1MA 04. VECTORS/1MA.04.1 Definicions 1MA.04.1.10DT COMPONENTS_ORIGEN_EXTREM  
Components d'un vector
Si A(x1,y1) és l'origen i B (x2,y2) és l'extrem, les components del vector són:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»AB«/mi»«mo»§#8594;«/mo»«/mover»«/math» = (x2 - x1, y2 - y1)
Cal recordar que:
origen = extrem - vector
extrem = origen + vector
]]> 0.0000000 0.0000000 0 1MA.04.1.11Q ComponentsEntersOrigenExtrem Determina els components d'un vector que té per origen «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»A«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math» i per extrem «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math».

Format de la resposta: [-5,3]

]]> 1.0000000 0.5000000 0 0 #v_42 <question><wirisCasSession>&lt;session lang=&quot;ca&quot; version=&quot;2.0&quot;&gt;&lt;library closed=&quot;false&quot;&gt;&lt;mtext style=&quot;color:#ffc800&quot; xml:lang=&quot;es&quot;&gt;variables&lt;/mtext&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;19&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;19&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;19&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;19&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;19&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;19&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;b_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;aleatori&lt;/mi&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;19&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;19&lt;/mn&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;v_1&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;b_1&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;v_2&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mi&gt;b_2&lt;/mi&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;v_42&lt;/mi&gt;&lt;mo&gt;=&lt;/mo&gt;&lt;mfenced close=&quot;]&quot; open=&quot;[&quot;&gt;&lt;mrow&gt;&lt;mi&gt;v_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;v_2&lt;/mi&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/library&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;a_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;a_2&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;b_2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mn&gt;15&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;1&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;9&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;v_1&lt;/mi&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mi&gt;v_2&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;24&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mi&gt;v_42&lt;/mi&gt;&lt;/math&gt;&lt;/input&gt;&lt;output&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;&gt;&lt;mfenced close=&quot;]&quot; open=&quot;[&quot;&gt;&lt;mrow&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;24&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mo&gt;-&lt;/mo&gt;&lt;mn&gt;10&lt;/mn&gt;&lt;/mrow&gt;&lt;/mfenced&gt;&lt;/math&gt;&lt;/output&gt;&lt;/command&gt;&lt;/group&gt;&lt;group&gt;&lt;command&gt;&lt;input&gt;&lt;math xmlns=&quot;http://www.w3.org/1998/Math/MathML&quot;/&gt;&lt;/input&gt;&lt;/command&gt;&lt;/group&gt;&lt;/session&gt;</wirisCasSession><correctAnswers><correctAnswer type="mathml"> #v_42 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Aplica: vector = extrem - origen:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»,«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»-«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mstyle»«/math»

]]> 1MA.04.1.12Q ComponentsRacionOrigenExtrem Determina els components d'un vector que té per origen «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math» i per extrem:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»
Format de la resposta: [-5,3]

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n11</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>19</mn></mrow></mfenced><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>d11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>n12</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>19</mn></mrow></mfenced><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>d12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>n21</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>19</mn></mrow></mfenced><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>d21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>n22</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>19</mn></mrow></mfenced><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>d22</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>d11</mi><mo>=</mo><mi>d12</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>d21</mi><mo>=</mo><mi>d22</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>d11</mi><mo>≠</mo><mi>d21</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mfrac><mi>n11</mi><mi>d11</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mfrac><mi>n12</mi><mi>d12</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mfrac><mi>n21</mi><mi>d21</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mfrac><mi>n22</mi><mi>d22</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>=</mo><mi>b1</mi><mo>-</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v2</mi><mo>=</mo><mi>b2</mi><mo>-</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v1</mi><mo>,</mo><mi>v2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>,</mo><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>14</mn><mn>15</mn></mfrac><mo>,</mo><mfrac><mn>4</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>,</mo><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v1</mi><mo>,</mo><mi>v2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>31</mn><mn>15</mn></mfrac><mo>,</mo><mfrac><mn>16</mn><mn>5</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><mn>31</mn><mn>15</mn></mfrac><mo>,</mo><mfrac><mn>16</mn><mn>5</mn></mfrac></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="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> Aplica: vector = extrem - origen:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mstyle»«/math»

]]> 1MA.04.1.13Q ExtremAmbOrigeniVector Determina l'extrem B d'un vector que té per origen «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math» i per components «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»AB«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math».

