*</mo><mi>n</mi><mo>+</mo><mi>C</mi></mrow></mfenced><msqrt><mrow><msup><mi>A</mi><mn>2</mn></msup><mo>+</mo><msup><mi>B</mi><mn>2</mn></msup></mrow></msqrt></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"> #r_1 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> 1MA 05. RECTES EN EL PLA/1MA.05.1 Equacions de la recta/1MA.05.1.1 Vect, Param, Cont 1MA.05.1.1.10 TEORIA Equacions vec_param_cont

Amb un punt A(x_A,y_A) i un vector (x_V,y_V)

Equació vectorial

(x,y) = (x_A,y_A) + k· (x_V,y_V)

]]> 0.0000000 0.0000000 0 1MA.05.1.1.11Q EqVectorial(A,v) Quina és l'equació vectorial de la recta que passa pel punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«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»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math» i que té per vector director «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¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfenced mathcolor=¨#003300¨»«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»?

Format: punts i vector amb claudàtors [2,3]; paràmetre: k

Amb un punt A(x_A,y_A) i un vector (x_V,y_V)

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»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»§#955;«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msub mathcolor=¨#FF0000¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»x«/mi»«mi mathvariant=¨bold¨»V«/mi»«/msub»«/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»«mi mathvariant=¨bold¨»§#955;«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msub mathcolor=¨#FF0000¨»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»y«/mi»«mi mathvariant=¨bold¨»V«/mi»«/msub»«/mtd»«/mtr»«/mtable»«/mfenced»«/math»

]]> 0.0000000 0.0000000 0 1MA.05.1.1.21Q EqParamètriques(A,v) Quines són les equacions paramètriques de la recta que passa pel punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«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»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math» i que té per vector director «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¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfenced mathcolor=¨#003300¨»«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»? (paràmetre: k)

]]> 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="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>9</mn><mo>,</mo><mn>9</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>9</mn><mo>,</mo><mn>9</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>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>v2</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>A</mi><mo>=</mo><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>sol1</mi><mo>=</mo><mi>x</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>sol2</mi><mo>=</mo><mi>y</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"/></input></command></group></library><group><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>3</mn><mo>,</mo><mn>0</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</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>x1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>3</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"><mo>-</mo><mi>k</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><mi>x</mi><mo>,</mo><mi>y</mi></mrow></mfenced><mo>=</mo><mfenced close="]" open="["><mrow><mn>7</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>3</mn><mo>,</mo><mo>-</mo><mi>k</mi></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><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><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_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> Els coeficients de k són #v1 i #v2

]]> 1MA.05.1.1.22Q EqParamètriques(A,v)_2 Quines són les equacions paramètriques de la recta que passa pel punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow mathcolor=¨#003300¨»«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»«/mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»i que té per vector director «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¨»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»?

Format: {x=k-3,y=2k+6)

]]> 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="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>9</mn><mo>,</mo><mn>9</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>9</mn><mo>,</mo><mn>9</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>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>v2</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>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>b1</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>v1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>v2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>v1</mi><mo>*</mo><mi>k</mi><mo>,</mo><mi>y</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>v2</mi><mo>*</mo><mi>k</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>b1</mi><mo>+</mo><mi>v1</mi><mo>*</mo><mi>k</mi><mo>,</mo><mi>y</mi><mo>=</mo><mi>b2</mi><mo>+</mo><mi>v2</mi><mo>*</mo><mi>k</mi></mtd></mtr></mtable></mfenced></math></input></command></group></library><group><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"><mfenced><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>6</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>13</mn></mrow></mfenced></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><mo>-</mo><mn>1</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>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>7</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>6</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><mi>x</mi><mo>=</mo><mo>-</mo><mi>k</mi><mo>-</mo><mn>3</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>7</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>13</mn></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>#sol1</mo><mspace linebreak="newline"/><mspace linebreak="newline"/><mspace linebreak="newline"/></math>]]></correctAnswer><correctAnswer id="1">#sol2</correctAnswer></correctAnswers><assertions><assertion name="equivalent_equations"/><assertion name="syntax_expression"/><assertion name="equivalent_equations" correctAnswer="1"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> només cal multiplicar k pels components del vector i sumar les coordenades de A

]]> 1MA.05.1.1.30DT EQ CONTÍNUA

Amb un punt A(x_A,y_A) i un vector (x_V,y_V)

Equació contínua

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#003300¨»«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=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«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»«/math»

]]> 0.0000000 0.0000000 0 1MA.05.1.1.31Q EqContínua(A,v) Quina l'equació contínua de la recta que passa pel punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold-italic¨»A«/mi»«mfenced»«mrow»«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»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math» i que té per vector director «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¨»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»?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathcolor=¨#FF0000¨ mathvariant=¨bold¨»(«/mo»«mo mathcolor=¨#FF0000¨ mathvariant=¨bold¨»#«/mo»«mi mathcolor=¨#FF0000¨ mathvariant=¨bold¨»a«/mi»«mn mathcolor=¨#FF0000¨ mathvariant=¨bold¨»1«/mn»«mo mathcolor=¨#FF0000¨ mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mo mathcolor=¨#007F00¨ mathvariant=¨bold¨»#«/mo»«mi mathcolor=¨#007F00¨ mathvariant=¨bold¨»v«/mi»«mn mathcolor=¨#007F00¨ mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathcolor=¨#FF0000¨ mathvariant=¨bold¨»(«/mo»«mo mathcolor=¨#FF0000¨ mathvariant=¨bold¨»#«/mo»«mi mathcolor=¨#FF0000¨ mathvariant=¨bold¨»a«/mi»«mn mathcolor=¨#FF0000¨ mathvariant=¨bold¨»2«/mn»«mo mathcolor=¨#FF0000¨ mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mo mathcolor=¨#007F00¨ mathvariant=¨bold¨»#«/mo»«mi mathcolor=¨#007F00¨ mathvariant=¨bold¨»v«/mi»«mn mathcolor=¨#007F00¨ mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/math»

]]> 1MA.05.1.1.32Q EqContínua(A,v)_2 Quina l'equació contínua de la recta que passa pel punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold-italic¨»A«/mi»«mfenced»«mrow»«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»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math» i que té per vector director «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¨»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»?

El vector en els denominadors.

]]> 1MA.05.1.1.33Q EqContínua(A,B) Quina és l'equació contínua de la recta que passa pels punt A«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«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 B «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«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»«/mrow»«/mstyle»«/math»?

]]>

Es resten les coordenades del punt A en els numeradors
I en els denominadors els components del vector AB

El vector es calcula amb extrem(B) - origen(A).

]]> 1MA 05. RECTES EN EL PLA/1MA.05.1 Equacions de la recta/1MA.05.1.2 Cart, Expl 1MA.05.1.2.40DT EQ CARTESIANA

A partir de l'equació contínua

Equació cartesiana

1. Es calcula el mcm (el mcm és sempre positiu)

2. Es redueixen les fraccions a denominador comú (multiplicant els numeradors pel mateix nombre amb el qual s'ha multiplicat el denominador)

3. S'eliminen els denominadors i es transposen tots els termes a l'esquerra.

Exemple: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«mn»1«/mn»«/mrow»«mn»9«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi mathvariant=¨normal¨»y«/mi»«mo»-«/mo»«mn»3«/mn»«/mrow»«mn»15«/mn»«/mfrac»«mo»§#8660;«/mo»«mfrac»«mrow»«mn»5«/mn»«mo»(«/mo»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«mn»1«/mn»«mo»)«/mo»«/mrow»«mn»45«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»(«/mo»«mi mathvariant=¨normal¨»y«/mi»«mo»-«/mo»«mn»3«/mn»«mo»)«/mo»«/mrow»«mn»45«/mn»«/mfrac»«/mrow»«/mstyle»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn»5«/mn»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«mn»5«/mn»«mo»=«/mo»«mn»3«/mn»«mi mathvariant=¨normal¨»y«/mi»«mo»-«/mo»«mn»9«/mn»«mo»§#8660;«/mo»«mn mathvariant=¨bold¨»5«/mn»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»3«/mn»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»14«/mn»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»0«/mn»«/mrow»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1MA.05.1.2.41Q Contínua→Cartesiana Troba l'equació cartesiana de la recta que té per equació contínua (emprant el mcm):

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

]]> La recta és #G1

El mcm és #mc.
Multipliquem el numerador de la 1a fracció per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/math»
Multipliquem el numerador de la 2a fracció per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»n«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/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»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold-italic¨»y«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«/math»

i traiem els denominadors:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/math»

]]> Un cop trets els denominadors, queda:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle displaystyle=¨false¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/mstyle»«/math»

Només cal treure els parèntesis:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle displaystyle=¨false¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mstyle»«/math»

I transposar-ho tot a l'esquerra del signe =.

]]> 1MA.05.1.2.42Q EqCartesiana(A,v) Troba l'equació cartesiana de la recta que passa per «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 que té per vector director «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«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»«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»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»

]]> La recta és #G1

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#0000FF¨»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/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»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Treu denominadors amb el seu mcm i transposa-ho tot a l'esquerra.

]]> 1MA.05.1.2.510DT EQ EXPLÍCITA

A partir de l'equació cartesiana

Equació explícita

A partir de l'equació cartesiana, s'aïlla la y.

Exemple: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn»3«/mn»«mi mathvariant=¨normal¨»x«/mi»«mo»+«/mo»«mn»2«/mn»«mi mathvariant=¨normal¨»y«/mi»«mo»-«/mo»«mn»6«/mn»«mo»=«/mo»«mn»0«/mn»«mo»§#8660;«/mo»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mstyle»«/math»

També es pot aïllar a partir de l'equació contínua

]]> 0.0000000 0.0000000 0 1MA.05.1.2.511Q Cartesiana→Explícita Troba l'equació explicita de la recta que té per equació cartesiana:

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

]]> La recta és #G1

Un vector director és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mover mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo»§#160;«/mo»«mo»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«/mstyle»«/math»

]]> 1MA.05.1.2.512Q Explícita(A,v) Troba l'equació explícita de la recta que passa per «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 que té per vector director «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«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»«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»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»

]]> La recta és #G1

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/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¨»p«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/math»

Es treuen denominadors, posant com a denominador comú el mcm de #v1 i #v2:

El mcm és #mc.
Multipliquem el numerador de la 1a fracció per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/math»
Multipliquem el numerador de la 2a fracció per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»n«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»mc«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/math»

i traiem els denominadors:

]]> Un cop trets els denominadors, queda:

Només cal treure els parèntesis:

I aïllar la y.

]]> 1MA.05.1.2.520DT 2 PUNTS→EXPLÍCITA

AMB 2 PUNTS A i B

Equació explícita

Es troba m i n per substitució

Exemple: L'equació explícita y=mx+n de la recta que passa per A(1,-1) i B(3,5) es troba substituint x i y per les coordenades dels punts: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo»-«/mo»«mn»1«/mn»«/mtd»«mtd»«mo»=«/mo»«mi»m«/mi»«mo»+«/mo»«mi»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mn»5«/mn»«/mtd»«mtd»«mo»=«/mo»«mn»3«/mn»«mi»m«/mi»«mo»+«/mo»«mi»n«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo»§#8660;«/mo»«mfenced open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi»m«/mi»«mo»=«/mo»«mn»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi»n«/mi»«mo»=«/mo»«mo»-«/mo»«mn»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mstyle»«/math»

i l'equació és y = 3x-4

]]> 0.0000000 0.0000000 0 1MA.05.1.2.521Q Explícita(A,B) Troba l'equació explícita de la recta que passa per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathcolor=¨#003300¨ mathvariant=¨bold¨»A«/mi»«mo mathcolor=¨#003300¨ mathvariant=¨bold¨»(«/mo»«mo mathcolor=¨#003300¨ mathvariant=¨bold¨»#«/mo»«mi mathcolor=¨#003300¨ mathvariant=¨bold¨»a«/mi»«mn mathcolor=¨#003300¨ mathvariant=¨bold¨»1«/mn»«mo mathcolor=¨#003300¨ mathvariant=¨bold¨»,«/mo»«mo mathcolor=¨#003300¨ mathvariant=¨bold¨»#«/mo»«mi mathcolor=¨#003300¨ mathvariant=¨bold¨»a«/mi»«mn mathcolor=¨#003300¨ mathvariant=¨bold¨»2«/mn»«mo mathcolor=¨#003300¨ mathvariant=¨bold¨»)«/mo»«/mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»i«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«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»«/mstyle»«/math»

]]> La recta és #G1

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«mtd»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«mtd»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Pots comprovar el pendent m que has trobat amb el vector director «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«/mrow»«/mstyle»«/math»

]]> 1MA.05.1.2.530DT VECTOR AMB COMPONENT NUL·LA

Amb un punt A(x_A,y_A) i un vector (0,y_V)

Si el vector és del tipus (0,3) és un vector vertical, i la recta és una recta vertical d'equació y = y_A (perquè passa pel punt!)

Amb un punt A(x_A,y_A) i un vector (x_V,0)

Si el vector és del tipus (0,5), és un vector horitzontal, i la recta és una recta horitzontal d'equació x = x_A(perquè passa pel punt!)

]]> 0.0000000 0.0000000 0 1MA.05.1.2.531Q RectaHoritzontal Quina és l'equació de la recta que passa pel punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow mathcolor=¨#003300¨»«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»«/mrow»«/mstyle»«/math» i que té per vector director «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 mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mstyle»«/math»?

]]> La recta és #G1

]]> 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="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><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>a2</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>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><mn>0</mn></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>sol</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>11</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>11</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi></mrow></mfenced></math></input></command></group></library><group><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"><mfenced><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mn>1</mn></mrow></mfenced></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>3</mn><mo>,</mo><mn>0</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"><mi>y</mi><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"><mi>y</mi><mo>=</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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_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> Com que el vector director és horitzontal, la recta és una recta horitzontal d'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«/mstyle»«/math» perquè passa pel punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»)«/mo»«/mrow»«/mstyle»«/math»:

#G1

]]> 1MA.05.1.2.531Q RectaVertical Quina és l'equació de la recta que passa pel punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow mathcolor=¨#003300¨»«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»«/mrow»«/mstyle»«/math» i que té per vector director «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 mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«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»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mstyle»«/math»?

]]> La recta és #G1

]]> 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="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><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>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>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>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><mn>0</mn><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>sol</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>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>11</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>11</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>10</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><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"><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mn>0</mn></mrow></mfenced></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>0</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>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>=</mo><mo>-</mo><mn>5</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"><mi>x</mi><mo>=</mo><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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_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> Com que el vector director és vertical, la recta és una recta vertical d'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«/mstyle»«/math» perquè passa pel punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»)«/mo»«/mrow»«/mstyle»«/math»:

#G1

]]> 1MA.05.1.2.540 GràficExplícita Quin és el gràfic que correspon a la recta d'equació: «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»?

]]> 1.0000000 0.5000000 0 true true abc #r_1 #r_2 #r_3 #r_4 <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><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><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>aleatori</mi><mo>(</mo><mo>{</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mfenced close="|" open="|"><mi>a</mi></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>a</mi><mo>></mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>d</mi><mo>=</mo><mo>"</mo><mi>amunt</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mo>"</mo><mi>positiu</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>d</mi><mo>=</mo><mo>"</mo><mi>avall</mi><mo>"</mo></mtd></mtr><mtr><mtd><mi>q1</mi><mo>=</mo><mo>"</mo><mi>negatiu</mi><mo>"</mo></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>=</mo><mo>-</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><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>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><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>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T3</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><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>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T4</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><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>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T1</mi><mo>,</mo><mi>f</mi><mo>(</mo><mi>x</mi><mo>)</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>g</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T3</mi><mo>,</mo><mi>h</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T4</mi><mo>,</mo><mi>i</mi><mo>(</mo><mi>x</mi><mo>)</mo></mrow></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>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T5</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><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>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>mostrar_eixos</mi><mo>=</mo><mi>fals</mi><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>0</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m3</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>1</mn><mo>,</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m4</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>a</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M</mi><mo>=</mo><mi>triangle</mi><mo>(</mo><mi>m1</mi><mo>,</mo><mi>m2</mi><mo>,</mo><mi>m3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T5</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>m1</mi><mo>,</mo><mi>m2</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>etiqueta</mi><mo>=</mo><mn>1</mn><mo>,</mo><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>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T5</mi><mo>,</mo><mi>segment</mi><mo>(</mo><mi>m2</mi><mo>,</mo><mi>m3</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>etiqueta</mi><mo>=</mo><mi>a</mi><mo>,</mo><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>T6</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mo>{</mo><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>12</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>12</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G3</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T6</mi><mo>,</mo><mi>m4</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>10</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></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></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>1</mn></math></output></command><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>3</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>t</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</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>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler4</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> Si l'equació de la recta és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«/mrow»«/mstyle»«/math»:

l'ordenada a l'origen és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/mi»«/mrow»«/mstyle»«/math»: la recta talla l'eix vertical en «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mn mathvariant=¨bold¨»0«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfenced»«/mstyle»«/math». #G3
el pendent és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«/mrow»«/mstyle»«/math» «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/math», vol dir que si ens movem 1 unitat cap a la dreta, sobre la recta ens movem «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math» unitats cap #d: #G2

]]> 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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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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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 (x_V,y_V) 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 (x_V,y_V) 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

]]>

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»

]]> 1MA 05. RECTES EN EL PLA/1MA.05.1 Equacions de la recta/1MA.05.1.4 Eq→ VectPuntPend 1MA.05.1.4.10DT EQRECTA→PUNTIVECTOR

Deduir vector i punt
Equació vectorial: (x,y)=(x_A,y_A)+ k· (x_V,y_V)	Punt (x_A,y_A). Vector = (x_V,y_V)
Equacions paramètriques: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨¨»«mtable»«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»«mi mathvariant=¨bold¨»k«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»V«/mi»«/msub»«/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»«mi mathvariant=¨bold¨»k«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«msub»«mi mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»V«/mi»«/msub»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»	Punt (x_A,y_A); vector = (x_V,y_V)
Equació contínua: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«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¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«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»«/mstyle»«/math»	Punt (x_A,y_A); vector = (x_V,y_V)
Equació cartesiana: ax + by + c = 0	Punt (0,-c/b); vector= (-b,a)
Equació explícita: y = mx+n	Punt (0,n); vector = (1,m)
La cartesiana i l'explícita es poden transformar a paramètriques per a determinar un punt i un vector!

]]> 0.0000000 0.0000000 0 1MA.05.1.4.11Q Paramètriques→Punt+Vector A partir de les equacions, determina un punt i un vector 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-italic¨»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-italic¨»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»

Format: punt = (1,2) i vector = [1,2]

]]> 1.0000000 0.5000000 0 0 punt=#sol1vector=#sol2]]> <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><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>sol2</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>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>p</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</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_equations"/></assertions><options><option name="tolerance">10^(-2)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> Les coordenades del punt són els termes independents i els components del vector són els coeficients de k.

