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

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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 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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>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 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"/></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>2</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>6</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>3</mn><mo>*</mo><mi>y</mi><mo>=</mo><mo>-</mo><mn>3</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>30</mn><mo>*</mo><mi>x</mi><mo>-</mo><mn>15</mn><mo>*</mo><mi>y</mi><mo>=</mo><mn>15</mn></math></output></command><command><input><math 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 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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 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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 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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>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 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 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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>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><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 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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>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 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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>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 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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 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 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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

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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>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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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>e2</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>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>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>3</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><mn>4</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>4</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"><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>y1</mi></math></input><output><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>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 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>u_1</mi><mo>*</mo><mi>v_2</mi><mo>≠</mo><mi>u_2</mi><mo>*</mo><mi>v_1</mi></mrow></apply></math></input></command><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Equació</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>recta</mi><mo> </mo><mi>r</mi></math></comment></maction><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><maction actiontype="comment"><comment><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Equació</mi><mo> </mo><mi>de</mi><mo> </mo><mi>la</mi><mo> </mo><mi>recta</mi><mo> </mo><mi>s</mi></math></comment></maction><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><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 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>450</mn><mo>,</mo><mi>amplada_finestra</mi><mo>=</mo><mn>450</mn><mo>,</mo><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><mo>,</mo><mi>r1</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>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><mn>3</mn></mfrac><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>3</mn><mn>4</mn></mfrac><mo>*</mo><mi>x</mi><mo>+</mo><mfrac><mn>5</mn><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mi>x</mi><mo>+</mo><mn>5</mn><mo>*</mo><mi>y</mi><mo>+</mo><mn>26</mn><mo>=</mo><mn>0</mn><mo>,</mo><mi>y</mi><mo>=</mo><mo>-</mo><mfrac><mn>2</mn><mn>5</mn></mfrac><mo>*</mo><mi>x</mi><mo>-</mo><mfrac><mn>26</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>S</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfenced close="}" open="{"><mtable 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 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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 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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 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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 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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»

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