Format de la resposta: [-5,3]

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mi>b_1</mi><mo>+</mo><mi>a_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mi>b_2</mi><mo>+</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v_1</mi><mo>,</mo><mi>v_2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7</mn><mo>,</mo><mo>-</mo><mn>14</mn><mo>,</mo><mo>-</mo><mn>4</mn><mo>,</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>v_1</mi><mo>,</mo><mi>v_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>11</mn><mo>,</mo><mo>-</mo><mn>14</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mo>-</mo><mn>11</mn><mo>,</mo><mo>-</mo><mn>14</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Aplica: extrem = origen + vector:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«/mstyle»«/math»

]]> 1MA.04.1.14Q OrigenAmbExtremiVector Determina l'origen A d'un vector que té per extrem «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math» i per components «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»AB«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math».

Format de la resposta: [-5,3]

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mi>a_1</mi><mo>-</mo><mi>b_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mi>a_2</mi><mo>-</mo><mi>b_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>v_1</mi><mo>,</mo><mi>v_2</mi></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>v_1</mi><mo>,</mo><mi>v_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>9</mn><mo>,</mo><mn>8</mn></mrow></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">textField</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Aplica: origen = extrem - vector:  

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

 

]]> 1MA.04.1.20DT MÒDUL ARGUMENT  
Mòdul i argument d'un vector
Un vector de components (x,y) té:
 
per mòdul «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#003300¨ open=¨||¨ close=¨||¨»«mfenced»«mrow»«mi mathvariant=¨bold¨»x«/mi»«mo mathvariant=¨bold¨»,«/mo»«mi mathvariant=¨bold¨»y«/mi»«/mrow»«/mfenced»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mi mathvariant=¨bold¨»y«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mrow»«/mstyle»«/math»
per argument «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»§#945;«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mo mathcolor=¨#003300¨»=«/mo»«mo mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»arc«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»tg«/mi»«mo mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»y«/mi»«mi mathvariant=¨bold¨»x«/mi»«/mfrac»«/mrow»«/mstyle»«/math»
Situa l'angle en el quadrant correcte
en funció dels signes de x i y
]]> 0.0000000 0.0000000 0 1MA.04.1.21Q MòdulAmbComponents Determina el mòdul del vector que té per components «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»

Format de la resposta: enter o arrel simplificada

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>19</mn><mo>,</mo><mn>19</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_4</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a_1</mi><mo>,</mo><mi>a_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="‖" open="‖"><mfenced close="]" open="["><mrow><mi>a_1</mi><mo>,</mo><mi>a_2</mi></mrow></mfenced></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mo>-</mo><mn>10</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>8</mn><mo>,</mo><mo>-</mo><mn>10</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_42</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>41</mn></msqrt></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^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula el mòdul amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mover»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mfenced»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mstyle»«/math» 

Atenció en com entres les dades a la calculadora.

Tot el radicand ha d'estar entre parèntesis.

I si un dels components és negatiu, el seu quadrat sempre és positiu: (-3)2 = 9

]]> 1MA.04.1.22Q MòdulAmbOrigeniExtrem Determina el mòdul d'un vector que té per origen «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math» i per extrem «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math».

Format de la resposta: enter o arrel simplificada

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><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"><mi>a_1</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_1</mi><mo>=</mo><mi>b_1</mi><mo>-</mo><mi>a_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_2</mi><mo>=</mo><mi>b_2</mi><mo>-</mo><mi>a_2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_4</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>sol</mi><mo>=</mo><mfenced close="‖" open="‖"><mfenced close="]" open="["><mrow><mi>v_1</mi><mo>,</mo><mi>v_2</mi></mrow></mfenced></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mi>b_1</mi><mo>,</mo><mi>b_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>,</mo><mo>-</mo><mn>18</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>12</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>v_1</mi><mo>,</mo><mi>v_2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>,</mo><mn>30</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>15</mn><mo>,</mo><mn>30</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>15</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula primer les coordenades: vector = extrem - origen:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mfenced mathcolor=¨#0000FF¨ open=¨[¨ close=¨]¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v_«/mi»«mn mathvariant=¨bold¨»1«/mn»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«/mrow»«/mstyle»«/math»

Després calcula el mòdul amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#0000FF¨»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»v_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mstyle»«/math»

]]> 1MA.04.1.23Q MòdulComponents(Racional) Determina el mòdul del vector que té per components «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»v«/mi»«/mstyle»«/math»