]]> 1MA.05.1.4.12Q Contínua→Punt+Vector A partir de les equacions, determina un punt i un vector de:

Format: punt(2,3) i vector [2,3]

]]> 1.0000000 0.5000000 0 0 punt=#sol1vector=#sol2]]> <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><mi>A</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>v</mi></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>p</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</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_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> El punt està restant en els numeradors.

Els components del vector són els denominadors

]]> 1MA.05.1.4.13Q Cartesiana→Punt+vector Troba el punt d'abscissa zero i el vector que es dedueix dels coeficients de la recta d'equació: «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»

Format del punt (0,2) i del vector: [-1,2]

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]]> 1.0000000 0.5000000 0 0 Punt=#pVector=#v]]> <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>x1</mi><mo>=</mo><mo>-</mo><mfrac><mi>B</mi><mi>A</mi></mfrac><mo>*</mo><mi>k</mi><mo>-</mo><mfrac><mi>C</mi><mi>A</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mi>C</mi><mi>A</mi></mfrac><mo>,</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mo>-</mo><mfrac><mi>B</mi><mi>A</mi></mfrac><mo>,</mo><mn>1</mn></mrow></mfenced></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>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>8</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"><mfrac><mn>3</mn><mn>5</mn></mfrac><mo>*</mo><mi>k</mi><mo>+</mo><mfrac><mn>8</mn><mn>5</mn></mfrac></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"><mi>k</mi></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="["><mrow><mfrac><mn>8</mn><mn>5</mn></mfrac><mo>,</mo><mn>0</mn></mrow></mfenced></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><mfrac><mn>3</mn><mn>5</mn></mfrac><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 type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi>V</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo>=</mo><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> El punt es calcula amb (0,-c/b) i el vector és [-b,a]

]]> 1MA.05.1.4.14Q Explícita→ Punt+Vector Troba un punt i un vector de la recta d'equació: «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»

Format del punt (0,2) i del vector [1,3]

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]]> 1.0000000 0.5000000 0 0 Punt=#pVector=#v]]> <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>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><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mi>n</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><mn>1</mn><mo>,</mo><mi>m</mi></mrow></mfenced></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>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</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>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>p</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>0</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced></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>1</mn><mo>,</mo><mo>-</mo><mn>3</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"><mi>P</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>p</mi><mspace linebreak="newline"/><mi>V</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo>=</mo><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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> De l'equació explícita y = mx + n es dedueix que el punt és (0,n) i el vector és [1,m]

]]> 1MA.05.1.4.20DT TROBAR PENDENT

Determinar el pendent

Els pendents es dedueixen:

si tenim el vector, en les equacions vectorial, paramètriques i contínua, el pendent és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«msub»«mi»y«/mi»«mi»v«/mi»«/msub»«msub»«mi»x«/mi»«mi»v«/mi»«/msub»«/mfrac»«/math»
En l'equació cartesiana Ax + By + C = 0, el pendent és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»-«/mo»«mfrac»«mi»A«/mi»«mi»B«/mi»«/mfrac»«/math»
En l'equació contínua y = mx + n, el pendent és m

]]> 0.0000000 0.0000000 0 1MA.05.1.4.20Q Equació→Pendent Determina el pendent de les rectes
a) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«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»«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¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x_«/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¨»y_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»k«/mi»«/mrow»«/mstyle»«/math» b) «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»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mrow»«/mstyle»«/math» c) «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»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«/mrow»«/mstyle»«/math» d) «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»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«/mrow»«/mstyle»«/math» e) «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»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»5«/mn»«/mrow»«/mstyle»«/math»

Format de la resposta: enter o fracció simplificada

]]> 1.0000000 0.3333333 0 0 a. =#m1b. =#m2c. =#m3d. =#m4e. =#m5]]> <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>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><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>x_2</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></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x_3</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>x_4</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>x_5</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>y_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>y_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>y_3</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>y_4</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>y_5</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>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>a_3</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>v_1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x_1</mi><mo>,</mo><mi>y_1</mi></mrow></mfenced></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>v_3</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x_3</mi><mo>,</mo><mi>y_3</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_4</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>x_4</mi><mo>,</mo><mi>y_4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_5</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mi>x_5</mi></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>e_2</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>x_2</mi><mo>*</mo><mi>k</mi></mtd></mtr><mtr><mtd><mi>y</mi><mo>=</mo><mi>a_2</mi><mo>+</mo><mi>y_2</mi><mo>*</mo><mi>k</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mi>a_1</mi></mtd></mtr></mtable></mfenced><mi>x_3</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mi>a_2</mi></mtd></mtr></mtable></mfenced><mi>y_3</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_4</mi><mo>=</mo><mi>y_4</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>x_4</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>a_3</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_5</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>x_5</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>y_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mi>y_1</mi><mi>x_1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mfrac><mi>y_2</mi><mi>x_2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m3</mi><mo>=</mo><mfrac><mi>y_3</mi><mi>x_3</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m4</mi><mo>=</mo><mfrac><mi>y_4</mi><mi>x_4</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m5</mi><mo>=</mo><mi>x_5</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>,</mo><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>6</mn><mo>,</mo><mn>5</mn></mrow></mfenced><mo>,</mo><mfrac><mn>5</mn><mn>6</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>,</mo><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mn>6</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>6</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi><mo>,</mo><mi>m3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>6</mn></mrow></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>8</mn></mrow></mfrac><mo>,</mo><mfrac><mn>4</mn><mn>3</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_4</mi><mo>,</mo><mi>m4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>7</mn><mo>=</mo><mn>0</mn><mo>,</mo><mfrac><mn>5</mn><mn>8</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_5</mi><mo>,</mo><mi>m5</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>3</mn><mo>,</mo><mo>-</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>m</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>m</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>m</mi><mn>3</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>m</mi><mn>4</mn><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>m</mi><mn>5</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 1MA 05. RECTES EN EL PLA/1MA.05.2 //// i ┴ 1MA.05.2.10DT PARAL·LELISME: VECTORS

Paral·lelisme: vectors

2 rectes són paral·leles si, i només si, els seus vectors directors són dependents (proporcionals):

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mstyle»«/math»

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 0.0000000 0.0000000 0 1MA.05.2.11Q //?(vectors) ParamCont Considera les rectes d'equacions:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«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»

a) Determina el vector director que resulta de l'equació de r. Format: [2,3]

b) Determina el vector director que resulta de l'equació de s. Format: [2,3]

c) Determina si són paral·leles. Format: S si ho són i N si no ho són.

]]> Si es representen els vectors a l'origen de coordenades,

el gràfic és #G1

]]> 1.0000000 0.5000000 0 0 a. =#sol1b. =#sol2c. =#r2]]> <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>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></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/></mtr></mtable><mrow><mi>A</mi><mo>≠</mo><mi>B</mi></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>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paral</mi><mo>·</mo><mi>leles</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><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mi>u12</mi><mo>*</mo><mi>v11</mi></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo> </mo><mi>Paral</mi><mo>·</mo><mi>leles</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><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mi>u22</mi><mo>*</mo><mi>v21</mi></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>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></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>e11</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>e11</mi><mo>,</mo><mi>e12</mi></mtd></mtr></mtable></mfenced></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>b1</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>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mi>n1</mi><mi>v1</mi></mfrac><mo>=</mo><mfrac><mi>n2</mi><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</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>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>B</mi><mo>,</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mo>(</mo><mi>u</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mo>(</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><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><mn>3</mn><mo>,</mo><mn>5</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"><mfenced close="]" open="["><mrow><mn>3</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>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></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"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>y</mi><mo>=</mo><mn>5</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</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>1</mn><mn>3</mn></mfrac><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</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><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><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"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math»

Un vector director de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«/mrow»«/mstyle»«/math»

Calcula «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mstyle»«/math» per esbrinar si són proporcionals

]]> 1MA.05.2.12Q //?(vectors) CartCont Considera les rectes d'equacions:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«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»

a) Determina el vector director que resulta de l'equació de r. Format: [2,3]

b) Determina el vector director que resulta de l'equació de s. Format: [2,3]

c) Determina si són paral·leles. Format: S si ho són i N si no ho són.

]]> Si es representen els vectors a l'origen de coordenades,

el gràfic és #G1

]]> 1.0000000 0.5000000 0 0 a. =#sol1b. =#sol2c. =#r2]]> <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>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></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/></mtr></mtable><mrow><mi>A</mi><mo>≠</mo><mi>B</mi></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>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paral</mi><mo>·</mo><mi>leles</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><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u11</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mi>u12</mi><mo>*</mo><mi>v11</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u11</mi><mo>,</mo><mi>u12</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo> </mo><mi>Paral</mi><mo>·</mo><mi>leles</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><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u21</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mi>u22</mi><mo>*</mo><mi>v21</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u21</mi><mo>,</mo><mi>u22</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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></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>e1</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>-</mo><mi>u1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>=</mo><mn>0</mn></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>b1</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>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n1</mi></mtd></mtr></mtable></mfenced><mi>v1</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n2</mi></mtd></mtr></mtable></mfenced><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</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>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>B</mi><mo>,</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mo>(</mo><mi>u</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mo>(</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><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><mn>1</mn><mo>,</mo><mn>4</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"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></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"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mn>11</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</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><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><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"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math» perquè amb ax+by+c=0 un vector director és (-b,a)

]]> 1MA.05.2.13Q //?(vectors) ExplCont Considera les rectes d'equacions:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«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»

a) Determina el vector director que resulta de l'equació de r. Format: [2,3]

b) Determina el vector director que resulta de l'equació de s. Format: [2,3]

c) Determina si són paral·leles. Format: S si ho són i N si no ho són.

]]> Si es representen els vectors a l'origen de coordenades,

el gràfic és #G1

]]> 1.0000000 0.5000000 0 0 a. =#sol1b. =#sol2c. =#r2]]> <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>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></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/></mtr></mtable><mrow><mi>A</mi><mo>≠</mo><mi>B</mi></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>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paral</mi><mo>·</mo><mi>leles</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><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u11</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mi>u12</mi><mo>*</mo><mi>v11</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u11</mi><mo>,</mo><mi>u12</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo> </mo><mi>Paral</mi><mo>·</mo><mi>leles</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><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u21</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mi>u22</mi><mo>*</mo><mi>v21</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u21</mi><mo>,</mo><mi>u22</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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></mrow></mfenced></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>e1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mi>u2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo></mrow><mi>u1</mi></mfrac><mo>+</mo><mi>a2</mi></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>b1</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>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n1</mi></mtd></mtr></mtable></mfenced><mi>v1</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n2</mi></mtd></mtr></mtable></mfenced><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>u</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</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>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>B</mi><mo>,</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mo>(</mo><mi>u</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mo>(</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><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><mn>1</mn><mo>,</mo><mfrac><mn>1</mn><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><mn>3</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>,</mo><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></mrow></mfenced><mo>,</mo><mi>y</mi><mo>=</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>1</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>,</mo><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>3</mn><mo>,</mo><mn>4</mn></mrow></mfenced><mo>,</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mn>3</mn></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>+</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</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><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><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"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math» perquè en l'equació explícita y=mx+n, un vector director és [1,m]

]]> 1MA.05.2.15Q Determinar m per r i s paral·leles Per a quin valor de m les rectes r i s són paral·leles?
r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«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¨»u«/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¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»
s: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mstyle»«/math»

Format de la resposta: -2/3: enter o fracció simplificada

Un vector director de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfenced»«/mstyle»«/math».

Per tal que siguin paral·leles, cal que els vectors siguin proporcionals i que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math»

]]> 1MA.05.2.20 DT PARAL·LELISME I PENDENT

Paral·lelisme: pendents

2 rectes són paral·leles si, i només si, els seus pendents són iguals.

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0.0000000 0.0000000 0 1MA.05.2.21Q //?(pendent) ParamCont (còpia) Considera les rectes d'equacions:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«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»

a) Determina el pendent de r. Format: enter o fracció simplificada

b) Determina el pendent de s. Format: enter o fracció simplificada

c) Determina si són paral·leles. Format: S si ho són i N si no ho són.

]]> El gràfic és #G1

]]> 1.0000000 0.5000000 0 0 a. =#sol1b. =#sol2c. =#r2]]> <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>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></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/></mtr></mtable><mrow><mi>A</mi><mo>≠</mo><mi>B</mi></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>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paral</mi><mo>·</mo><mi>leles</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><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mi>u12</mi><mo>*</mo><mi>v11</mi></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo> </mo><mi>Paral</mi><mo>·</mo><mi>leles</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><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mi>u22</mi><mo>*</mo><mi>v21</mi></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>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></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>e11</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>e11</mi><mo>,</mo><mi>e12</mi></mtd></mtr></mtable></mfenced></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>b1</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>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mi>n1</mi><mi>v1</mi></mfrac><mo>=</mo><mfrac><mi>n2</mi><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</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>v1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>B</mi><mo>,</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><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><mn>3</mn><mo>,</mo><mn>5</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"><mfenced close="]" open="["><mrow><mn>3</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>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></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"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>=</mo><mo>-</mo><mn>3</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>2</mn><mo>,</mo><mi>y</mi><mo>=</mo><mn>5</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</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>1</mn><mn>3</mn></mfrac><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>3</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</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><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><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"/><data name="inputCompound">true</data></localData></question> El pendent de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mstyle»«/math»

El pendent de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mstyle»«/math»

Compara'ls

]]> 1MA.05.2.22Q //?(pendent) CartCont Considera les rectes d'equacions:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«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»

a) Determina el pendent de r. Format: enter o fracció simplificada

b) Determina el pendent de s. Format: enter o fracció simplificada

c) Determina si són paral·leles. Format: S si ho són i N si no ho són.

]]> El gràfic és #G1

]]> 1.0000000 0.5000000 0 0 a. =#sol1b. =#sol2c. =#r2]]> <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>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></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/></mtr></mtable><mrow><mi>A</mi><mo>≠</mo><mi>B</mi></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>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paral</mi><mo>·</mo><mi>leles</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><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u11</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mi>u12</mi><mo>*</mo><mi>v11</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u11</mi><mo>,</mo><mi>u12</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo> </mo><mi>Paral</mi><mo>·</mo><mi>leles</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><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u21</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mi>u22</mi><mo>*</mo><mi>v21</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u21</mi><mo>,</mo><mi>u22</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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></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>e1</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo><mo>-</mo><mi>u1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>a2</mi><mo>)</mo><mo>=</mo><mn>0</mn></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>b1</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>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n1</mi></mtd></mtr></mtable></mfenced><mi>v1</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n2</mi></mtd></mtr></mtable></mfenced><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</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>v1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>recta</mi><mfenced><mrow><mi>B</mi><mo>,</mo><mi>v</mi></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><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"><mo>-</mo><mn>1</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"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></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>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mn>1</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</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><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><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"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»u«/mi»«/mstyle»«/math» perquè amb ax+by+c=0 un vector director és (-b,a)

Un vector de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«/mstyle»«/math» ja que, en l'equació contínua, els components són els denominadors.

Calcula els pendents i compara.

]]> 1MA.05.2.23Q //?(pendent) ContExplícita Considera les rectes d'equacions:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«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»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»

a) Determina el pendent de r. Format: enter o fracció simplificada

b) Determina el pendent de s. Format: enter o fracció simplificada

c) Determina si són paral·leles. Format: S si ho són i N si no ho són.

]]> El gràfic és #G1

]]> 1.0000000 0.5000000 0 0 a. =#sol1b. =#sol2c. =#r2]]> <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>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></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/></mtr></mtable><mrow><mi>A</mi><mo>≠</mo><mi>B</mi></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>u1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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>u2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Paral</mi><mo>·</mo><mi>leles</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><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u11</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mi>u12</mi><mo>*</mo><mi>v11</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u11</mi><mo>,</mo><mi>u12</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo> </mo><mi>Paral</mi><mo>·</mo><mi>leles</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><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u21</mi><mo>*</mo><mi>v22</mi><mo>≠</mo><mi>u22</mi><mo>*</mo><mi>v21</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>u21</mi><mo>,</mo><mi>u22</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"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>S</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr></mtable><mtable><mtr><mtd><mi>r2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></mrow></mfenced></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>e1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mi>u2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a1</mi><mo>)</mo></mrow><mi>u1</mi></mfrac><mo>+</mo><mi>a2</mi></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>b1</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>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n1</mi></mtd></mtr></mtable></mfenced><mi>v1</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>n2</mi></mtd></mtr></mtable></mfenced><mi>v2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</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>v1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>4</mn><mn>5</mn></mfrac></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>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>N</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mn>1</mn><mo>,</mo><mo>-</mo><mfrac><mn>4</mn><mn>5</mn></mfrac></mrow></mfenced><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>4</mn><mn>5</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>37</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>3</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>4</mn></mrow></mfenced><mo>,</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>1</mn></mrow></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</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><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>.</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>r</mi><mn>2</mn><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"/><data name="inputCompound">true</data></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»v«/mi»«/mstyle»«/math» perquè, en l'equació contínua, el vector ve determinat pels denominadors

Un vector director de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»u«/mi»«/mstyle»«/math» perquè, en l'equació explícita y =mx+n, el vector és [1,m]

Calcula els pendents i compara'ls

]]> 1MA.05.2.30DT TROBAR RECTA //

Escriure l'equació d'una recta paral·lela

AMB VECTORS

Per escriure l'equació de la recta s, paral·lela a la recta r, fem servir el punt per on passa s i un vector director de r.

Exemple: Si r és 2x-3y+5=0 té, (3,2) també és vector director de s. Si s passa pel punt (2,-2) la seva equació contínua és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨normal¨»x«/mi»«mo»-«/mo»«mn»2«/mn»«/mrow»«mn»3«/mn»«/mfrac»«mo mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mi mathvariant=¨normal¨»y«/mi»«mo»+«/mo»«mn»2«/mn»«/mrow»«mn»2«/mn»«/mfrac»«/mrow»«/mstyle»«/math» d'on es poden deduir les altres equacions.

AMB PENDENTS

Una recta paral·lela a la recta r té el mateix pendent que r.

Exemple: Una recta paral·lela a r: =2x-1 té per pendent 2 i s'escriu y = 2x + n.

Si passa pel punt (2,-2), substituint x i y es troba que -2 = 2·2 + n, o sigui n = -6.

L'equació explícita és doncs y = 2x-6

]]> 0.0000000 0.0000000 0 1MA.05.2.31Q EqContinuaDe // cartesiana Troba l'equació contínua d'una recta s que és paral·lela a la recta r d'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»i que passa per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/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»«/mstyle»«/math».