Format de la resposta: enter o arrel simplificada

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n11</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>19</mn></mrow></mfenced><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>d11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>n12</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>19</mn></mrow></mfenced><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>d12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>19</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mi>d11</mi><mo>=</mo><mi>d12</mi></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>a1</mi><mo>=</mo><mfrac><mi>n11</mi><mi>d11</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mfrac><mi>n12</mi><mi>d12</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a1</mi><mo>,</mo><mi>a2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfenced close="‖" open="‖"><mfenced close="]" open="["><mrow><mi>a1</mi><mo>,</mo><mi>a2</mi></mrow></mfenced></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mfrac><mn>13</mn><mn>9</mn></mfrac><mo>,</mo><mfrac><mn>5</mn><mn>3</mn></mfrac></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><msqrt><mn>394</mn></msqrt><mn>9</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Calcula el mòdul amb:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#0000FF¨ open=¨|¨ close=¨|¨»«mfenced open=¨|¨ close=¨|¨»«mover»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«/mfenced»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«msqrt mathcolor=¨#0000FF¨»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mstyle»«/math»

Presta atenció a com entres les dades a la calculadora

]]> 1MA.04.1.24Q MòdulArgument Quin és el mòdul i l'argument del vector «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mover mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»v«/mi»«mo mathvariant=¨bold¨»§#8594;«/mo»«/mover»«mo»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mstyle»«/math»?  Fixa't en el quadrant!

Format de la resposta:

Mòdul: Fracció o arrel simplificada

35º (arrodonit a la unitat).

]]> El vector és:

#G1

]]> 1.0000000 0.5000000 0 0 mòdul =#sol1argument =#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>2</mn><mo>,</mo><mn>7</mn></mrow></mfenced><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>5</mn><mo>,</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mfrac><mi>a2</mi><mi>a1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a1</mi><mo>,</mo><mi>a2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msqrt><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a2</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mi>atan</mi><mo>(</mo><mi>c</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mfrac><mrow><mi>m1</mi><mo>*</mo><mn>180</mn></mrow><pi/></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m3</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>arrodoneix</mi><mo>(</mo><mi>m2</mi><mo>)</mo></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>&gt;</mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>Q</mi><mo>=</mo><mo>&quot;</mo><mn>1</mn><mi>r</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>Q2</mi><mo>=</mo><mo>&quot;</mo><mi>entre</mi><mo>&nbsp;</mo><mn>0</mn><mo>&nbsp;</mo><mi>i</mi><mo>&nbsp;</mo><mn>90</mn><mo>°</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>Q3</mi><mo>=</mo><mo>&quot;</mo><mi>α</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mi>m3</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>Q</mi><mo>=</mo><mo>&quot;</mo><mn>4</mn><mi>t</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>Q2</mi><mo>=</mo><mo>&quot;</mo><mi>entre</mi><mo>&nbsp;</mo><mn>270</mn><mo>°</mo><mo>&nbsp;</mo><mi>i</mi><mo>&nbsp;</mo><mn>360</mn><mo>°</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>Q3</mi><mo>=</mo><mo>&quot;</mo><mn>360</mn><mo>°</mo><mo>-</mo><mfenced close="|" open="|"><mi>α</mi></mfenced><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mn>360</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>-</mo><mi>m3</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></mtd></mtr></mtable></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>&gt;</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>Q</mi><mo>=</mo><mo>&quot;</mo><mn>2</mn><mi>n</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>Q2</mi><mo>=</mo><mo>&quot;</mo><mi>entre</mi><mo>&nbsp;</mo><mn>90</mn><mo>°</mo><mo>&nbsp;</mo><mi>i</mi><mo>&nbsp;</mo><mn>180</mn><mo>°</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>Q3</mi><mo>=</mo><mo>&quot;</mo><mn>180</mn><mo>°</mo><mo>-</mo><mfenced close="|" open="|"><mi>α</mi></mfenced><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mn>180</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>-</mo><mi>m3</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></mtd></mtr><mtr><mtd/></mtr></mtable><mtable><mtr><mtd><mi>Q</mi><mo>=</mo><mo>&quot;</mo><mn>3</mn><mi>r</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>Q2</mi><mo>=</mo><mo>&quot;</mo><mi>entre</mi><mo>&nbsp;</mo><mn>180</mn><mo>°</mo><mo>&nbsp;</mo><mi>i</mi><mo>&nbsp;</mo><mn>270</mn><mo>°</mo><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>Q3</mi><mo>=</mo><mo>&quot;</mo><mn>180</mn><mo>°</mo><mo>+</mo><mi>α</mi><mo>&quot;</mo></mtd></mtr><mtr><mtd><mi>sol2</mi><mo>=</mo><mn>180</mn><csymbol definitionURL="http://.../units/degree/angular">°</csymbol><mo>+</mo><mi>m3</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></mtd></mtr></mtable></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mostrar_eixos</mi><mo>=</mo><mi>fals</mi></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>3</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>v</mi><mo>,</mo><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="]" open="["><mrow><mn>4</mn><mo>,</mo><mo>-</mo><mn>5</mn></mrow></mfenced><mo>,</mo><msqrt><mn>41</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mn>5</mn><mn>4</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0.89606</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>51.34</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>51</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>4t</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>entre</ms><mo>&nbsp;</mo><ms>270</ms><mo>°</mo><mo>&nbsp;</mo><ms>i</ms><mo>&nbsp;</mo><ms>360</ms><mo>°</mo></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>Q3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>360</ms><mo>°</mo><mo>-</mo><mfenced close="|" open="|"><mi>α</mi></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 mathvariant="normal">m</mi><mi>&#xF2;</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi><mn>1</mn><mspace linebreak="newline"/><mi>a</mi><mi>r</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><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> L'argument és l'arc tangent de la segona component dividida per la primera:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»arc«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»tg«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

#G1

Si et fixes en el signe de les components, l'angle està en el #Q quadrant, o sigui #Q2. Es calcula doncs amb: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»Q«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»3«/mn»«/mrow»«/mstyle»«/math»

]]> 1MA.04.1.30DT VECTOR POSICIÓ  
Vector posició

Si A(x,y) és un punt qualsevol, anomenem vector posició de A, el vector que va de l'origen de coordenades O(0,0) al punt A. Les seves components són:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mover accent=¨true¨»«mi mathvariant=¨bold¨»v«/mi»«mo»§#8594;«/mo»«/mover»«/math» = (x,y)
]]> 0.0000000 0.0000000 0 1MA.04.1.31Q VectorPosició_Mòdul Quin és el mòdul del vector posició associat al punt «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»)«/mo»«/mrow»«/mstyle»«/math»?

Format de la resposta: enter o arrel simplificada

]]> El vector és #G

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a1</mi><mo>*</mo><mi>a2</mi><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msqrt><mrow><msup><mi>a1</mi><mn>2</mn></msup><mo>+</mo><msup><mi>a2</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a1</mi><mo>,</mo><mi>a2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>20</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>20</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>9</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mo>-</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>61</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</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^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Com que les coordenades del punt són els components del vector, el seu mòdul és:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#0000FF¨»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mstyle»«/math»

]]> 1MA.04.1.32Q VectorPosició_Argument Quin és l'argument del vector associat al punt de coordenades (#a_1,#a_2)?

Format de la resposta: en radians, arrodonit als deu mil·lèsims, amb punt enlloc de coma (poseu el nombre que us dona la calculadora). Si l'angle surt negatiu, es posa negatiu.

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>9</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfenced><mrow><mi>a1</mi><mo>∧</mo><mi>a2</mi></mrow></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>≠</mo><mn>0</mn></mrow><mtable><mtr><mtd><mi>c</mi><mo>=</mo><mfrac><mi>a2</mi><mi>a1</mi></mfrac></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mi>atan</mi><mo>(</mo><mi>c</mi><mo>)</mo><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mtd></mtr><mtr><mtd/></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mfrac><pi/><mn>2</mn></mfrac><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mrow><mrow><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>10000</mn><mo>*</mo><mfrac><mrow><mn>3</mn><mo>*</mo><pi/></mrow><mn>2</mn></mfrac><mo>)</mo></mrow><mn>10000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mrow></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mi>punt</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a1</mi><mo>,</mo><mi>a2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>amplada</mi><mo>=</mo><mn>20</mn><mo>,</mo><mi>altura</mi><mo>=</mo><mn>20</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mida_punt</mi><mo>=</mo><mn>9</mn><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G</mi><mo>=</mo><mi>dibuixa</mi><mfenced><mrow><mi>T1</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>color</mi><mo>=</mo><mi>html_darkblue</mi><mo>,</mo><mi>amplada_línia</mi><mo>=</mo><mn>2</mn></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>,</mo><mo>-</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced><mrow><mn>7</mn><mo>,</mo><mo>-</mo><mn>7</mn></mrow></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</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>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>0.7854</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'argument és l'arc tangent de la segona component dividida per la primera:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»arc«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»tg«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a_«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Pensa en posar la calculadora en RADIANS!