#G1

]]> L'equació 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¨»u«/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¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

i les rectes són #G2

]]> 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>c1</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>u1</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>u2</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>b1</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>b2</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/></mtr></mtable><mrow><mi>u2</mi><mo>*</mo><mi>b1</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>b2</mi><mo>+</mo><mi>c1</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math 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open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c1</mi><mo>=</mo><mn>0</mn><mo>)</mo></mrow></mfenced></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>u1</mi><mo>,</mo><mi>u2</mi><mo>,</mo><mi>c1</mi><mo>,</mo><mi>e1</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>8</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>6</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>8</mn><mo>=</mo><mn>0</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"><mfenced><mrow><mo>-</mo><mn>7</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>n1</mi><mo>,</mo><mi>n2</mi><mo>,</mo><mi>u</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>7</mn><mo>,</mo><mi>y</mi><mo>+</mo><mn>9</mn><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>6</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>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>6</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>7</mn><mn>6</mn></mfrac><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>9</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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_equations"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math».

Com que s és paral·lela a r, aquest vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math» també és director de s.

Per escriure l'equació contínua de s, ja tenim:

un punt A«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»A«/mi»«/mrow»«/mstyle»«/math» → als numeradors
i un vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math» → als denominadors

]]> 1MA.05.2.32Q EqCartesianaDe // paramètriques Troba l'equació cartesiana d'una recta s que és paral·lela a la recta r d'equacions «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» i que passa per «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».

#G1

]]> El gràfic és: #G2

]]> 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>r1</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>r2</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>R</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>r1</mi><mo>,</mo><mi>r2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>u1</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>u2</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>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>R</mi><mo>,</mo><mi>u</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</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>a2</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</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>A</mi><mo>∉</mo><mi>r</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>r1</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>r2</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u11</mi><mo>=</mo><mo>-</mo><mi>u1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mo>(</mo><mi>u2</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>u11</mi><mo>)</mo><mo>*</mo><mi>y</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi><mo>=</mo><mo>-</mo><mi>u2</mi><mo>*</mo><mi>a1</mi><mo>-</mo><mi>u11</mi><mo>*</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>u11</mi><mo>)</mo><mo>*</mo><mi>y</mi><mo>+</mo><mi>u1</mi><mo>*</mo><mi>a2</mi><mo>-</mo><mi>u2</mi><mo>*</mo><mi>a1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>r</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>recta</mi><mo>(</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>u11</mi><mo>)</mo><mo>*</mo><mi>y</mi><mo>+</mo><mi>u1</mi><mo>*</mo><mi>a2</mi><mo>-</mo><mi>u2</mi><mo>*</mo><mi>a1</mi><mo>=</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></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><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>u1</mi><mo>,</mo><mi>u2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mi>m</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mfrac><mi>m</mi><mi>u2</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>,</mo><mi>u</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>6</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mn>7</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"><mfenced><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced></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>x</mi><mo>=</mo><mo>-</mo><mn>5</mn><mo>*</mo><mi>k</mi><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>k</mi><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>y</mi></math></output></command><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>4</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>16</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"><mi>x</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>16</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>,</mo><mi>G2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi><mo>,</mo><mi>tauler2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>,</mo><mi>m</mi><mo>,</mo><mi>m1</mi><mo>,</mo><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>,</mo><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn><mo>,</mo><mi>y</mi><mo>-</mo><mn>4</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_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">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que són paral·leles, el vector director de r, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math», és director de s.

Mètode 1: escrius l'equació contínua amb el punt A i el vector de r: «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¨»u«/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¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» i la transformes a cartesiana

Mètode 2: l'equació cartesiana d'una recta que té per vector director «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math» és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/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¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math». Per trobar el valor de c, només cal pensar que la recta passa per A, i substituir x i y per les coordenades de A.

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Mètode 1: Es treuen denominadors amb el mcm dels denominadors «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfenced»«/mstyle»«/math»: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mstyle»«/math» i es transposen tots els termes a l'esquerra per igualar a zero

Mètode 2: L'equació és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/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¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math». Calcula c substituint x i y per les coordenades de A: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«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»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«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¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»0«/mn»«/mrow»«/mstyle»«/math»

]]> 1MA.05.2.33Q EqExplícitaDe // explícita Troba l'equació explícita d'una recta s que passa per A«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«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 que és paral·lela a la recta r d'equació «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»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math».

#G1

]]> Gràficament: #G2

]]> 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>m</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>n</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>a1</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>a2</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/></mtr></mtable><mrow><mi>a2</mi><mo>≠</mo><mi>m</mi><mo>*</mo><mi>a1</mi><mo>+</mo><mi>n</mi></mrow></apply></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>x</mi><mo>+</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>a2</mi><mo>-</mo><mi>m</mi><mo>*</mo><mi>a1</mi><mo>)</mo></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>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>y</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>y</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mo>(</mo><mi>a2</mi><mo>-</mo><mi>m</mi><mo>*</mo><mi>a1</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T2</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>r</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G2</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T2</mi><mo>,</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></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>8</mn><mo>,</mo><mn>6</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><mn>3</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>r</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>,</mo><mi>y</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30</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"><mi>y</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>30</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">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que són paral·leles, tenen el mateix pendent, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«/mrow»«/mstyle»«/math», i l'equació de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y«/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¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«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¨»n«/mi»«/mrow»«/mstyle»«/math».

Per a trobar n, cal substituir x i y per les coordenades del punt: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/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»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«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¨»n«/mi»«/mrow»«/mstyle»«/math»

]]> 1MA.05.2.40DT PERPENDICULARITAT(VECTORS)

Condició de perpendicularitat amb vectors

2 rectes són perpendiculars si, i només si, els seus vectors directors són perpendiculars, o sigui si el seu producte escalar és 0:

x_1·x₂ + y_1·y₂ = 0

]]> 0.0000000 0.0000000 0 1MA.05.2.41Q ┴ vectorsContCont Considera les rectes d'equacions:
«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¨»§#160;«/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¨»u«/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¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»3«/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¨»4«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

a) Calcula el producte escalar dels seus vectors directors

b) Esbrina si són perpendiculars: S per si, N per no.

]]> Gràfic (r en blau, s en verd)

#G1

]]> 1.0000000 0.5000000 0 0 a. Producte escalar=#sol1b. Perpendiculars?(S/N) =#sol2]]> <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><mn>1</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>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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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>b2</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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Perpendiculars</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><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v11</mi><mo>+</mo><mi>u12</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo> </mo><mi>Perpendiculars</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><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v21</mi><mo>+</mo><mi>u22</mi><mo>*</mo><mi>v22</mi><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">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></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>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><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>u1</mi><mo>*</mo><mi>v1</mi><mo>+</mo><mi>u2</mi><mo>*</mo><mi>v2</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>sol1</mi><mo>=</mo><mn>0</mn></mrow><mrow><mi>sol2</mi><mo>=</mo><mi>S</mi></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>u1</mi></mfrac><mo>=</mo><mfrac><mi>n2</mi><mi>u2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mi>n3</mi><mi>v1</mi></mfrac><mo>=</mo><mfrac><mi>n4</mi><mi>v2</mi></mfrac></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>u</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>B</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></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>e1</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>2</mn></mfrac><mo>*</mo><mi>y</mi><mo>-</mo><mfrac><mn>5</mn><mn>2</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mi>x</mi><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac><mo>*</mo><mi>y</mi><mo>,</mo><mi>y</mi><mo>=</mo><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>u</mi><mo>,</mo><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>2</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced><mo>,</mo><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>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mi>S</mi></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>P</mi><mi>r</mi><mi>o</mi><mi mathvariant="normal">d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo> </mo><mi mathvariant="normal">e</mi><mi>s</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>a</mi><mi>r</mi><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><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>u</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>s</mi><mo>?</mo><mo>(</mo><mi>S</mi><mo>/</mo><mi>N</mi><mo>)</mo><mo> </mo><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> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math»

El producte escalar és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«/mstyle»«/math»

]]> 1MA.05.2.42Q ┴ vectorsContCart Considera les rectes d'equacions:
«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¨»§#160;«/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¨»u«/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¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»21«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

a) Calcula el producte escalar dels seus vectors directors

b) Esbrina si són perpendiculars: S per si, N per no.

]]> Gràfic (r en blau, s en verd)

#G1

]]> 1.0000000 0.5000000 0 0 a. Producte escalar=#sol1b. Perpendiculars?(S/N) =#sol2]]> <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><mn>1</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>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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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>b2</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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Perpendiculars</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><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v11</mi><mo>+</mo><mi>u12</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo> </mo><mi>Perpendiculars</mi></math></comment></maction><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>k1</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mi>S</mi></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>P</mi><mi>r</mi><mi>o</mi><mi mathvariant="normal">d</mi><mi>u</mi><mi>c</mi><mi>t</mi><mi mathvariant="normal">e</mi><mo> </mo><mi mathvariant="normal">e</mi><mi>s</mi><mi>c</mi><mi>a</mi><mi>l</mi><mi>a</mi><mi>r</mi><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><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>u</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>s</mi><mo>?</mo><mo>(</mo><mi>S</mi><mo>/</mo><mi>N</mi><mo>)</mo><mo> </mo><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> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math»

]]> 1MA.05.2.43Q ┴ vectorsParamCart Considera les rectes d'equacions:
«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»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«/mtd»«mtd»«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¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«/mtd»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»21«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

a) Calcula el producte escalar dels seus vectors directors

b) Esbrina si són perpendiculars: S per si, N per no.

]]> Gràfic (r en blau, s en verd)

#G1

]]> 1.0000000 0.5000000 0 0 a. Producte escalar=#sol1b. Perpendiculars?(S/N) =#sol2]]> <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><mn>1</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>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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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>b2</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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo> </mo><mi>Perpendiculars</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol 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mathvariant="normal">i</mi><mi>c</mi><mi>u</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>s</mi><mo>?</mo><mo>(</mo><mi>S</mi><mo>/</mo><mi>N</mi><mo>)</mo><mo> </mo><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> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math»

]]> 1MA.05.2.50DT PERPENDICULARITAT(PENDENTS)

Perpendicularitat amb pendents

2 rectes són perpendiculars si, i només si, els seus pendents m i m' són tal que:

m · m' = -1

]]> 0.0000000 0.0000000 0 1MA.05.2.51Q ┴ pendentContCart Considera les rectes d'equacions:
«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¨»§#160;«/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¨»u«/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¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»21«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

a) Calcula el producte dels seus pendents

b) Esbrina si són perpendiculars: S per si, N per no.

]]> Gràfic (r en blau, s en verd)

#G1

]]> 1.0000000 0.5000000 0 0 a. Producte=#sol1b. Perpendiculars?(S/N) =#sol2]]> <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><mn>1</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>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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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>b2</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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</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>sol1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mrow><mrow><mi>sol2</mi><mo>=</mo><mi>S</mi></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>u1</mi></mfrac><mo>=</mo><mfrac><mi>n2</mi><mi>u2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>=</mo><mi>n3</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>n4</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable 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align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>B</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></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>e1</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi><mo>-</mo><mn>1</mn><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>y</mi><mo>+</mo><mfrac><mn>5</mn><mn>4</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>4</mn><mo>=</mo><mn>0</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><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>u</mi><mo>,</mo><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>4</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>,</mo><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mi>S</mi></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>P</mi><mi>r</mi><mi>o</mi><mi mathvariant="normal">d</mi><mi>u</mi><mi>c</mi><mi>t</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>b</mi><mo>.</mo><mo> </mo><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>u</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>s</mi><mo>?</mo><mo>(</mo><mi>S</mi><mo>/</mo><mi>N</mi><mo>)</mo><mo> </mo><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 pendent de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mstyle»«/math»

El pendent de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mstyle»«/math»

Multiplica'ls

]]> 1MA.05.2.52Q ┴ pendentExplícitaCartesiana Considera les rectes d'equacions:
«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¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»11«/mn»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»21«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

a) Calcula el producte dels seus pendents

b) Esbrina si són perpendiculars: S per si, N per no.

]]> Gràfic (r en blau, s en verd)

#G1

]]> 1.0000000 0.5000000 0 0 a. Producte=#sol1b. Perpendiculars?(S/N) =#sol2]]> <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><mn>1</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>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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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>b2</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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Perpendiculars</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><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v11</mi><mo>+</mo><mi>u12</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo> </mo><mi>Perpendiculars</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><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v21</mi><mo>+</mo><mi>u22</mi><mo>*</mo><mi>v22</mi><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">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></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>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><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>p1</mi><mo>*</mo><mi>p2</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>sol1</mi><mo>=</mo><mo>-</mo><mn>1</mn></mrow><mrow><mi>sol2</mi><mo>=</mo><mi>S</mi></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>N</mi></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e11</mi><mo>=</mo><mi>r</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>=</mo><mi>n3</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>n4</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>B</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>8</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></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>e11</mi><mo>,</mo><mi>r</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mi>x</mi><mo>+</mo><mn>6</mn><mo>,</mo><mi>y</mi><mo>=</mo><mi>x</mi><mo>+</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>0</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mi>x</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>,</mo><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>,</mo><mi>p2</mi><mo>,</mo><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><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"><mi>k1</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mi>S</mi></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>P</mi><mi>r</mi><mi>o</mi><mi mathvariant="normal">d</mi><mi>u</mi><mi>c</mi><mi>t</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>b</mi><mo>.</mo><mo> </mo><mi>P</mi><mi mathvariant="normal">e</mi><mi>r</mi><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi>u</mi><mi>l</mi><mi>a</mi><mi>r</mi><mi>s</mi><mo>?</mo><mo>(</mo><mi>S</mi><mo>/</mo><mi>N</mi><mo>)</mo><mo> </mo><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 pendent de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mstyle»«/math»

El pendent de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mstyle»«/math»

Multiplica'ls

]]> 1MA.05.2.55Q Tobar m per ┴ (vec/pend) Considera les rectes d'equacions:
«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»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«/mtd»«mtd»«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¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«/mtd»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold-italic¨»m«/mi»«mo mathvariant=¨bold¨»§#183;«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mspace linebreak=¨newline¨/»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»21«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

Per quin valor de m són perpendiculars?

]]> 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="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><mn>1</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>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>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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>b2</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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Perpendiculars</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><mtable><mtr><mtd><mi>u11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr></mtable><mrow><mi>u11</mi><mo>*</mo><mi>v11</mi><mo>+</mo><mi>u12</mi><mo>*</mo><mi>v12</mi><mo>=</mo><mn>0</mn></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>No</mi><mo> </mo><mi>Perpendiculars</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><mtable><mtr><mtd><mi>u21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr></mtable><mrow><mi>u21</mi><mo>*</mo><mi>v21</mi><mo>+</mo><mi>u22</mi><mo>*</mo><mi>v22</mi><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">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u11</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u12</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v11</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v12</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>u1</mi><mo>=</mo><mi>u21</mi></mtd></mtr><mtr><mtd><mi>u2</mi><mo>=</mo><mi>u22</mi></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>v21</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>v22</mi></mtd></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>m</mi></mrow></mfenced></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>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><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n3</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n4</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>u1</mi><mo>*</mo><mi>v1</mi></mrow><mi>v2</mi></mfrac></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>e1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>u1</mi></mfrac><mo>=</mo><mfrac><mi>n2</mi><mi>m</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>=</mo><mi>n3</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>n4</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>u</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>v</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>=</mo><mfrac><mi>m</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p2</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></math></input></command></group></library><group><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"><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>=</mo><mfrac><mrow><mi>y</mi><mo>-</mo><mn>5</mn></mrow><mi>m</mi></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e21</mi><mo>,</mo><mi>s</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mn>24</mn><mo>=</mo><mn>0</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>,</mo><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>4</mn><mo>,</mo><mi>m</mi></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p1</mi><mo>,</mo><mi>p2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>1</mn><mn>4</mn></mfrac><mo>*</mo><mi>m</mi><mo>,</mo><mo>-</mo><mn>4</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>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"><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>

Resolució amb els vectors directors

Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»u«/mi»«/mrow»«/mstyle»«/math»

Cal que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mstyle»«/math»= 0

Resolució amb els pendents

El pendent de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«/mrow»«/mstyle»«/math»

El pendent de s és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»p«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mrow»«/mstyle»«/math»

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

]]> 1MA.05.2.60DT EQ RECTA PERPENDICULAR

Escriure l'equació d'una recta perpendicular

AMB VECTORS

Per escriure l'equació de la recta perpendicular a la recta r de vector director (A,B) fem servir un punt i el vector (-B,A) que és perpendicular a (A,B)

Exemple: Una perpendicular a r : 2x-3y+5=0 té per vector director (-2,3). Si passa pel punt (2,-2) la seva equació contínua és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac»«mrow»«mi»x«/mi»«mo»-«/mo»«mn»2«/mn»«/mrow»«mrow»«mo»-«/mo»«mn»2«/mn»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mi»y«/mi»«mo»+«/mo»«mn»2«/mn»«/mrow»«mn»3«/mn»«/mfrac»«/mrow»«/mstyle»«/math» d'on es poden deduir les altres equacions.

AMB PENDENTS

Una recta perpendicular a la recta r (de pendent m) té un pendent m' tal que:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»`«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mfrac mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mi mathvariant=¨bold¨»m«/mi»«/mfrac»«/mrow»«/mstyle»«/math»

Exemple: Una recta perpendicular a r: =2x-1 té per pendent -1/2 i s'escriu y = -1/2·x + n.

Si passa pel punt (2,-2), substituint x i y es troba que -2 = -1/2·2 + n, o sigui n = -1.

L'equació explícita és doncs y = -1/2·x-1

]]> 0.0000000 0.0000000 0 1MA.05.2.61Q EqContinua ┴ cartesiana Troba l'equació contínua d'una recta s que és perpendicular a la recta r d'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math» i que passa per A «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»«/mstyle»«/math».

#G1

]]> Resposta: «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¨»u«/mi»«mn mathvariant=¨bold¨»21«/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¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

#G2

]]> 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>c1</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>u1</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>u2</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>b1</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>b2</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 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>9</mn><mo>=</mo><mn>0</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"><mfenced><mrow><mn>6</mn><mo>,</mo><mn>3</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"><mo>-</mo><mi>x</mi><mo>+</mo><mn>6</mn><mo>=</mo><mfrac><mn>1</mn><mn>3</mn></mfrac><mo>*</mo><mi>y</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>#sol</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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un vector director de r és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mstyle»«/math».

Un vector perpendicular a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mstyle»«/math» és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»21«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mstyle»«/math»

Per escriure l'equació contínua de s, ja tenim:

un punt A«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»b«/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¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«/mstyle»«/math» → als numeradors
i un vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»21«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mstyle»«/math» → als denominadors

]]> 1MA.05.2.62Q EqExplícita ┴ explícita Troba l'equació explícita de la recta s que passa per A«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«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 que és perpendicular a la recta r d'equació «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»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math».

#G1

]]> #G2

]]> 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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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> Per l'equació explicita y = mx + n

Mètode ràpid: determinar m i n amb les dades del problema.

Com que són perpendiculars, si m`és el pendent de r, el pendent m de s és tal que m·m'=-1: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»`«/mo»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«mfrac mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«/mrow»«/mstyle»«/math»

L'equació de s s'escriu «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»x«/mi»«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¨»n«/mi»«/mrow»«/mstyle»«/math»

Per calcular n, cal substituir x i y per les coordenades del punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»A«/mi»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#FF0000¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#FF0000¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»)«/mo»«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¨»n«/mi»«/mrow»«/mstyle»«/math»

Mètode interminable: fent servir vectors i el producte escalar

Determinar el vector director de r, fent nul el producte escalar i a partir de l'equació contínua, amb el punt i el vector, arribar fins l'equació explícita.

]]> 1MA 05. RECTES EN EL PLA/1MA.05.3 PosRelativa Intersecció/1MA.05.3.1 Posició relativa 1MA.05.3.1.00DT Posició relativa Rectes secants Rectes paral·leles Rectes coincidents Tenen els vectors directors independents Tenen els vectors directors dependents Tenen els vectors directors dependents Tenen pendents diferents Tenen el mateix pendent Tenen el mateix pendent UN punt comú Cap punt comú TOTS els punts comuns

Cal doncs:

1. Comparar vector/pendents

2. Si els vectors són dependents (o els pendents iguals), cal mirar:

- - si un punt de l'una es troba sobre l'altra (substituint les coordenades)
  - o si els vectors directors i un vector que les uneix són dependents

]]> 0.0000000 0.0000000 0 1MA.05.3.1.10DT PRSECANTS VECTORS

Posició relativa (vectors)

Si dues rectes tenen la mateixa direcció, paral·leles o coincidents, els seus vectors directors són dependents (proporcionals).

Si dues rectes són secants, en canvi, els seus vectors directors són independents (NO proporcionals).

Es recorda que 2 vectors són dependents si «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow mathcolor=¨#007F00¨»«mfrac»«msub»«mi mathvariant=¨bold-italic¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«msub»«mi mathvariant=¨bold-italic¨»y«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«msub»«mi mathvariant=¨bold-italic¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«msub»«mi mathvariant=¨bold-italic¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mfrac»«mo mathvariant=¨bold¨»§#8660;«/mo»«msub»«mi mathvariant=¨bold-italic¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«msub»«mi mathvariant=¨bold-italic¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»=«/mo»«msub»«mi mathvariant=¨bold-italic¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«msub»«mi mathvariant=¨bold-italic¨»y«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«/mrow»«/mstyle»«/math»

Per distingir si són paral·leles o coincidents es pot comprovar

si un punt de l'una pertany a l'altra

]]> 0.0000000 0.0000000 0 1MA.05.3.1.11Q PR param_cont VECTORS Esbrina quina és la posició relativa de les dues rectes:
r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» i s: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»21«/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¨»22«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math».

Format de la resposta:

vector= [1,-2]
PR =posició relativa: 1 si secants, 2 si coincidents, 3 si paral·leles.

]]> La situació és #G1

]]> 1.0000000 0.5000000 0 0 vector de r =#vrvector de s =#vsPR(1,2,3)=#t1]]> <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>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>3</mn></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>t1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><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>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable 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align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>v31</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>v32</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>u1</mi><mo>*</mo><mi>vv2</mi><mo>-</mo><mi>u2v1</mi><mo>≠</mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>independents</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t1</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>v31</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>v32</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr></mtable><mrow><mfenced><mrow><mi>u1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>u2</mi><mo>*</mo><mi>v1</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>u2</mi><mo>*</mo><mi>v31</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>v32</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a1</mi><mo>≠</mo><mi>b1</mi></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mo>=</mo><mi>u1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b1</mi></mrow></mfenced><mo>=</mo><mi>v1</mi><mo>*</mo><mfenced><mrow><mi>y</mi><mo>-</mo><mi>b2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>v31</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>v32</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd><mi>D12</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u1</mi></mtd><mtd><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>u2</mi></mtd><mtd><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>u2</mi><mo>*</mo><mi>v1</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>D12</mi><mo>≠</mo><mn>0</mn></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</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>vp</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v31</mi><mo>,</mo><mi>v32</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n11</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>n12</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n21</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n22</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ps</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></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>vr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>vs</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>60</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>60</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn><mo>,</mo><mo> </mo><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>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mo> </mo><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"><mi>p11</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</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>e11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>39</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>28</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>300</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>,</mo><mi>vs</mi><mo>,</mo><mi>vp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>2</mn><mo>,</mo><mo>-</mo><mn>7</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>8</mn><mo>,</mo><mn>28</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mn>12</mn><mo>,</mo><mn>15</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>r</mi><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>s</mi><mspace linebreak="newline"/><mi>P</mi><mi>R</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>=</mo><mo>#</mo><mi>t</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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un vector de r és #vr

Un vector de s és #vs

#c1

]]> 1MA.05.3.1.12Q PR cont_cont VECTORS Esbrina quina és la posició relativa de les dues rectes:
r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/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¨»12«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» i s: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»21«/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¨»22«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math».

Format de la resposta:

vector= [1,-2]
PR =posició relativa: 1 si secants, 2 si coincidents, 3 si paral·leles.

]]> La situació és #G1

]]> 1.0000000 0.5000000 0 0 vector de r =#vrvector de s =#vsPR(1,2,3)=#t1]]> <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>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>3</mn></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>t1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>v1</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>v2</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>v31</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>v32</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>u1</mi><mo>*</mo><mi>vv2</mi><mo>-</mo><mi>u2v1</mi><mo>≠</mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>independents</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t1</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>v31</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>v32</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr></mtable><mrow><mfenced><mrow><mi>u1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>u2</mi><mo>*</mo><mi>v1</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>u2</mi><mo>*</mo><mi>v31</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>v32</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a1</mi><mo>≠</mo><mi>b1</mi></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mo>=</mo><mi>u1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b1</mi></mrow></mfenced><mo>=</mo><mi>v1</mi><mo>*</mo><mfenced><mrow><mi>y</mi><mo>-</mo><mi>b2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>v31</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>v32</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd><mi>D12</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u1</mi></mtd><mtd><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>u2</mi></mtd><mtd><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>u2</mi><mo>*</mo><mi>v1</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>D12</mi><mo>≠</mo><mn>0</mn></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</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>vp</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v31</mi><mo>,</mo><mi>v32</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n11</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>n12</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n21</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n22</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ps</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></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>vr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>vs</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>60</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>60</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>3</mn><mo>,</mo><mo> </mo><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>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mo> </mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</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>e11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>38</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</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>9</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>4</mn><mo>,</mo><mo>-</mo><mn>6</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"><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>r</mi><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>s</mi><mspace linebreak="newline"/><mi>P</mi><mi>R</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>=</mo><mo>#</mo><mi>t</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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un vector de r és #vr

Un vector de s és #vs

#c1

]]> 1MA.05.3.1.13Q PR cont_cartes VECTORS Esbrina quina és la posició relativa de les dues rectes:
r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/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¨»12«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» i s: «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»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mrow»«/mstyle»«/math».

Format de la resposta:

vector= [1,-2]
PR =posició relativa: 1 si secants, 2 si coincidents, 3 si paral·leles.

]]> 1.0000000 0.5000000 0 0 vector de r =#vrvector de s =#vsPR(1,2,3)=#t1]]> <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>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>3</mn></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>t1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>v1</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>v2</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>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>rang</mi><mfenced><mtable><mtr><mtd><mi>u2</mi></mtd><mtd><mo>-</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi></mtd><mtd><mo>-</mo><mi>v1</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mn>2</mn></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>independents</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t1</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>a1</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>a2</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>u1</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>u2</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>b1</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mfrac><mrow><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mrow><mrow><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mrow></mfrac><mo>≠</mo><mfrac><mi>u2</mi><mi>v2</mi></mfrac></mrow></mfenced></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</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>n11</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>n12</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n21</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n22</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>e12</mi></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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></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>vr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>vs</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>60</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>60</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn><mo>,</mo><mo> </mo><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>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mo> </mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</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"><mo>(</mo><mi>u1</mi><mo>,</mo><mi>u2</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>v1</mi><mo>,</mo><mi>v2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>4</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>48</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>4</mn><mo>,</mo><mn>12</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"><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>r</mi><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>s</mi><mspace linebreak="newline"/><mi>P</mi><mi>R</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>=</mo><mo>#</mo><mi>t</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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un vector de r és #vr

Un vector de s és #vs

#c1

]]> 1MA.05.3.1.14Q PR ParamExpl VECTORS Quina és la posició relativa 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¨»§#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» i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math»?
Format de la resposta:

a) vector director de r: [-3,5/3]

b) vector director de s: [1,5/3]

c) PR (posició relativa): 1 per secants, 2 per coincidents, 3 per paral·leles

]]> La situació és: r en blau, s en vermell

#G1

]]> 1.0000000 0.5000000 0 0 a) vr=#sol1b) vs=#sol2c) PR=#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"><mi>t11</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></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>t11</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol3</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><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>1</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></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u1</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>u2</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>v1</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>v2</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>D</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u1</mi></mtd><mtd><mi>v1</mi></mtd></mtr><mtr><mtd><mi>u2</mi></mtd><mtd><mi>v2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>D</mi><mo>≠</mo><mn>0</mn></mrow></apply></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t11</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>sol3</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><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>1</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></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>u1</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>u2</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>v1</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>v2</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>D</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u1</mi></mtd><mtd><mi>v1</mi></mtd></mtr><mtr><mtd><mi>u2</mi></mtd><mtd><mi>v2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>D2</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u1</mi></mtd><mtd><mi>a2</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>u2</mi></mtd><mtd><mi>b2</mi><mo>-</mo><mi>b1</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>D</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>D2</mi><mo>=</mo><mn>0</mn></mrow></mfenced></mrow></apply></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol3</mi><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><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>1</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></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u1</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>u2</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>v1</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>v2</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>D</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u1</mi></mtd><mtd><mi>v1</mi></mtd></mtr><mtr><mtd><mi>u2</mi></mtd><mtd><mi>v2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>D2</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u1</mi></mtd><mtd><mi>a2</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>u2</mi></mtd><mtd><mi>b2</mi><mo>-</mo><mi>b1</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>D</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>D2</mi><mo>≠</mo><mn>0</mn></mrow></mfenced></mrow></apply></mtd></mtr></mtable></apply></mtd></mtr><mtr><mtd/></mtr></mtable></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</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>e1</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mi>a1</mi></mtd></mtr></mtable></mfenced><mi>u1</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mi>a2</mi></mtd></mtr></mtable></mfenced><mi>u2</mi></mfrac></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>u1</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>a2</mi><mo>+</mo><mi>u2</mi><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mi>v2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>b1</mi><mo>)</mo><mo>+</mo><mi>v1</mi><mo>*</mo><mi>b2</mi></mrow><mi>v1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>vr</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>vs</mi></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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></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>vr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>vs</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>60</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>60</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>3</mn><mo>,</mo><mo> </mo><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>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mo> </mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><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"><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>+</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>4</mn></mrow></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>+</mo><mn>4</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>4</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><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>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>4</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>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><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>A</mi><mo>,</mo><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mo>-</mo><mn>4</mn></mrow></mfenced><mo>,</mo><mfenced><mrow><mo>-</mo><mn>5</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>t11</mi><mo>,</mo><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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><msub><mi>v</mi><mi>r</mi></msub><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><msub><mi>v</mi><mi>s</mi></msub><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>P</mi><mi>R</mi><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> Els vectors són «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»vr«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»vs«/mi»«/mstyle»«/math»

#c1

]]> 1MA.05.3.1.20DT SECANTS? PENDENTS

Posició relativa (pendents)

Si dues rectes tenen la mateixa direcció, paral·leles o coincidents, els pendents són iguals.

Si dues rectes són secants, en canvi, els seus pendents són diferents

Es recorda que pendents diferents «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mfrac mathcolor=¨#007F00¨»«msub»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8800;«/mo»«mfrac mathcolor=¨#007F00¨»«msub»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«msub»«mi mathvariant=¨bold-italic¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mfrac»«/mstyle»«/math»

Per distingir si són paral·leles o coincidents es pot comprovar

si un punt de l'una pertany a l'altra

]]> 0.0000000 0.0000000 0 1MA.05.3.1.21Q PR param_cont PENDENTS Esbrina quina és la posició relativa de les dues rectes:
r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» i s: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»21«/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¨»22«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math».

Format de la resposta:

pendent = enter o fracció simplificada
PR =posició relativa: 1 si secants, 2 si coincidents, 3 si paral·leles.

]]> La situació és #G1

]]> 1.0000000 0.5000000 0 0 pendent de r =#prpendent de s =#psPR(1,2,3)=#t1]]> <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>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>3</mn></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>t1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><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>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>,</mo><mi>pr</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mn>6</mn></mrow></mfenced><mo>,</mo><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</mi><mo>,</mo><mi>ps</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>15</mn><mo>,</mo><mo>-</mo><mn>30</mn></mrow></mfenced><mo>,</mo><mo>-</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi>r</mi><mspace linebreak="newline"/><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi>s</mi><mspace linebreak="newline"/><mi>P</mi><mi>R</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>=</mo><mo>#</mo><mi>t</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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un vector de r és #vr i el pendent és #pr

Un vector de s és #vs i el pendent és #ps

#c1

]]> 1MA.05.3.1.22Q PR cont_cont PENDENTS Esbrina quina és la posició relativa de les dues rectes:
r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/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¨»12«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» i s: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»21«/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¨»22«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math».

Format de la resposta:

pendent = enter o fracció simplificada
PR =posició relativa: 1 si secants, 2 si coincidents, 3 si paral·leles.

]]> La situació és #G1

]]> 1.0000000 0.5000000 0 0 pendent de r =#prpendent de s =#psPR(1,2,3)=#t1]]> <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>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>3</mn></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>t1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>v1</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>v2</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>v31</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>v32</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>u1</mi><mo>*</mo><mi>vv2</mi><mo>-</mo><mi>u2v1</mi><mo>≠</mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>independents</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t1</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>v31</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>v32</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr></mtable><mrow><mfenced><mrow><mi>u1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>u2</mi><mo>*</mo><mi>v1</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>u2</mi><mo>*</mo><mi>v31</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>v32</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a1</mi><mo>≠</mo><mi>b1</mi></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mo>=</mo><mi>u1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b1</mi></mrow></mfenced><mo>=</mo><mi>v1</mi><mo>*</mo><mfenced><mrow><mi>y</mi><mo>-</mo><mi>b2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>v31</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>v32</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd><mi>D12</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u1</mi></mtd><mtd><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>u2</mi></mtd><mtd><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>u2</mi><mo>*</mo><mi>v1</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>D12</mi><mo>≠</mo><mn>0</mn></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</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>vp</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v31</mi><mo>,</mo><mi>v32</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n11</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>n12</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n21</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n22</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ps</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></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>vr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>vs</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>60</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>60</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn><mo>,</mo><mo> </mo><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>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mo> </mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</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>vr</mi><mo>,</mo><mi>vs</mi><mo>,</mo><mi>vp</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>4</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>24</mn><mo>,</mo><mn>16</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mn>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>16</mn><mo>=</mo><mn>6</mn><mo>*</mo><mi>y</mi><mo>-</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>16</mn><mo>=</mo><mo>-</mo><mn>24</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>72</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</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>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>24</mn><mo>,</mo><mn>16</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"><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo> </mo><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi>r</mi><mspace linebreak="newline"/><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi>s</mi><mspace linebreak="newline"/><mi>P</mi><mi>R</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>=</mo><mo>#</mo><mi>t</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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un vector de r és #vr i el seu pendent és #pr

Un vector de s és #vs i el seu pendent és #ps

#c1

]]> 1MA.05.3.1.23Q PR cont_cartes PENDENTS Esbrina quina és la posició relativa de les dues rectes:
r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/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¨»12«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» i s: «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»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mrow»«/mstyle»«/math».

Format de la resposta:

pendent = enter o fracció simplificada
PR =posició relativa: 1 si secants, 2 si coincidents, 3 si paral·leles.

]]> 1.0000000 0.5000000 0 0 pendent de r =#prpendent de s =#psPR(1,2,3)=#t1]]> <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>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>3</mn></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>t1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>v1</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>v2</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>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>rang</mi><mfenced><mtable><mtr><mtd><mi>u2</mi></mtd><mtd><mo>-</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi></mtd><mtd><mo>-</mo><mi>v1</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mn>2</mn></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>pendents</mi><mo> </mo><mi>són</mi><mo> </mo><mi>diferents</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t1</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>a1</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>a2</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>u1</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>u2</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>b1</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>pendents</mi><mo> </mo><mi>són</mi><mo> </mo><mi>iguals</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mfrac><mrow><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mrow><mrow><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mrow></mfrac><mo>≠</mo><mfrac><mi>u2</mi><mi>v2</mi></mfrac></mrow></mfenced></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>pendents</mi><mo> </mo><mi>són</mi><mo> </mo><mi>iguals</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</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>n11</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>n12</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n21</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n22</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>e12</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ps</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></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>vr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>vs</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>60</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>60</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn><mo>,</mo><mo> </mo><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>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mo> </mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</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"><mo>(</mo><mi>u1</mi><mo>,</mo><mi>u2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mo>-</mo><mn>2</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>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</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>2</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>5</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"><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi>r</mi><mspace linebreak="newline"/><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>p</mi><mi>s</mi><mspace linebreak="newline"/><mi>P</mi><mi>R</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>=</mo><mo>#</mo><mi>t</mi><mn>1</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un vector de r és #vr i el seu pendent és #pr

Un vector de s és #vs i el seu pendent és #ps

#c1

]]> 1MA.05.3.1.24Q PR ParamExpl PENDENTS Quina és la posició relativa 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¨»§#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» i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math»?
Format de la resposta:

pendent = enter o fracció simplificada
PR (posició relativa): 1 per secants, 2 per coincidents, 3 per paral·leles

]]> La situació és: r en blau, s en vermell

#G1

]]> 1.0000000 0.5000000 0 0 pendent de r=#prpendent de s=#psPR=#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"><mi>t11</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></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>t11</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol3</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><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>1</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></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u1</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>u2</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>v1</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>v2</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>D</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u1</mi></mtd><mtd><mi>v1</mi></mtd></mtr><mtr><mtd><mi>u2</mi></mtd><mtd><mi>v2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>D</mi><mo>≠</mo><mn>0</mn></mrow></apply></mtd></mtr></mtable><mtable><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t11</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>sol3</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><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>1</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></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>u1</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>u2</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>v1</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>v2</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>D</mi><mo>=</mo><mfenced 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open="["><mrow><mn>4</mn><mo>,</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>,</mo><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>5</mn><mo>,</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mfenced><mrow><mn>4</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>t11</mi><mo>,</mo><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>r</mi><mo>=</mo><mo>#</mo><mi>p</mi><mi>r</mi><mspace linebreak="newline"/><mi>p</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mo>=</mo><mo>#</mo><mi>p</mi><mi>s</mi><mspace linebreak="newline"/><mi>P</mi><mi>R</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>3</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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> Els pendents són #pr i #ps

#c1

]]> 1MA.05.3.1.50DT PR: VECTOR PUNTS Rectes secants Rectes paral·leles Rectes coincidents Tenen els vectors directors independents Tenen els vectors directors dependents Tenen els vectors directors dependents Tenen pendents diferents Tenen el mateix pendent Tenen el mateix pendent UN punt comú Cap punt comú TOTS els punts comuns

Cal doncs:

1. Comparar vector/pendents

2. Si els vectors són dependents es pot determinar si un dels vectors directors i un vector que les uneix són dependents

]]> 0.0000000 0.0000000 0 1MA.05.3.1.51Q PR param_cont(3 vectors) Considera les dues rectes:
r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» i s: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»21«/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¨»22«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math».

a) Troba el vector director de r inclòs en l'enunciat

b) Troba el vector director de s inclòs en l'enunciat

c) Troba el vector que va de r a s a partir dels punts de l'enunciat

d) Determina la posició relativa de r i s

Format de la resposta:

vector= [1,-2]
PR =posició relativa: 1 si secants, 2 si coincidents, 3 si paral·leles.