]]> 1MA.04.1.34Q VectPosicióMòdulArgumentGrau Quin és el mòdul i l'argument del vector associat al punt de coordenades «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mstyle»«/math»?

Format de la resposta:

a) mòdul: arrel simplificada

b) angle: 122º (arrodonit als graus)

]]> El vector és:

#G1

]]> 1.0000000 0.5000000 0 0 a) mòdul=#sol1b) argument =#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"><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><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>7</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mo>-</mo><mn>1</mn><mo>,</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr></mtable></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>=</mo><mfenced close="]" open="["><mrow><mi>a1</mi><mo>,</mo><mi>a2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>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>sol1</mi><mo>=</mo><mfenced close="‖" open="‖"><mi>v</mi></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ag</mi><mo>=</mo><mi>argument</mi><mo>(</mo><mi>v</mi><mo>)</mo><mo>*</mo><mfrac><mn>180</mn><pi/></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol21</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>ag</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>sol21</mi><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>T1</mi><mo>=</mo><mi>tauler</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_finestra</mi><mo>=</mo><mn>350</mn><mo>,</mo><mi>altura_finestra</mi><mo>=</mo><mn>350</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi><mo>=</mo><mi>dibuixa</mi><mo>(</mo><mi>T1</mi><mo>,</mo><mi>v</mi><mo>,</mo><mi>punt</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>0</mn><mo>)</mo><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>amplada_línia</mi><mo>=</mo><mn>4</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>blau</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>T1</mi><mo>,</mo><mi>A</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>mida_punt</mi><mo>=</mo><mn>9</mn><mo>,</mo><mi>color</mi><mo>=</mo><mi>vermell</mi><mo>,</mo><mi>mostrar_etiqueta</mi><mo>=</mo><mi>cert</mi></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>&gt;</mo><mn>0</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>Q</mi><mo>=</mo><mo>&quot;</mo><mi>I</mi><mo>&quot;</mo></mrow><mrow><mi>Q</mi><mo>=</mo><mo>&quot;</mo><mi>IV</mi><mo>&quot;</mo></mrow></apply><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>&gt;</mo><mn>0</mn></mrow><mrow><mi>Q</mi><mo>=</mo><mo>&quot;</mo><mi>II</mi><mo>&quot;</mo></mrow><mrow><mi>Q</mi><mo>=</mo><mo>&quot;</mo><mi>III</mi><mo>&quot;</mo></mrow></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>v</mi><mo>,</mo><mi>Q</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>4</mn></mrow></mfenced><mo>,</mo><ms>IV</ms></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ag</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>296.57</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>297</mn><mo>&nbsp;</mo><csymbol definitionURL="http://.../units/degree/angular">°</csymbol></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>G1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>tauler1</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo>&#x2009;</mo><mi mathvariant="normal">m</mi><mi>&#xF2;</mi><mi>d</mi><mi>u</mi><mi mathvariant="normal">l</mi><mo>=</mo><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">b</mi><mo>)</mo><mo>&#xA0;</mo><mi>a</mi><mi>r</mi><mi mathvariant="normal">g</mi><mi>u</mi><mi mathvariant="normal">m</mi><mi mathvariant="normal">e</mi><mi>n</mi><mi>t</mi><mo>&#xA0;</mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">s</mi><mi>o</mi><mi mathvariant="normal">l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="check_simplified"/><assertion name="syntax_quantity"><param name="units"><![CDATA[m, s, g, °, ', ", $, ¥, €, £, kr, Fr, ₩, ₹, руб, BTC, %, ‰, A, K, mol, cd, rad, sr, h, min, l, N, Pa, Hz, W, J, C, V, Ω, F, S, Wb, b, H, T, lx, lm, Gy, Bq, Sv, kat]]></param><param name="decimalseparators">., \,</param><param name="unitprefixes">M, k, c, m</param><param name="groupoperators">(,[,{</param></assertion><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">8</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/><data name="inputCompound">true</data></localData></question> El mòdul es calcula amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#0000FF¨»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨»+«/mo»«msup»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«/msqrt»«/mstyle»«/math» i CAL SIMPLIFICAR

L'argument és l'arc tangent de la segona component dividida per la primera:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#945;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»arc«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»tg«/mi»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

ATENCIÓ: L'ANGLE ÉS UN ANGLE DEL QUADRANT  «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#FF0000¨»Q«/mi»«/math»

#G1

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