]]> La situació és #G1

]]> 1.0000000 0.5000000 0 0 vector de r =#vrvector de s =#vsvector de r a s =#vpPR(1,2,3)=#t1]]> <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>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>3</mn></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>t1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>v1</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>v2</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>v31</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>v32</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>u1</mi><mo>*</mo><mi>vv2</mi><mo>-</mo><mi>u2v1</mi><mo>≠</mo><mn>0</mn></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>independents</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t1</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>v31</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>v32</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr></mtable><mrow><mfenced><mrow><mi>u1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>u2</mi><mo>*</mo><mi>v1</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>u2</mi><mo>*</mo><mi>v31</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>v32</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a1</mi><mo>≠</mo><mi>b1</mi></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>a1</mi></mrow></mfenced><mo>=</mo><mi>u1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>a2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mfenced><mrow><mi>x</mi><mo>-</mo><mi>b1</mi></mrow></mfenced><mo>=</mo><mi>v1</mi><mo>*</mo><mfenced><mrow><mi>y</mi><mo>-</mo><mi>b2</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>v31</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>v32</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd><mi>D12</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u1</mi></mtd><mtd><mi>b1</mi><mo>-</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>u2</mi></mtd><mtd><mi>b2</mi><mo>-</mo><mi>a2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>u1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>u2</mi><mo>*</mo><mi>v1</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>D12</mi><mo>≠</mo><mn>0</mn></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</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>vp</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v31</mi><mo>,</mo><mi>v32</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n11</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>n12</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n21</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n22</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ps</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></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>B</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo></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>vr</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s</mi><mo>=</mo><mi>recta</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>vs</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada</mi><mo>=</mo><mn>60</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>60</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>r</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn><mo>,</mo><mo> </mo><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>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>s</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn><mo>,</mo><mo> </mo><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>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>vector</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo><mo>,</mo><mi>A</mi><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"><mi>p11</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</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>e11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>7</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>8</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>27</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>,</mo><mi>vs</mi><mo>,</mo><mi>vp</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>7</mn><mo>,</mo><mo>-</mo><mn>3</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mo>-</mo><mn>8</mn><mo>,</mo><mn>1</mn></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mn>10</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>A</mi><mo>,</mo><mi>B</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>5</mn><mo>,</mo><mn>6</mn></mrow></mfenced><mo>,</mo><mfenced><mrow><mn>5</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>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>r</mi><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>s</mi><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>r</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>p</mi><mspace linebreak="newline"/><mi>P</mi><mi>R</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>=</mo><mo>#</mo><mi>t</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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> El vector de r és #vr

El vector de s és #vs

El punt de r és #A i el punt de s és #B: el vector de r a s és #vp

Determina si són independents 2 a 2.

]]> 1MA.05.3.1.52Q PR cont_cont (3 vectors) Considera les dues rectes:
r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/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¨»12«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» i s: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»21«/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¨»22«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math».

a) Troba el vector director de r inclòs en l'enunciat

b) Troba el vector director de s inclòs en l'enunciat

c) Troba el vector que va de r a s a partir dels punts de l'enunciat

d) Determina la posició relativa de r i s

Format de la resposta:

vector= [1,-2]
PR =posició relativa: 1 si secants, 2 si coincidents, 3 si paral·leles.

]]> La situació és #G1

]]> 1.0000000 0.5000000 0 0 vector de r =#vrvector de s =#vsvector entre r i s =#vpPR(1,2,3)=#t1]]> <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>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>1</mn><mo>,</mo><mn>3</mn></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>t1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><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>1</mn><mo>,</mo><mn>9</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>r</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>r</mi><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>s</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>s</mi><mspace linebreak="newline"/><mi>v</mi><mi mathvariant="normal">e</mi><mi>c</mi><mi>t</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mi>r</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>r</mi><mo> </mo><mi mathvariant="normal">i</mi><mo> </mo><mi>s</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>p</mi><mspace linebreak="newline"/><mi>P</mi><mi>R</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>)</mo><mo>=</mo><mo>#</mo><mi>t</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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Un vector de r és #vr

Un vector de s és #vs

Un vector entre r i s és #vp

Són independents de 2 en 2?

]]> 1MA 05. RECTES EN EL PLA/1MA.05.3 PosRelativa Intersecció/1MA.05.3.2 Intersecció2Rectes 1MA.05.3.2.00DT INTERSECCIÓ 2 RECTES

Punt d'intersecció de 2 rectes

Per trobar el punt d'intersecció de 2 rectes secants,

es resol el sistema

format per les equacions de la forma més adient.

]]> 0.0000000 0.0000000 0 1MA.05.3.2.10DT PINTERSECCIÓ REDUCCIÓ

Punt d'intersecció: reducció

Si tens les equacions cartesianes, ho pots resoldre per reducció.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow mathcolor=¨#00007F¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mn mathvariant=¨bold¨ mathsize=¨12px¨»3«/mn»«mi mathvariant=¨bold¨ mathsize=¨12px¨»x«/mi»«mo mathvariant=¨bold¨ mathsize=¨12px¨»+«/mo»«mn mathvariant=¨bold¨ mathsize=¨12px¨»2«/mn»«mi mathvariant=¨bold-italic¨ mathsize=¨12px¨»y«/mi»«mo mathvariant=¨bold¨ mathsize=¨12px¨»=«/mo»«mn mathvariant=¨bold¨ mathsize=¨12px¨»8«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨ mathsize=¨12px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨12px¨»2«/mn»«mi mathvariant=¨bold¨ mathsize=¨12px¨»x«/mi»«mo mathvariant=¨bold¨ mathsize=¨12px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨12px¨»3«/mn»«mi mathvariant=¨bold-italic¨ mathsize=¨12px¨»y«/mi»«mo mathvariant=¨bold¨ mathsize=¨12px¨»=«/mo»«mo mathvariant=¨bold¨ mathsize=¨12px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨12px¨»7«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#8660;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mn mathvariant=¨bold¨ mathsize=¨12px¨»6«/mn»«mi mathvariant=¨bold¨ mathsize=¨12px¨»x«/mi»«mo mathvariant=¨bold¨ mathsize=¨12px¨»+«/mo»«mn mathvariant=¨bold¨ mathsize=¨12px¨»4«/mn»«mi mathvariant=¨bold¨ mathsize=¨12px¨»y«/mi»«mo mathvariant=¨bold¨ mathsize=¨12px¨»=«/mo»«mn mathvariant=¨bold¨ mathsize=¨12px¨»16«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨ mathsize=¨12px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨12px¨»6«/mn»«mi mathvariant=¨bold¨ mathsize=¨12px¨»x«/mi»«mo mathvariant=¨bold¨ mathsize=¨12px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨12px¨»9«/mn»«mi mathvariant=¨bold¨ mathsize=¨12px¨»y«/mi»«mo mathvariant=¨bold¨ mathsize=¨12px¨»=«/mo»«mo mathvariant=¨bold¨ mathsize=¨12px¨»-«/mo»«mn mathvariant=¨bold¨ mathsize=¨12px¨»21«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨».«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#8658;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨ mathsize=¨12px¨»x«/mi»«mo mathvariant=¨bold¨ mathsize=¨12px¨»=«/mo»«mn mathvariant=¨bold¨ mathsize=¨12px¨»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨ mathsize=¨12px¨»y«/mi»«mo mathvariant=¨bold¨ mathsize=¨12px¨»=«/mo»«mn mathvariant=¨bold¨ mathsize=¨12px¨»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/math»

Es tallen en el punt (2,1).

Si dona 0y=0, són coincidents.

Si dona 0y≠0, són paral·leles.

]]> 0.0000000 0.0000000 0 1MA.05.3.2.11Q PR+Intersecció CartCart Determina, per reducció, la posició relativa de les rectes i, si s'escau, les coordenades del seu punt d'intersecció:

Format de la resposta:

a) Equació (obtinguda després d'eliminar l'abscissa x): 8y=-12

b) Punt d'intersecció = (-1/3,2/3) entre parèntesis i simplificat

#G1

]]> 1.0000000 0.3333333 0 0 a) Equació =#sol1b) Punt =#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>a_1</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></mtd></mtr><mtr><mtd><mi>a_2</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><mo> 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>400</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>400</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>e11</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>3</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>e12</mi><mo>,</mo><mfenced close="}" open="{"><mtable 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xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>4</mn><mo>,</mo><mn>42</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>48</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi><mo>,</mo><mi>e22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>42</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>14</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>28</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m5</mi><mo>,</mo><mi>m6</mi><mo>,</mo><mi>m7</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>42</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>7</mn></math></output></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>d_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>40</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</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>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>P1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>0.6</mn><mo>,</mo><mo>-</mo><mn>0.1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>,</mo><mi>q2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>,</mo><mi>q2</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w2</mi></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"><mfenced><mtable><mtr><mtd><mn>42</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>48</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>24</mn></mtd></mtr><mtr><mtd><mo>-</mo><mn>42</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>14</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>28</mn></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>M2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>62</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mi>E</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><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><mi>P</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</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> És millor resoldre el sistema: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#007F00¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» per reducció

a) Elimina la y igualant els coeficients de la x:

Com que el mcm de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨11px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#233;s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»5«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»:«/mo»«/mrow»«/mstyle»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#007F00¨ open=¨{¨ close=¨¨»«mtable columnspacing=¨1.4ex¨ columnalign=¨left¨»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»11«/mn»«mo mathvariant=¨bold¨»§#8594;«/mo»«mi mathvariant=¨bold¨»multiplica«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»per«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»6«/mn»«mfenced»«mrow»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mtd»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»21«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»12«/mn»«mo mathvariant=¨bold¨»§#8594;«/mo»«mi mathvariant=¨bold¨»multiplica«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»per«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»7«/mn»«mfenced»«mrow»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»a«/mi»«mi mathvariant=¨bold-italic¨»_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mtd»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»22«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Ara, resta la 2a equació de la primera (canviant els signes)

]]> Per calcular x, l'abscissa del punt, substitueix l'ordenada y per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»y«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»11«/mn»«/mstyle»«/math» en qualsevol de les dues equacions.

Si ho fas amb la primera:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»+«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»0«/mn»«/mrow»«/mstyle»«/math»

]]> 1MA.05.3.2.20DT: PINTERSECCIÓ: IGUALACIÓ

Punt d'intersecció: igualació

Per igualar, escrivim les dues equacions explícites i igualem per calcular x:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mrow mathcolor=¨#003300¨»«mfenced open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathsize=¨12px¨ mathvariant=¨bold¨»y«/mi»«mo mathsize=¨12px¨ mathvariant=¨bold¨»=«/mo»«mn mathsize=¨12px¨ mathvariant=¨bold¨»3«/mn»«mi mathsize=¨12px¨ mathvariant=¨bold¨»x«/mi»«mo mathsize=¨12px¨ mathvariant=¨bold¨»+«/mo»«mn mathsize=¨12px¨ mathvariant=¨bold¨»2«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi mathsize=¨12px¨ mathvariant=¨bold¨»y«/mi»«mo mathsize=¨12px¨ mathvariant=¨bold¨»=«/mo»«mo mathsize=¨12px¨ mathvariant=¨bold¨»-«/mo»«mn mathsize=¨12px¨ mathvariant=¨bold¨»2«/mn»«mi mathsize=¨12px¨ mathvariant=¨bold¨»x«/mi»«mo mathsize=¨12px¨ mathvariant=¨bold¨»-«/mo»«mn mathsize=¨12px¨ mathvariant=¨bold¨»3«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathsize=¨12px¨ mathvariant=¨bold¨»§#8660;«/mo»«mn mathsize=¨12px¨ mathvariant=¨bold¨»3«/mn»«mi mathsize=¨12px¨ mathvariant=¨bold¨»x«/mi»«mo mathsize=¨12px¨ mathvariant=¨bold¨»+«/mo»«mn mathsize=¨12px¨ mathvariant=¨bold¨»2«/mn»«mo mathsize=¨12px¨ mathvariant=¨bold¨»=«/mo»«mo mathsize=¨12px¨ mathvariant=¨bold¨»-«/mo»«mn mathsize=¨12px¨ mathvariant=¨bold¨»2«/mn»«mi mathsize=¨12px¨ mathvariant=¨bold¨»x«/mi»«mo mathsize=¨12px¨ mathvariant=¨bold¨»-«/mo»«mn mathsize=¨12px¨ mathvariant=¨bold¨»3«/mn»«mo mathsize=¨12px¨ mathvariant=¨bold¨»§#8660;«/mo»«mn mathsize=¨12px¨ mathvariant=¨bold¨»5«/mn»«mi mathsize=¨12px¨ mathvariant=¨bold¨»x«/mi»«mo mathsize=¨12px¨ mathvariant=¨bold¨»=«/mo»«mo mathsize=¨12px¨ mathvariant=¨bold¨»-«/mo»«mn mathsize=¨12px¨ mathvariant=¨bold¨»5«/mn»«mo mathsize=¨12px¨ mathvariant=¨bold¨»§#8660;«/mo»«mi mathsize=¨12px¨ mathvariant=¨bold¨»x«/mi»«mo mathsize=¨12px¨ mathvariant=¨bold¨»=«/mo»«mo mathsize=¨12px¨ mathvariant=¨bold¨»-«/mo»«mn mathsize=¨12px¨ mathvariant=¨bold¨»1«/mn»«/mrow»«mstyle mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨/»«/math»

Per calcular y, substituïm x per (-1) en qualsevol de les dues equacions: y = 3·(-1) + 2 = -1 i es tallen en el punt (-1,-1).

Si dona 0x=0, són coincidents.

Si dona 0x≠0, són paral·leles.

]]> 0.0000000 0.0000000 0 1MA.05.3.2.21Q InterseccióExplExpl Igualació Considera les rectes d'equacions

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math» i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math»

Determina per igualació en quin punt es tallen.

Format de la resposta:

a) Escriu l'equació en x que et queda un cop igualat: 3x=15

b) Punt: (-3,5/3) simplificat i amb parèntesis

]]> Les rectes es tallen en el punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#7F0000¨»2«/mn»«/mrow»«/mstyle»«/math»

#G1

]]> 1.0000000 0.5000000 0 0 a) Equació =#sol1b) Punt =#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><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</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>m2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</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>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</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>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</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/></mtr></mtable><mrow><mfenced><mrow><mi>m1</mi><mo>≠</mo><mi>m2</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mfenced close="|" open="|"><mrow><mi>n2</mi><mo>-</mo><mi>n1</mi></mrow></mfenced><mo>⩽</mo><mn>5</mn><mo>*</mo><mfenced close="|" open="|"><mrow><mi>m1</mi><mo>-</mo><mi>m2</mi></mrow></mfenced></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd><mi>x1</mi><mo>=</mo><mfrac><mrow><mi>n2</mi><mo>-</mo><mi>n1</mi></mrow><mrow><mi>m1</mi><mo>-</mo><mi>m2</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mi>y1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>x1</mi><mo>+</mo><mi>n1</mi></mtd></mtr></mtable><mfenced><mrow><mfenced close="|" open="|"><mi>y1</mi></mfenced><mo>⩽</mo><mn>5</mn></mrow></mfenced></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>e1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n1</mi></math></input></command><command><input><math 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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>E</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><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><mi>P</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo> </mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</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> Es resol el sistema per igualació:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»f«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»f«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8660;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«/mstyle»«/math»

I es troba la 1a coordenada del punt.

]]> Per trobar la 2a coordenada cal substituir el valor trobat de x, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«/mrow»«/mstyle»«/math», en qualsevol de les dues equacions, per exemple, la primera:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»s«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]> 1MA.05.3.2.25Q. NoTall CartExpl Considera les rectes d'equacions
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math» i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math»

Determina per igualació la posició relativa de les rectes i, si s'escau, el seu punt d'intersecció

Format de la resposta:

a) Equació obtinguda per igualació = 3x=15

b) Posició relativa =1 si es tallen; 2 si són coincidents i 3 si són paral·leles

c) Punt =(-2,5/3) simplificat i entre parèntesis si existeix, 0(zero) si no es tallen.

]]> Les rectes són #f11

#G1

]]> 1.0000000 0.5000000 0 0 a) Equació = #sol1a) Posició relativa =#sol2b) Punt de tall =#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"><mi>w</mi><mo>=</mo><mi>aleatori</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></math></input></command><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>e12</mi><mo>=</mo><mi>m2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e13</mi><mo>=</mo><mo>(</mo><mi>m1</mi><mo>-</mo><mi>m2</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>=</mo><mi>n2</mi><mo>-</mo><mi>n1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>e13</mi></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>e11</mi><mo>=</mo><mi>e12</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>x1</mi><mo>+</mo><mi>n1</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>w</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>f11</mi><mo>=</mo><mo>"</mo><mi>secants</mi><mo>"</mo></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>w</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mn>2</mn></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>f11</mi><mo>=</mo><mo>"</mo><mi>coincidents</mi><mo>"</mo></mtd></mtr></mtable><mtable><mtr><mtd><mi>sol2</mi><mo>=</mo><mn>3</mn></mtd></mtr><mtr><mtd><mi>sol3</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>f11</mi><mo>=</mo><mo>"</mo><mi>paral</mi><mo>·</mo><mi>leles</mi><mo>"</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>400</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>400</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>40</mn><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>40</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>e1</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>e2</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m_1</mi><mo>,</mo><mi>n_1</mi><mo>,</mo><mi>m_2</mi><mo>,</mo><mi>n_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>,</mo><mi>n_1</mi><mo>,</mo><mi>m_2</mi><mo>,</mo><mi>n_2</mi></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><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</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>e3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>=</mo><mo>-</mo><mn>3</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/></mtr></mtable></mfenced></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>x1</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"><ms>P</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>paral·leles</ms></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>E</mi><mi>q</mi><mi>u</mi><mi>a</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</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>a</mi><mo>)</mo><mo> </mo><mi>P</mi><mi>o</mi><mi>s</mi><mi mathvariant="normal">i</mi><mi>c</mi><mi mathvariant="normal">i</mi><mi>ó</mi><mo> </mo><mi>r</mi><mi mathvariant="normal">e</mi><mi>l</mi><mi>a</mi><mi>t</mi><mi mathvariant="normal">i</mi><mi>v</mi><mi>a</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mi>P</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>t</mi><mi>a</mi><mi>l</mi><mi>l</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>3</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> Es transforma l'equació cartesiana en explícita:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow mathcolor=¨#007F00¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#8660;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mstyle»«/math»

Es resol el sistema per igualació; s'escriu y = y

I es determina la posició relativa, i el punt(si s'escau) amb «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¨»13«/mn»«/mrow»«/mstyle»«/math»

]]> 1MA.05.3.2.30DT PINTERSECCIÓ SUBSTITUCIÓ

Punt d'intersecció: substitució

Si tenim les equacions paramètriques (o la contínua o la vectorial) podem emprar el mètode de substitució «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold-italic¨»k«/mi»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mi mathvariant=¨bold-italic¨»k«/mi»«/mtd»«/mtr»«/mtable»«/mfenced»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mstyle»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»Substituint«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»per«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»les«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»equacions«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»param§#232;triques«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»:«/mo»«mspace linebreak=¨newline¨/»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»+«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»+«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»4«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»0«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨ mathsize=¨12px¨»4«/mn»«/math»

Substituïm la k en les equacions paramètriques, i trobem el punt d'intersecció (-1,2).

Si dona 0k=0, són coincidents.

Si dona 0k≠0, són paral·leles.

]]> 0.0000000 0.0000000 0 1MA.05.3.2.31Q Intersecció ContCart Substitució Emprant el mètode de substitució, determina en quin punt es tallen les dues rectes d'equacions:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«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¨»u_«/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¨»u_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math» i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math».

Format de la resposta:

a) Valor de k obtingut amb la substitució: k=2/3 (simplificat)

b) Punt de tall: (5/3,-2/3) simplificat i amb parèntesis.

]]> Les rectes es tallen en el punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#7F0000¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»per«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#7F0000¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#7F0000¨»1«/mn»«/mstyle»«/math»

#G1

]]> 1.0000000 0.3333333 0 0 a) Valor de k=#sol1b) Punt =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Dades</mi><mo> </mo><mi>perquè</mi><mo> </mo><mi>es</mi><mo> </mo><mi>tallin</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><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</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>4</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>4</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>4</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>u_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>u_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>D</mi><mo>=</mo><mfenced 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>e4</mi><mo>=</mo><mi>b_1</mi><mo>+</mo><mi>u_2</mi><mo>*</mo><mi>k</mi></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Determinar</mi><mo> </mo><mi>k</mi><mo> </mo><mi>en</mi><mo> </mo><mi>el</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>tall</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>v_2</mi><mo>*</mo><mo>(</mo><mi>a_1</mi><mo>+</mo><mi>u_1</mi><mo>*</mo><mi>k</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>-</mo><mi>v_1</mi><mo>*</mo><mo>(</mo><mi>b_1</mi><mo>+</mo><mi>u_2</mi><mo>*</mo><mi>k</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>k</mi><mo>=</mo><msub><mi>S</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><msub><mi>S</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Trobar</mi><mo> </mo><mi>el</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>tall</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>u_1</mi><mo>*</mo><mi>k1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>b_1</mi><mo>+</mo><mi>u_2</mi><mo>*</mo><mi>k1</mi></math></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><mi>u_2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>-</mo><mi>u_1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>b_1</mi><mo>)</mo><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>v_2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>-</mo><mi>v_1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>punt</mi><mfenced><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><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Pistes</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>v_1</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>s51</mi><mo>=</mo><mo>"</mo><mo>-</mo><mo>"</mo></mrow><mrow><mi>s51</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>v11</mi><mo>=</mo><mfenced close="|" open="|"><mi>v_1</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c52</mi><mo>=</mo><mo>-</mo><mi>v_2</mi><mo>*</mo><mi>a_2</mi><mo>+</mo><mi>v_1</mi><mo>*</mo><mi>b_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>c52</mi><mo>></mo><mn>0</mn></mrow><mrow><mi>s52</mi><mo>=</mo><mo>"</mo><mo>+</mo><mo>"</mo></mrow><mrow><mi>c52</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>c51</mi><mo>=</mo><mfenced close="|" open="|"><mi>c52</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e6</mi><mo>=</mo><mfenced><mrow><mi>v_2</mi><mo>*</mo><mo>(</mo><mi>a_1</mi><mo>+</mo><mi>u_1</mi><mo>*</mo><mi>k</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>-</mo><mi>v_1</mi><mo>*</mo><mo>(</mo><mi>b_1</mi><mo>+</mo><mi>u_2</mi><mo>*</mo><mi>k</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><mo>=</mo><mn>0</mn></mrow></mfenced></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Gràfic</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u_1</mi><mo>,</mo><mi>u_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v_1</mi><mo>,</mo><mi>v_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mfenced><mrow><mi>a_1</mi><mo>,</mo><mi>b_1</mi></mrow></mfenced><mo>,</mo><mi>u1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mfenced><mrow><mi>a_2</mi><mo>,</mo><mi>b_2</mi></mrow></mfenced><mo>,</mo><mi>v1</mi></mrow></mfenced></math></input></command><command><input><math 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align="center"><mtr><mtd><mi>k</mi><mo>=</mo><mo>-</mo><mn>6</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></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"><mi>k</mi><mo>=</mo><mo>-</mo><mn>6</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><mn>22</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>14</mn></mtd></mtr></mtable></mfenced></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><mrow><mn>22</mn><mo>,</mo><mo>-</mo><mn>14</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e6</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>k</mi><mo>+</mo><mn>42</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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>V</mi><mi>a</mi><mi>l</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>k</mi><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><mi>P</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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> Escriu les equacions paramètriques de r:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#007F00¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold-italic¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold-italic¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

substitueix x i y en l'equació de s, «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¨»2«/mn»«/mstyle»«/math», per trobar el valor de k:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»v«/mi»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»s«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»51«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»11«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»s«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»52«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#007F00¨»c«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»51«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»0«/mn»«/mstyle»«/math»

]]> Si resols:

trobes el valor de k: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«/mrow»«/mstyle»«/math»

Substituint k per aquest valor en les equacions paramètriques, troba les coordenades (abscissa i ordenada) del punt d'intersecció.

]]> 1MA.05.3.2.32Q IntersContExpl Substitució Resolent el sistema per substitució determina en quin punt es tallen les dues rectes d'equacions:

Format de la resposta:

a) Valor de k =-2/3

b) Punt de tall: (-1/3,5/3), simplificat i amb parèntesis

]]> Les rectes es tallen en el punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#7F0000¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»per«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#7F0000¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#7F0000¨»1«/mn»«/mstyle»«/math»

#G1

]]> 1.0000000 0.5000000 0 0 a) Valor de k =#sol1b) Punt =#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>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</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>4</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>4</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>4</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>u_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>u_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>v_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>v_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>D</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u_1</mi></mtd><mtd><mi>v_1</mi></mtd></mtr><mtr><mtd><mi>u_2</mi></mtd><mtd><mi>v_2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>D</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mi>a_1</mi></mtd></mtr></mtable></mfenced><mi>u_1</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mi>b_1</mi></mtd></mtr></mtable></mfenced><mi>u_2</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>a_1</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>b_1</mi></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>e_2</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mfenced><mrow><mi>a_2</mi><mo>,</mo><mi>b_2</mi></mrow></mfenced><mo>,</mo><mfenced close="]" open="["><mrow><mi>v_1</mi><mo>,</mo><mi>v_2</mi></mrow></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>u_1</mi><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e4</mi><mo>=</mo><mi>b_1</mi><mo>+</mo><mi>u_2</mi><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>v_2</mi><mo>*</mo><mo>(</mo><mi>a_1</mi><mo>+</mo><mi>u_1</mi><mo>*</mo><mi>k</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>-</mo><mi>v_1</mi><mo>*</mo><mo>(</mo><mi>b_1</mi><mo>+</mo><mi>u_2</mi><mo>*</mo><mi>k</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><mo>=</mo><mn>0</mn></mrow></mfenced></math></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><mi>u_2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>-</mo><mi>u_1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>b_1</mi><mo>)</mo><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>v_2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>-</mo><mi>v_1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><msub><mi>S</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>k1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>u_1</mi><mo>*</mo><mi>k1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>b_1</mi><mo>+</mo><mi>u_2</mi><mo>*</mo><mi>k1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>punt</mi><mfenced><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><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Gràfic</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u_1</mi><mo>,</mo><mi>u_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v_1</mi><mo>,</mo><mi>v_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mfenced><mrow><mi>a_1</mi><mo>,</mo><mi>b_1</mi></mrow></mfenced><mo>,</mo><mi>u1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mfenced><mrow><mi>a_2</mi><mo>,</mo><mi>b_2</mi></mrow></mfenced><mo>,</mo><mi>v1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura</mi><mo>=</mo><mn>100</mn><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>100</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r1</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r2</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>sol2</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>5</mn></mrow></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>5</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>3</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><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>e4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</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>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>1</mn><mn>5</mn></mfrac></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><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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>V</mi><mi>a</mi><mi>l</mi><mi>o</mi><mi>r</mi><mo> </mo><mi mathvariant="normal">d</mi><mi mathvariant="normal">e</mi><mo> </mo><mi>k</mi><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><mi>P</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><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> Escriu les equacions paramètriques de r:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#007F00¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold-italic¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold-italic¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Substitueix x i y en l'equació de s, «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¨»2«/mn»«/mstyle»«/math», per trobar el valor de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»k«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«/mrow»«/mstyle»«/math».

Amb aquest valor de k, substituint k en les equacions paramètriques de r, pots trobar les coordenades del punt

]]> 1MA.05.3.2.33Q Intersecció ParaCart Substitució Resolent el sistema per substitució, determina en quin punt es tallen les dues rectes d'equacions:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math» i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math»?
Format de la resposta:

a) Valor de k=-2/3 (simplificat)

b) Punt =(2/3,-1/3) simplificat i entre parèntesis.

]]> Les rectes es tallen en el punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#7F0000¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»per«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#7F0000¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#7F0000¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#7F0000¨»sol«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#7F0000¨»1«/mn»«/mstyle»«/math»

#G1

]]> 1.0000000 0.5000000 0 0 a) k=#sol1b) Punt =#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>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>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>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_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>u_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>u_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>v_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>v_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>D</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>u_1</mi></mtd><mtd><mi>v_1</mi></mtd></mtr><mtr><mtd><mi>u_2</mi></mtd><mtd><mi>v_2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>D</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mi>a_1</mi></mtd></mtr></mtable></mfenced><mi>u_1</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mi>b_1</mi></mtd></mtr></mtable></mfenced><mi>u_2</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>a_1</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>b_1</mi></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>e_2</mi><mo>=</mo><mi>v_2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>-</mo><mi>v_1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>u_1</mi><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e4</mi><mo>=</mo><mi>b_1</mi><mo>+</mo><mi>u_2</mi><mo>*</mo><mi>k</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>v_2</mi><mo>*</mo><mo>(</mo><mi>a_1</mi><mo>+</mo><mi>u_1</mi><mo>*</mo><mi>k</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>-</mo><mi>v_1</mi><mo>*</mo><mo>(</mo><mi>b_1</mi><mo>+</mo><mi>u_2</mi><mo>*</mo><mi>k</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><mo>=</mo><mn>0</mn></mrow></mfenced></math></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><mi>u_2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_1</mi><mo>)</mo><mo>-</mo><mi>u_1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>b_1</mi><mo>)</mo><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd><mi>v_2</mi><mo>*</mo><mo>(</mo><mi>x</mi><mo>-</mo><mi>a_2</mi><mo>)</mo><mo>-</mo><mi>v_1</mi><mo>*</mo><mo>(</mo><mi>y</mi><mo>-</mo><mi>b_2</mi><mo>)</mo><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k1</mi><mo>=</mo><msub><mi>S</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>k1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>u_1</mi><mo>*</mo><mi>k1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>b_1</mi><mo>+</mo><mi>u_2</mi><mo>*</mo><mi>k1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>punt</mi><mfenced><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><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Gràfic</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u_1</mi><mo>,</mo><mi>u_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v_1</mi><mo>,</mo><mi>v_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mfenced><mrow><mi>a_1</mi><mo>,</mo><mi>b_1</mi></mrow></mfenced><mo>,</mo><mi>u1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>recta</mi><mfenced><mrow><mi>punt</mi><mfenced><mrow><mi>a_2</mi><mo>,</mo><mi>b_2</mi></mrow></mfenced><mo>,</mo><mi>v1</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura</mi><mo>=</mo><mn>100</mn><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>100</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r1</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>r2</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>sol2</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mn>9</mn></mtd></mtr></mtable></mfenced><mn>1</mn></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mn>3</mn></mtd></mtr></mtable></mfenced><mrow><mo>-</mo><mn>6</mn></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>90</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_4</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"><mi>k</mi><mo>=</mo><mfrac><mn>177</mn><mn>41</mn></mfrac></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><mrow><mfrac><mn>546</mn><mn>41</mn></mfrac><mo>,</mo><mo>-</mo><mfrac><mn>939</mn><mn>41</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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>k</mi><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><mi>P</mi><mi>u</mi><mi>n</mi><mi>t</mi><mo> </mo><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> Amb les equacions paramètriques de r:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#007F00¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold-italic¨»x«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mtd»«/mtr»«mtr»«mtd»«mi mathvariant=¨bold-italic¨»y«/mi»«mo mathvariant=¨bold¨»=«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»4«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Substitueix k per aquest valor en les equacions paramètriques de r, i trobaràs les coordenades del punt

]]> 1MA.05.3.2.50DT MÈTODE INTERSECCIÓ

Millor mètode

Per trobar el punt d'intersecció de 2 rectes secants, pots escollir entre reducció, igualació o substitució.

El millor mètode no existeix però cal tenir en compte:

quin està més adaptat a les dades. Per exemple, amb dues explícites, el mètode aconsellable seria el d'igualació.
quin està més adaptat a tu! Sempre serà el que domines més i amb el qual vas més ràpid... sempre i quan això no t'obligui a realitzar masses conversions entre equacions.

]]> 0.0000000 0.0000000 0 1MA.05.3.2.51Q InterseccióCartExpl Igualació? Considera les rectes d'equacions

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math» i «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math»
Quina és la seva posició relativa? Si es tallen, determina les coordenades del seu punt d'intersecció)

Format de la resposta: (1,-3/4)_simplificada_si es tallen; C si són coincidents i P si són paral·leles

]]> Les rectes són #t11

#G1

]]> 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"><mi>k1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></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>k1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><mi>t11</mi><mo>=</mo><mo>"</mo><mi>secants</mi><mo>"</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>m2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>n3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>D1</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>m1</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>m2</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mi>D1</mi><mo>≠</mo><mn>0</mn></mrow></mfenced></apply></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>t11</mi><mo>=</mo><mo>"</mo><mi>coincidents</mi><mo>"</mo></mtd></mtr><mtr><mtd><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>m2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>n3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>D1</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>m1</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr><mtr><mtd><mi>m2</mi></mtd><mtd><mo>-</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd><mi>D2</mi><mo>=</mo><mfenced close="|" open="|"><mtable><mtr><mtd><mi>m1</mi></mtd><mtd><mi>n1</mi></mtd></mtr><mtr><mtd><mi>m2</mi></mtd><mtd><mi>n2</mi></mtd></mtr></mtable></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>D1</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>D2</mi><mo>=</mo><mn>0</mn></mrow></mfenced></mrow></apply></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>m2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>n3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>D1</mi><mo>=</mo><mfenced 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xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mn>2</mn><mo>*</mo><mo>(</mo><mi>m2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mi>n2</mi><mo>)</mo><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>m2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e11</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi><mo>=</mo><mi>m2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>n2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e13</mi><mo>=</mo><mo>(</mo><mi>m1</mi><mo>-</mo><mi>m2</mi><mo>)</mo><mo>*</mo><mi>x</mi><mo>=</mo><mi>n2</mi><mo>-</mo><mi>n1</mi></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>e11</mi><mo>=</mo><mi>e12</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x1</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>x1</mi><mo>+</mo><mi>n1</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>k1</mi><mo>=</mo><mn>1</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>x1</mi><mo>,</mo><mi>y1</mi><mo>)</mo></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>k1</mi><mo>=</mo><mn>2</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mo>"</mo><mi>C</mi><mo>"</mo></mrow><mrow><mi>sol</mi><mo>=</mo><mo>"</mo><mi>P</mi><mo>"</mo></mrow></apply></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>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura_finestra</mi><mo>=</mo><mn>400</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>400</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>50</mn><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>50</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>e1</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>4</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>e2</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>sol</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>9</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m_1</mi><mo>,</mo><mi>n_1</mi><mo>,</mo><mi>m_2</mi><mo>,</mo><mi>n_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>,</mo><mi>n_1</mi><mo>,</mo><mi>m_2</mi><mo>,</mo><mi>n_2</mi></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><mn>5</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</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>e3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mn>5</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</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/></mtr></mtable></mfenced></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>x1</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"><ms>P</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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="check_simplified"/><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> Es transforma l'equació cartesiana a explícita:

Es resol el sistema per igualació; s'escriu y = y

També es pot fer amb un altre mètode de resolució

]]> Resolent «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¨»13«/mn»«/mstyle»«/math» es troba la primera coordenada (abscissa) del punt, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»x«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«/mrow»«/mstyle»«/math».

Per trobar la 2a coordenada (ordenada) del punt es pot substituir x en l'equació explícita:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»+«/mo»«mfenced mathcolor=¨#007F00¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

]]> 1MA 05. RECTES EN EL PLA/1MA.05.4 Angles i distàncies 1MA.05.4.10DT Angle entre rectes

Angle entre rectes

L'angle entre dues rectes és el que formen els seus vectors directors (o el seu suplementari, si l'angle és obtús)

L'angle entre dos vectors és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#003300¨»«mover»«mrow»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8640;«/mo»«/mover»«mo mathvariant=¨bold¨»,«/mo»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8640;«/mo»«/mover»«/mrow»«mo mathvariant=¨bold¨»^«/mo»«/mover»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»acos«/mi»«mfrac mathcolor=¨#003300¨»«mrow»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8640;«/mo»«/mover»«mo mathvariant=¨bold¨»§#183;«/mo»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8640;«/mo»«/mover»«/mrow»«mrow»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8640;«/mo»«/mover»«/mfenced»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8640;«/mo»«/mover»«/mfenced»«/mfenced»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1MA.05.4.11Q AngleRectes Cont_Cont Considera les dues rectes?
r: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/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¨»12«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» i s: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»21«/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¨»22«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math».

a) Troba el vector de r inclòs en l'enunciat

b) Troba el vector de s inclòs en l'enunciat

c) Determina l'angle entre les dues rectes
Format de la resposta:

vector: [1,2]

angle en graus, arrodonit a la unitat:37º

]]> Gràficament: #G1

]]> 1.0000000 0.5000000 0 0 vr =#vrvs =#vsangle =#sol4]]> <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>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></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>t1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>v1</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>v2</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>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>rang</mi><mfenced><mtable><mtr><mtd><mi>u2</mi></mtd><mtd><mo>-</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi></mtd><mtd><mo>-</mo><mi>v1</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mn>2</mn></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>independents</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t1</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>a1</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>a2</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>u1</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>u2</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>b1</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mfrac><mrow><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mrow><mrow><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mrow></mfrac><mo>≠</mo><mfrac><mi>u2</mi><mi>v2</mi></mfrac></mrow></mfenced></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</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>n11</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>n12</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n21</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n22</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pe</mi><mo>=</mo><apply><scalarproduct/><mi>vr</mi><mi>vs</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pm</mi><mo>=</mo><mfenced close="‖" open="‖"><mi>vr</mi></mfenced><mo>*</mo><mfenced close="‖" open="‖"><mi>vs</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>co</mi><mo>=</mo><mfrac><mi>pe</mi><mi>pm</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mrow><mi>acos</mi><mfrac><mi>pe</mi><mi>pm</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>sol2</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>sol2</mi><mo>⩽</mo><mn>90</mn></mrow><mrow><mi>sol3</mi><mo>=</mo><mi>sol2</mi></mrow><mrow><mi>sol3</mi><mo>=</mo><mn>180</mn><mo>-</mo><mi>sol2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>sol3</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><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>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>recta</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo><mo>,</mo><mi>vr</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>recta</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo><mo>,</mo><mi>vs</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>vr</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>vs</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</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>e11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>+</mo><mn>7</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>6</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>70</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>7</mn><mo>,</mo><mn>1</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>6</mn><mo>,</mo><mn>2</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"><msub><mi>v</mi><mi>r</mi></msub><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>r</mi><mspace linebreak="newline"/><msub><mi>v</mi><mi>s</mi></msub><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>s</mi><mspace linebreak="newline"/><mi>a</mi><mi>n</mi><mi>g</mi><mi>l</mi><mi mathvariant="normal">e</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>4</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> Un vector de r és #vr

Un vector de s és #vs

L'angle es calcula amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»acos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«msqrt»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«mo»§#160;«/mo»«mo»§#160;«/mo»«mo»§#160;«/mo»«msqrt»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»acos«/mi»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»pe«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»pm«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 1MA.05.4.12Q AngleRectes Cont_Cart Considera les dues rectes
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«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¨»11«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/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¨»12«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mrow»«/mstyle»«/math»

a) Troba el vector de r inclòs en l'enunciat

b) Troba el vector de s inclòs en l'enunciat

c) Determina l'angle entre les dues rectes

Format de la resposta:

vectors: [1,2]

angle en graus, arrodonit a la unitat: 54º

]]> Gràficament: #G1

]]> 1.0000000 0.5000000 0 0 vr =#vrvs =#vsangle =#sol4]]> <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>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></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>t1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><apply><csymbol 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align="center"><mtr><mtd><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>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>recta</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo><mo>,</mo><mi>vr</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>recta</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo><mo>,</mo><mi>vs</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>vr</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>vs</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</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"><mo>(</mo><mi>u1</mi><mo>,</mo><mi>u2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</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"><mn>2</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>+</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>2</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>19</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>4</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>vs</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>72</mn><mo> </mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></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"><msub><mi>v</mi><mi>r</mi></msub><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>r</mi><mspace linebreak="newline"/><msub><mi>v</mi><mi>s</mi></msub><mo> </mo><mo>=</mo><mo>#</mo><mi>v</mi><mi>s</mi><mspace linebreak="newline"/><mi>a</mi><mi>n</mi><mi>g</mi><mi>l</mi><mi mathvariant="normal">e</mi><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>4</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> Un vector de r és #vr

Un vector de s és #vs

L'angle es calcula amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#00066F¨»acos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00066F¨»§#160;«/mo»«mfrac mathcolor=¨#00066F¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«msqrt»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«mo»§#160;«/mo»«mo»§#160;«/mo»«msqrt»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00066F¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00066F¨»acos«/mi»«mfrac mathcolor=¨#00066F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»pe«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»pm«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

La situació és aquesta: #G1

]]> 1MA.05.4.13Q AngleRectes Expl_Cart Quin angle formen les dues rectes?
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mstyle displaystyle=¨false¨»«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»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/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»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/mstyle»«/math»

Format de la resposta: angle en graus, arrodonit a la unitat: 34º

]]> Gràficament: #G1

]]> 1.0000000 0.5000000 0 0 #sol4 <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>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></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>t1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>v1</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>v2</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 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align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>u2</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>b1</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>pendents</mi><mo> </mo><mi>són</mi><mo> </mo><mi>iguals</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mfrac><mrow><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mrow><mrow><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mrow></mfrac><mo>≠</mo><mfrac><mi>u2</mi><mi>v2</mi></mfrac></mrow></mfenced></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>pendents</mi><mo> </mo><mi>són</mi><mo> </mo><mi>iguals</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr</mi><mo>=</mo><mfrac><mi>u2</mi><mi>u1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ps</mi><mo>=</mo><mfrac><mi>v2</mi><mi>v1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mrow><mrow><mo>-</mo><mi>u1</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>-</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>+</mo><mi>b2</mi><mo>*</mo><mi>v1</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi><mo>=</mo><mi>y</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mrow><mrow><mo>-</mo><mi>v1</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</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>pe</mi><mo>=</mo><apply><scalarproduct/><mi>vr</mi><mi>vs</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pm</mi><mo>=</mo><mfenced close="‖" open="‖"><mi>vr</mi></mfenced><mo>*</mo><mfenced close="‖" open="‖"><mi>vs</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>co</mi><mo>=</mo><mfrac><mi>pe</mi><mi>pm</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mrow><mi>acos</mi><mfrac><mi>pe</mi><mi>pm</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>sol2</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>sol2</mi><mo>⩽</mo><mn>90</mn></mrow><mrow><mi>sol3</mi><mo>=</mo><mi>sol2</mi></mrow><mrow><mi>sol3</mi><mo>=</mo><mn>180</mn><mo>-</mo><mi>sol2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>sol3</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><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>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>recta</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo><mo>,</mo><mi>vr</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>recta</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo><mo>,</mo><mi>vs</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>vr</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>vs</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</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"><mo>(</mo><mi>u1</mi><mo>,</mo><mi>u2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mn>7</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"><mn>1</mn><mo>,</mo><mo>-</mo><mn>9</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>7</mn><mn>5</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>73</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>-</mo><mi>y</mi><mo>+</mo><mn>68</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y</mi><mo>=</mo><mo>-</mo><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>68</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pr</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>7</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ps</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</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>42</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol4</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> Un vector de r és #vr

Un vector de s és #vs

L'angle es calcula amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»acos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«msqrt»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«mo mathvariant=¨bold¨»§#183;«/mo»«msqrt»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»acos«/mi»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»pe«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»pm«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

La situació és aquesta: #G1

]]> 1MA.05.4.14Q AngleRectes Para_Cont Quin angle formen les rectes «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨}¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«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¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»21«/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¨»22«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» ?

Format de la resposta:

angle en graus arrodonit a la unitat: 34º

]]> Gràficament: #G1

]]> 1.0000000 0.5000000 0 0 #sol4 <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>t1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>3</mn></mtd></mtr></mtable></mfenced></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>t1</mi><mo>=</mo><mn>1</mn></mrow><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>v1</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>v2</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>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>rang</mi><mfenced><mtable><mtr><mtd><mi>u2</mi></mtd><mtd><mo>-</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi></mtd><mtd><mo>-</mo><mi>v1</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mn>2</mn></mrow></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>independents</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>t1</mi><mo>=</mo><mn>2</mn></mrow><mtable><mtr><mtd><mi>a1</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>a2</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>u1</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>u2</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>b1</mi><mo>=</mo><mi>a1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>a2</mi></mtd></mtr><mtr><mtd><mi>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><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>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>a2</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>u1</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>u2</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>b1</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>b2</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>m1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mi>m1</mi><mo>*</mo><mi>u2</mi></mtd></mtr><mtr><mtd><mi>e11</mi><mo>=</mo><mi>u2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>u1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mtd></mtr><mtr><mtd><mi>e12</mi><mo>=</mo><mi>v2</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>v1</mi><mo>*</mo><mi>y</mi><mo>=</mo><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mfrac><mrow><mi>a1</mi><mo>*</mo><mi>u2</mi><mo>-</mo><mi>a2</mi><mo>*</mo><mi>u1</mi></mrow><mrow><mi>b1</mi><mo>*</mo><mi>v2</mi><mo>-</mo><mi>b2</mi><mo>*</mo><mi>v1</mi></mrow></mfrac><mo>≠</mo><mfrac><mi>u2</mi><mi>v2</mi></mfrac></mrow></mfenced></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mo>"</mo><mi>Els</mi><mo> </mo><mi>vectors</mi><mo> </mo><mi>són</mi><mo> </mo><mi>dependents</mi><mo>;</mo><mo> </mo><mi>cal</mi><mo> </mo><mi>esbrinar</mi><mo> </mo><mi>si</mi><mo> </mo><mi>un</mi><mo> </mo><mi>punt</mi><mo> </mo><mi>de</mi><mo> </mo><mi>r</mi><mo> </mo><mi>pertany</mi><mo> </mo><mi>a</mi><mo> </mo><mi>s</mi><mo>"</mo></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>u1</mi><mo>,</mo><mi>u2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</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>p11</mi><mo>=</mo><mi>x</mi><mo>=</mo><mi>a1</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p12</mi><mo>=</mo><mi>y</mi><mo>=</mo><mi>a2</mi><mo>+</mo><mi>k</mi><mo>*</mo><mi>u2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n21</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n22</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>b2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pe</mi><mo>=</mo><apply><scalarproduct/><mi>vr</mi><mi>vs</mi></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pm</mi><mo>=</mo><mfenced close="‖" open="‖"><mi>vr</mi></mfenced><mo>*</mo><mfenced close="‖" open="‖"><mi>vs</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>co</mi><mo>=</mo><mfrac><mi>pe</mi><mi>pm</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced><mrow><mi>acos</mi><mfrac><mi>pe</mi><mi>pm</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>sol2</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>sol2</mi><mo>⩽</mo><mn>90</mn></mrow><mrow><mi>sol3</mi><mo>=</mo><mi>sol2</mi></mrow><mrow><mi>sol3</mi><mo>=</mo><mn>180</mn><mo>-</mo><mi>sol2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>sol3</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><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>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>recta</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo><mo>,</mo><mi>vr</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>recta</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo><mo>,</mo><mi>vs</mi><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>1</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>vr</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>blau</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>vs</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t1</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>e11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>3</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>22</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>8</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>41</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vr</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>3</mn><mo>,</mo><mn>4</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>vs</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>8</mn><mo>,</mo><mn>9</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"><mn>78.503</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>79</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pe</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>pm</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msqrt><mn>145</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>co</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>12</mn><mo>*</mo><msqrt><mn>145</mn></msqrt></mrow><mn>725</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>#sol4</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> Un vector de r és #vr

Un vector de s és #vs

L'angle es calcula amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»acos«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«mrow»«msqrt»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u«/mi»«mn mathvariant=¨bold¨»2«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«mo mathvariant=¨bold¨»§#183;«/mo»«msqrt»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»acos«/mi»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»pe«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»pm«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

La situació és aquesta: #G1

]]> 1MA.05.4.15Q Trobar m/ 2RectesFormenAngle60º Per quin(s) valor(s) de m les 2 rectes que tenen les equacions següents formen un angle de 60º?

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mstyle»«/math»

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mfrac»«mrow»«mn mathvariant=¨bold¨»3«/mn»«msqrt»«mn mathvariant=¨bold¨»5«/mn»«/msqrt»«/mrow»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨»+«/mo»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«mo mathvariant=¨bold¨»,«/mo»«mfrac»«mrow»«mn mathvariant=¨bold¨»3«/mn»«msqrt»«mn mathvariant=¨bold¨»5«/mn»«/msqrt»«/mrow»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨»+«/mo»«mfrac»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»4«/mn»«/mfrac»«/mrow»«/mfenced»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #sol1 <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><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a11</mi><mo>=</mo><mi>m</mi></mtd></mtr><mtr><mtd><mi>b11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>c11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v1</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>b11</mi><mo>,</mo><mi>m</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>a12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>b12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>c12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</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></mtd></mtr><mtr><mtd><mi>v2</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>b12</mi><mo>,</mo><mi>a12</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mn>3</mn><mo>*</mo><msup><mfenced><mi>a12</mi></mfenced><mn>2</mn></msup><mo>-</mo><msup><mfenced><mi>b12</mi></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mn>8</mn><mo>*</mo><mi>b11</mi><mo>*</mo><mi>b12</mi><mo>*</mo><mi>a12</mi></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mn>3</mn><mo>*</mo><msup><mfenced><mi>b11</mi></mfenced><mn>2</mn></msup><mo>*</mo><msup><mfenced><mi>b12</mi></mfenced><mn>2</mn></msup><mo>-</mo><msup><mfenced><mi>b11</mi></mfenced><mn>2</mn></msup><mo>*</mo><msup><mfenced><mi>a12</mi></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><msup><mi>b</mi><mn>2</mn></msup><mo>-</mo><mn>4</mn><mo>*</mo><mi>a</mi><mo>*</mo><mi>c</mi></mtd></mtr></mtable><mfenced><mrow><mi>d</mi><mo>></mo><mn>0</mn></mrow></mfenced></apply></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>m1</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>+</mo><msqrt><mi>d</mi></msqrt></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac></mtd></mtr><mtr><mtd><mi>m2</mi><mo>=</mo><mfrac><mrow><mo>-</mo><mi>b</mi><mo>-</mo><msqrt><mi>d</mi></msqrt></mrow><mrow><mn>2</mn><mo>*</mo><mi>a</mi></mrow></mfrac></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mi>m1</mi><mo>*</mo><mi>m2</mi><mo>∈</mo><rationals/></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>e_1</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b11</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c11</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><mi>a12</mi><mo>*</mo><mi>x</mi><mo>-</mo><mi>b12</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c12</mi><mo>=</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>m1</mi><mo>,</mo><mi>m2</mi></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><mfrac><apply><scalarproduct/><mi>v1</mi><mi>v2</mi></apply><mrow><mfenced close="‖" open="‖"><mi>v1</mi></mfenced><mo>*</mo><mfenced close="‖" open="‖"><mi>v2</mi></mfenced></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f11</mi><mo>=</mo><mfenced><mrow><mn>2</mn><mo>*</mo><apply><scalarproduct/><mi>v1</mi><mi>v2</mi></apply></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f12</mi><mo>=</mo><msup><mfenced><mrow><mn>2</mn><mo>*</mo><apply><scalarproduct/><mi>v1</mi><mi>v2</mi></apply></mrow></mfenced><mn>2</mn></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f21</mi><mo>=</mo><mfenced><mrow><mfenced close="‖" open="‖"><mi>v1</mi></mfenced><mo>*</mo><mfenced close="‖" open="‖"><mi>v2</mi></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f22</mi><mo>=</mo><msup><mfenced><mrow><mfenced close="‖" open="‖"><mi>v1</mi></mfenced><mo>*</mo><mfenced close="‖" open="‖"><mi>v2</mi></mfenced></mrow></mfenced><mn>2</mn></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</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>e_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mi>x</mi><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>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>40</mn><mo>,</mo><mn>50</mn><mo>,</mo><mn>1200</mn></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>5</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>-</mo><mn>10</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"><mfrac><mrow><mo>-</mo><mi>m</mi><mo>-</mo><mn>5</mn></mrow><mrow><msqrt><mn>2</mn></msqrt><mo>*</mo><msqrt><mrow><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mn>25</mn></mrow></msqrt></mrow></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f11</mi><mo>,</mo><mi>f12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>2</mn><mo>*</mo><mi>m</mi><mo>-</mo><mn>10</mn><mo>,</mo><mn>4</mn><mo>*</mo><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mn>40</mn><mo>*</mo><mi>m</mi><mo>+</mo><mn>100</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f21</mi><mo>,</mo><mi>f22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt><mo>*</mo><msqrt><mrow><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mn>25</mn></mrow></msqrt><mo>,</mo><mn>2</mn><mo>*</mo><msup><mi>m</mi><mn>2</mn></msup><mo>+</mo><mn>50</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"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>-</mo><mn>10</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>-</mo><mn>10</mn></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>#sol1</correctAnswer></correctAnswers><assertions><assertion name="equivalent_symbolic"/><assertion name="syntax_expression"/></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> Els vectors directors de les rectes són «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mover mathcolor=¨#00007F¨»«mrow»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»1«/mn»«mo»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mover mathcolor=¨#00007F¨»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#00007F¨»v«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«/mstyle»«/math»

Per una banda, el cosinus de l'angle que formen les rectes és

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»cosa«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8201;«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨»§#183;«/mo»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mrow»«mrow»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mfenced»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mfenced»«/mfenced»«/mrow»«/mfrac»«/mstyle»«/math»

per altra banda, el cosinus de 60º és 1/2.

Cal doncs resoldre:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8201;«/mo»«mfrac mathcolor=¨#00007F¨»«mrow»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨»§#183;«/mo»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mrow»«mrow»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mfenced»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfenced open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mfenced»«/mfenced»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«/mstyle»«/math»

]]> Cal resoldre:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»21«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mfrac mathcolor=¨#00007F¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8660;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#183;«/mo»«mfenced mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«mn mathvariant=¨bold¨»11«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»f«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»21«/mn»«/mrow»«/mstyle»«/math»

Si elevem els dos membres al quadrat, obtenim una equació de 2n grau:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»f«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»12«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»§#8201;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»f«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#00007F¨»22«/mn»«/mrow»«/mstyle»«/math»

]]> 1MA.05.4.21Q Trobar 3 angles d'un triangle Dibuixa el triangle de vèrtex «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«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»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«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»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»C«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»,
i determina els angles que corresponen a cada vèrtex.

Format: 54º (arrodonit en graus)

]]> #G1

]]> 1.0000000 0.5000000 0 0 A=#sol1B=#sol2C=#sol3]]> <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>enunciat</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><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b1</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>·</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>c2</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></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>C</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>distància</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>B</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>distància</mi><mo>(</mo><mi>A</mi><mo>,</mo><mi>C</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>d3</mi><mo>=</mo><mi>distància</mi><mo>(</mo><mi>B</mi><mo>,</mo><mi>C</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>T</mi><mo>=</mo><mi>triangle</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>A1</mi><mo>=</mo><mi>arrodonir</mi><mo>(</mo><mfrac><mn>180</mn><pi/></mfrac><mo>*</mo><mi>angle</mi><mo>(</mo><mi>T</mi><mo>,</mo><mn>1</mn><mo>)</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>B1</mi><mo>=</mo><mi>arrodonir</mi><mfenced><mrow><mfrac><mn>180</mn><pi/></mfrac><mo>*</mo><mi>angle</mi><mo>(</mo><mi>T</mi><mo>,</mo><mn>2</mn><mo>)</mo></mrow></mfenced></mtd></mtr><mtr><mtd><mi>C1</mi><mo>=</mo><mi>arrodonir</mi><mfenced><mrow><mfrac><mn>180</mn><pi/></mfrac><mo>*</mo><mi>angle</mi><mo>(</mo><mi>T</mi><mo>,</mo><mn>3</mn><mo>)</mo></mrow></mfenced></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mi>A1</mi><mo>+</mo><mi>B1</mi><mo>+</mo><mi>C1</mi><mo>=</mo><mn>180</mn></mrow></mfenced></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Gràfic</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>altura</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>12</mn><mo>,</mo><mi>mostrar_eixos</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>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mo> </mo><mi>mida_punt</mi><mo>=</mo><mn>7</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>B</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mo> </mo><mi>mida_punt</mi><mo>=</mo><mn>7</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>C</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mo> </mo><mi>mida_punt</mi><mo>=</mo><mn>7</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>triangle</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>b1</mi><mo>,</mo><mi>b2</mi><mo>)</mo><mo>,</mo><mi>punt</mi><mo>(</mo><mi>c1</mi><mo>,</mo><mi>c2</mi><mo>)</mo><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_línia</mi><mo>=</mo><mn>3</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blau</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Vectors</mi><mo> </mo><mi>pista</mi></math></comment></maction><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AB1</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AB2</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AC1</mi><mo>=</mo><mi>c1</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>AC2</mi><mo>=</mo><mi>c2</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>BC1</mi><mo>=</mo><mi>c1</mi><mo>-</mo><mi>b1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>BC2</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>c2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>BA1</mi><mo>=</mo><mo>-</mo><mi>AB1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>BA2</mi><mo>=</mo><mo>-</mo><mi>AB2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>CA1</mi><mo>=</mo><mo>-</mo><mi>AC1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>CA2</mi><mo>=</mo><mo>-</mo><mi>AC2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>CB1</mi><mo>=</mo><mo>-</mo><mi>BC1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>CB2</mi><mo>=</mo><mo>-</mo><mi>BC2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>A1</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>B1</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>C1</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>,</mo><mi>A1</mi><mo>,</mo><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>4</mn><mo>,</mo><mn>4</mn></mrow></mfenced><mo>,</mo><mn>81</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>B</mi><mo>,</mo><mi>B1</mi><mo>,</mo><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mo>-</mo><mn>3</mn><mo>,</mo><mn>4</mn></mrow></mfenced><mo>,</mo><mn>45</mn><mo>,</mo><msqrt><mn>37</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>C</mi><mo>,</mo><mi>C1</mi><mo>,</mo><mi>d3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>3</mn><mo>,</mo><mo>-</mo><mn>2</mn></mrow></mfenced><mo>,</mo><mn>54</mn><mo>,</mo><mn>6</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></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"><mn>81</mn><mo> </mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>,</mo><mn>45</mn><mo> </mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>,</mo><mn>54</mn><mo> </mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></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>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>B</mi><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>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> N'hi ha prou amb calcular l'angle entre els 3 vectors, agafats de 2 en 2:
A és el vèrtex que correspon als vectors «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mover mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»AB«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»AB«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»AB«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«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»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»AC«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»AC«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mstyle»«/math»
B és el vèrtex que correspon als vectors «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mover mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»BA«/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»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»B«/mi»«mi mathvariant=¨bold-italic¨»A«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»BA«/mi»«mn mathvariant=¨bold¨»12«/mn»«/mrow»«/mfenced»«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¨»BC«/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»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»B«/mi»«mi mathvariant=¨bold-italic¨»C«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»B«/mi»«mi mathvariant=¨bold-italic¨»C«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mstyle»«/math»
C és el vèrtex que correspon als vectors «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mover mathcolor=¨#000066¨»«mi mathvariant=¨bold¨»CA«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»C«/mi»«mi mathvariant=¨bold-italic¨»A«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»C«/mi»«mi mathvariant=¨bold-italic¨»A«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«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¨»CB«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mfenced mathcolor=¨#000066¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»C«/mi»«mi mathvariant=¨bold-italic¨»B«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»C«/mi»«mi mathvariant=¨bold-italic¨»B«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mstyle»«/math».

L'angle entre els vectors es calcula amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#00007F¨»«mover»«mrow»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨»,«/mo»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mrow»«mo mathvariant=¨bold¨»^«/mo»«/mover»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»acos«/mi»«mfrac mathcolor=¨#00007F¨»«mrow»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨»§#183;«/mo»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mrow»«mrow»«mfenced open=¨||¨ close=¨||¨»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced open=¨||¨ close=¨||¨»«mover»«msub»«mi mathvariant=¨bold¨»v«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mfenced»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»acos«/mi»«mfrac mathcolor=¨#00007F¨»«mrow»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mo mathvariant=¨bold¨»+«/mo»«msub»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«msub»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«/mrow»«mrow»«msqrt»«msup»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«msub»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«mo mathvariant=¨bold¨»§#183;«/mo»«msqrt»«msup»«msub»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«msub»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msub»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Cal comprovar que sumin 180º
La situació és #G1
Els angles d'un triangle són tots positius!!

]]> Per exemple, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#00007F¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#00007F¨»acos«/mi»«mfrac mathcolor=¨#00007F¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»AB«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»AC«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»A«/mi»«mi mathvariant=¨bold-italic¨»B«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»A«/mi»«mi mathvariant=¨bold-italic¨»C«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»A«/mi»«mi mathvariant=¨bold-italic¨»B«/mi»«msup»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»AB«/mi»«msup»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«mo mathvariant=¨bold¨»§#183;«/mo»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»AC«/mi»«msup»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»AC«/mi»«msup»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 1MA.05.4.50DT Distància entre dos punts

Distància entre dos punts

És el mòdul del vector que els uneix:

]]> 0.0000000 0.0000000 0 1MA.05.4.51Q Distància entre dos punts Quina és la distància entre els punts «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»p«/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¨»p«/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¨»Q«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»q«/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¨»q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»?

Format de la resposta: radical simplificat

]]>

]]> 1MA.05.4.60DT Distància d'un punt a una recta

Distància d'un punt a una recta
És la longitud de la perpendicular traçada des del punt fins a la recta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«mo mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mo mathcolor=¨#003300¨»,«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathcolor=¨#003300¨»)«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mfenced open=¨\|¨ close=¨\|¨»«mrow»«msub»«mi mathvariant=¨bold¨»ax«/mi»«mi mathvariant=¨bold¨»P«/mi»«/msub»«mo»+«/mo»«msub»«mi mathvariant=¨bold¨»by«/mi»«mi mathvariant=¨bold¨»P«/mi»«/msub»«mo»+«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«msqrt»«msup»«mi mathvariant=¨bold¨»a«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mi mathvariant=¨bold¨»b«/mi»«mn»2«/mn»«/msup»«/msqrt»«/mfrac»«/math»
Exemple, amb P(1,2) i r una recta d'equació és 3x-5y+6=0: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold-italic¨»d«/mi»«mo mathvariant=¨bold¨»(«/mo»«mi mathvariant=¨bold-italic¨»P«/mi»«mo mathvariant=¨bold¨»,«/mo»«mi mathvariant=¨bold-italic¨»r«/mi»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mfenced open=¨\|¨ close=¨\|¨»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«mo mathvariant=¨bold¨»§#183;«/mo»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»+«/mo»«mn mathvariant=¨bold¨»6«/mn»«/mrow»«/mfenced»«msqrt»«msup»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»-«/mo»«mn mathvariant=¨bold¨»5«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mn mathvariant=¨bold¨»4«/mn»«msqrt»«mn mathvariant=¨bold¨»34«/mn»«/msqrt»«/mfrac»«mo mathvariant=¨bold¨»=«/mo»«mfrac»«mrow»«mn mathvariant=¨bold¨»2«/mn»«msqrt»«mn mathvariant=¨bold¨»34«/mn»«/msqrt»«/mrow»«mn mathvariant=¨bold¨»17«/mn»«/mfrac»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold-italic¨»u«/mi»«mo mathvariant=¨bold¨».«/mo»«mi mathvariant=¨bold-italic¨»d«/mi»«mo mathvariant=¨bold¨».«/mo»«/mrow»«/mstyle»«/math»
Si no recordeu l'expressió, la podeu retrobar cercant el punt d'intersecció Q entre la recta r i la recta perpendicular a r que passa per P. Trobat Q, es pot calcular el mòdul del vector PQ

]]> 0.0000000 0.0000000 0 1MA.05.4.61Q Distància d'un punt a una recta Quina és la distància entre el punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»P«/mi»«mfenced mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math» i la recta r d'equació «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mstyle»«/math»?

Format de la resposta: radical simplificat

]]>

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»d«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»P«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»,«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»r«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mfrac mathcolor=¨#000066¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p_«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»3«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mfenced»«msqrt»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»1«/mn»«msup»«mo mathvariant=¨bold¨»)«/mo»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1MA.05.4.70DT Distància entre rectes paral·leles

Distància entre rectes paral·leles

S'agafa un punt de l'una i es calcula la seva distància a l'altra:

Si r≡ax+by+c=0 i S és un punt de s:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«mo mathcolor=¨#003300¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathcolor=¨#003300¨»,«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mo mathcolor=¨#003300¨»)«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«msub»«mi mathvariant=¨bold¨»ax«/mi»«mi mathvariant=¨bold¨»S«/mi»«/msub»«mo»+«/mo»«msub»«mi mathvariant=¨bold¨»by«/mi»«mi mathvariant=¨bold¨»S«/mi»«/msub»«mo»+«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfenced»«msqrt»«msup»«mi mathvariant=¨bold¨»a«/mi»«mn»2«/mn»«/msup»«mo»+«/mo»«msup»«mi mathvariant=¨bold¨»b«/mi»«mn»2«/mn»«/msup»«/msqrt»«/mfrac»«/math»

]]> 0.0000000 0.0000000 0 1MA.05.4.71Q Distància entre dues rectes paral·leles Quina és la distància entre les dues rectes d'equacions
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«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¨»u_«/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¨»u_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8801;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»e_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mrow»«/mstyle»«/math»?

Format de la resposta: radical simplificat

]]>

]]> 1.0000000 0.5000000 0 0 #r_55]]> <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>p_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>p_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>u_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>u_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>e_1</mi><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mi>p_1</mi></mtd></mtr></mtable></mfenced><mi>u_1</mi></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>-</mo><mi>p_2</mi></mtd></mtr></mtable></mfenced><mi>u_2</mi></mfrac></mtd></mtr><mtr><mtd><mi>n1</mi><mo>=</mo><mi>x</mi><mo>-</mo><mi>p_1</mi></mtd></mtr><mtr><mtd><mi>n2</mi><mo>=</mo><mi>y</mi><mo>-</mo><mi>p_2</mi></mtd></mtr><mtr><mtd><mi>q_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>q_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>q_3</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>e_2</mi><mo>=</mo><mi>q_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>q_2</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>q_3</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>rang</mi><mfenced><mtable><mtr><mtd><mi>u_1</mi></mtd><mtd><mo>-</mo><mi>q_2</mi></mtd></mtr><mtr><mtd><mi>u_2</mi></mtd><mtd><mi>q_1</mi></mtd></mtr></mtable></mfenced><mo>=</mo><mn>1</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>q21</mi><mo>=</mo><mo>-</mo><mi>q_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_55</mi><mo>=</mo><mi>distància</mi><mo>(</mo><mi>punt</mi><mo>(</mo><mi>p_1</mi><mo>,</mo><mi>p_2</mi><mo>)</mo><mo>,</mo><mi>q_1</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>q_2</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>q_3</mi><mo>=</mo><mn>0</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>p_1</mi><mo>,</mo><mi>p_2</mi><mo>,</mo><mi>u_1</mi><mo>,</mo><mi>u_2</mi><mo>,</mo><mi>q_1</mi><mo>,</mo><mi>q_2</mi><mo>,</mo><mi>q_3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>,</mo><mo>-</mo><mn>6</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>x</mi><mo>-</mo><mn>2</mn></mtd></mtr></mtable></mfenced><mn>1</mn></mfrac><mo>=</mo><mfrac><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>y</mi><mo>+</mo><mn>5</mn></mtd></mtr></mtable></mfenced><mn>6</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mn>9</mn><mo>=</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_55</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>26</mn><mo>*</mo><msqrt><mn>37</mn></msqrt></mrow><mn>37</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"><mo>#</mo><mi>r</mi><mo>_</mo><mn>55</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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Primer cal esbrinar si són paral·leles, calculant el determinant amb els vectors directors: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#000066¨ open=¨|¨ close=¨|¨»«mtable»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q«/mi»«mn mathvariant=¨bold¨»21«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»u_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mtd»«mtd»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mstyle»«/math»

Després s'aplica l'expressió de la distància d'un punt de l'una R(#p_1,#p_2) a l'altra, s:#e_2:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»d«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»(«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»R«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»,«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»s«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mfrac mathcolor=¨#000066¨»«mfenced open=¨|¨ close=¨|¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#183;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»p_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»+«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»3«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«msqrt»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»q_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mfrac»«/mrow»«/mstyle»«/math»

]]> 1MA.05.4.80DT Com es treu un valor absolut

Treure valor absolut

Com que: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#003300¨ open=¨|¨ close=¨|¨»«mi mathvariant=¨bold¨»a«/mi»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfenced mathcolor=¨#003300¨ open=¨{¨ close=¨¨»«mtable»«mtr»«mtd»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»si«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#62;«/mo»«mn mathvariant=¨bold¨»0«/mn»«/mtd»«/mtr»«mtr»«mtd»«mo mathvariant=¨bold¨»-«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»si«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§lt;«/mo»«mn mathvariant=¨bold¨»0«/mn»«/mtd»«/mtr»«/mtable»«/mfenced»«/mrow»«/mstyle»«/math»

quan traiem el valor absolut de l'equació |ax+by+c|=d, apareixen dues equacions (i 2 solucions possibles):

ax+by+c = d
ax+by+c = -d

]]> 0.0000000 0.0000000 0 1MA.05.4.81Q Recta // a distància fixa(rac) Troba l'equació cartesiana d'una recta paral·lela a la recta r d'equació «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»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«/mrow»«/mstyle»«/math» i que en sigui distant de «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»v«/mi»«/mrow»«/mstyle»«/math» unitats.

Atenció: pot ser que hi hagi més d'una solució

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced open=¨{¨ close=¨}¨»«mrow»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»-«/mo»«mn»5«/mn»«mo»=«/mo»«mn»0«/mn»«mo»,«/mo»«mn»3«/mn»«mi»x«/mi»«mo»+«/mo»«mi»y«/mi»«mo»+«/mo»«mn»7«/mn»«mo»=«/mo»«mn»0«/mn»«/mrow»«/mfenced»«/mstyle»«/math»

]]> Solucions en verd: #G1

]]> 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</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</mi><mo>=</mo><mn>1</mn></mtd></mtr><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><mo>(</mo><mo>{</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>d</mi><mo>=</mo><mo>-</mo><mi>c</mi></mtd></mtr><mtr><mtd><mi>P</mi><mo>=</mo><mo>(</mo><mn>0</mn><mo>,</mo><mo>-</mo><mi>c</mi><mo>)</mo></mtd></mtr><mtr><mtd><mi>e_1</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></mtd></mtr><mtr><mtd><mi>e_2</mi><mo>=</mo><mi>a</mi><mo>*</mo><mn>0</mn><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>c</mi><mo>=</mo><mn>0</mn></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>r_50</mi><mo>=</mo><mfrac><mfenced close="|" open="|"><mrow><mo>-</mo><mi>c</mi><mo>+</mo><mi>m</mi></mrow></mfenced><msqrt><mrow><msup><mfenced><mi>a</mi></mfenced><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></msqrt></mfrac></mtd></mtr><mtr><mtd><mi>v</mi><mo>=</mo><msqrt><mrow><msup><mi>a</mi><mn>2</mn></msup><mo>+</mo><mn>1</mn></mrow></msqrt></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr><mtr><mtd><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mfrac><mfenced close="|" 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align="center"><mtr><mtd><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>r_1</mi><mo>=</mo><mn>0</mn><mo>,</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mi>r_2</mi><mo>=</mo><mn>0</mn></mtd></mtr></mtable></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>recta</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></mrow></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>recta</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>r_1</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>recta</mi><mo>(</mo><mi>a</mi><mo>*</mo><mi>x</mi><mo>+</mo><mi>b</mi><mo>*</mo><mi>y</mi><mo>+</mo><mi>r_2</mi><mo>=</mo><mn>0</mn></mrow></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>verd</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>q_1</mi><mo>,</mo><mi>q_2</mi><mo>,</mo><mi>q_3</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q_1</mi><mo>,</mo><mi>q_2</mi><mo>,</mo><mi>q_3</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi></math></input><output><math 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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>62</mn></mtd></mtr></mtable></mfenced><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>m</mi><mo>=</mo><mn>68</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>62</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>68</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="{"><mtable align="center"><mtr><mtd><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>-</mo><mn>62</mn><mo>=</mo><mn>0</mn><mo>,</mo><mn>8</mn><mo>*</mo><mi>x</mi><mo>+</mo><mi>y</mi><mo>+</mo><mn>68</mn><mo>=</mo><mn>0</mn></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>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La recta paral·lela té el mateix vector director i,
per tant, la seva equació és de la forma #a x + y + c = 0.
Un punt de la recta que ens donen és (0,#d) que es troba substituint x per 0: #e_2 «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo»§#8658;«/mo»«mi»y«/mi»«mo»=«/mo»«/math»d
Es calcula la distància d'aquest punt (0, #d) a #a x + y + c = 0 i s'iguala a #v.
Al treure els valors absoluts, surten dues possibilitats pels signes, per tant dues equacions.

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