1rBTX 01. NOMBRES REALS/1.1.1 Aproximació i error 1.1.1.10DT NOMENCLATURA APROXIMACIÓ Aproximació: nomenclatura

Als dècims: 1 xifra,

als centèsimes: 2 xifres.

als mil·lèsims 3 xifres,

als deumil·lèsims: 4 xifres,

als centmil·lèsims: 5 xifres,

als milionèsims: 6 xifres.

]]> 0.0000000 0.0000000 0 1.1.1.11Q VocabulariAproximació Quants decimals hem de deixar si aproximem als

a) #a1 ?

b) #a2 ?

c) #a3 ?

d) #a4 ?

]]> 1.0000000 0.5000000 0 0 a) =#sol1b) =#sol2c) =#sol3d) =#sol4]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>dècims</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>centèsims</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>deu</mi><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>cent</mi><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>dècims</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>centèsims</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>deu</mi><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>cent</mi><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a3</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>dècims</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>centèsims</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>deu</mi><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>cent</mi><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a4</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mo>"</mo><mi>dècims</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>centèsims</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo><mo>,</mo><mo>"</mo><mi>deu</mi><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo><mo>,</mo><mo> </mo><mo>"</mo><mi>cent</mi><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>a1</mi><mo>≠</mo><mi>a2</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a1</mi><mo>≠</mo><mi>a3</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a1</mi><mo>≠</mo><mi>a4</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a2</mi><mo>≠</mo><mi>a3</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a2</mi><mo>≠</mo><mi>a4</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a3</mi><mo>≠</mo><mi>a4</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>=</mo><mo>"</mo><mi>dècims</mi><mo>"</mo></mrow><mrow><mi>sol1</mi><mo>=</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>=</mo><mo>"</mo><mi>centèsims</mi><mo>"</mo></mrow><mrow><mi>sol1</mi><mo>=</mo><mn>2</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>=</mo><mo>"</mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo></mrow><mrow><mi>sol1</mi><mo>=</mo><mn>3</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a1</mi><mo>=</mo><mo>"</mo><mi>deu</mi><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo></mrow><mrow><mi>sol1</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>sol1</mi><mo>=</mo><mn>5</mn></mrow></apply></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>=</mo><mo>"</mo><mi>dècims</mi><mo>"</mo></mrow><mrow><mi>sol2</mi><mo>=</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>=</mo><mo>"</mo><mi>centèsims</mi><mo>"</mo></mrow><mrow><mi>sol2</mi><mo>=</mo><mn>2</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>=</mo><mo>"</mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo></mrow><mrow><mi>sol2</mi><mo>=</mo><mn>3</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a2</mi><mo>=</mo><mo>"</mo><mi>deu</mi><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo></mrow><mrow><mi>sol2</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>sol2</mi><mo>=</mo><mn>5</mn></mrow></apply></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a3</mi><mo>=</mo><mo>"</mo><mi>dècims</mi><mo>"</mo></mrow><mrow><mi>sol3</mi><mo>=</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a3</mi><mo>=</mo><mo>"</mo><mi>centèsims</mi><mo>"</mo></mrow><mrow><mi>sol3</mi><mo>=</mo><mn>2</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a3</mi><mo>=</mo><mo>"</mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo></mrow><mrow><mi>sol3</mi><mo>=</mo><mn>3</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a3</mi><mo>=</mo><mo>"</mo><mi>deu</mi><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo></mrow><mrow><mi>sol3</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>sol3</mi><mo>=</mo><mn>5</mn></mrow></apply></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a4</mi><mo>=</mo><mo>"</mo><mi>dècims</mi><mo>"</mo></mrow><mrow><mi>sol4</mi><mo>=</mo><mn>1</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a4</mi><mo>=</mo><mo>"</mo><mi>centèsims</mi><mo>"</mo></mrow><mrow><mi>sol4</mi><mo>=</mo><mn>2</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a4</mi><mo>=</mo><mo>"</mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo></mrow><mrow><mi>sol4</mi><mo>=</mo><mn>3</mn></mrow><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a4</mi><mo>=</mo><mo>"</mo><mi>deu</mi><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>"</mo></mrow><mrow><mi>sol4</mi><mo>=</mo><mn>4</mn></mrow><mrow><mi>sol4</mi><mo>=</mo><mn>5</mn></mrow></apply></apply></apply></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>,</mo><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>centèsims</ms><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>dècims</ms><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>,</mo><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>cent</ms><mo> </mo><ms>mil·lèsims</ms><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>,</mo><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>mil·lèsims</ms><mo>,</mo><mn>3</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>3</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>4</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">4</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> 10 té un zero; als dècims deixem un decimal;

100 té dos zeros; als centèsims deixem dos decimals.

1.000 té tres zeros; als mil·lèsims deixem tres decimals.

10.000 té quatre zeros; als deu mil·lèsims deixem quatre decimals.

100.000 té cinc zeros; als cent mil·lèsims deixem cinc decimals...

]]> 1.1.1.20DT TRUNCAMENT Aproximació per truncament Per aproximar per truncament, n'hi ha prou amb eliminar totes les xifres fins l'ordre escollit.
Exemple:
a les centenes, 35243 el truncament és 35200 ]]> 0.0000000 0.0000000 0 1.1.1.21Q TruncaMil·lèsims Trunca les quantitats següents als mil·lèsims:
Posa punt en lloc de coma

Quantitat

a) #a_1

b) #a_2

c) #a_3

d) #a_4

]]> 1.0000000 0.5000000 0 0 a) =#c_1b) =#c_2c) =#c_3d) =#c_4]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m_7</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>m_1</mi><mo>+</mo><mi>m_2</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>m_3</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>*</mo><mi>m_4</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>*</mo><mi>m_5</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0001</mn><mo>*</mo><mi>m_6</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>00001</mn><mo>*</mo><mi>m_7</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>m_1</mi><mo>+</mo><mi>m_2</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>m_3</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>*</mo><mi>m_4</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>*</mo><mi>m_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n_7</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</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><mn>10</mn><mo>*</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>n_3</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>*</mo><mi>n_4</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>*</mo><mi>n_5</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0001</mn><mo>*</mo><mi>n_6</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>00001</mn><mo>*</mo><mi>n_7</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>n_1</mi><mo>+</mo><mi>n_2</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>n_3</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>*</mo><mi>n_4</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>*</mo><mi>n_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>o_7</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>o_1</mi><mo>+</mo><mi>o_2</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>o_3</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>*</mo><mi>o_4</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>*</mo><mi>o_5</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0001</mn><mo>*</mo><mi>o_6</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>00001</mn><mo>*</mo><mi>o_7</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_3</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>o_1</mi><mo>+</mo><mi>o_2</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>o_3</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>*</mo><mi>o_4</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>*</mo><mi>o_5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_6</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p_7</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>0</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>p_1</mi><mo>+</mo><mi>p_2</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>p_3</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>*</mo><mi>p_4</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>*</mo><mi>p_5</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0001</mn><mo>*</mo><mi>p_6</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>00001</mn><mo>*</mo><mi>p_7</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_4</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>p_1</mi><mo>+</mo><mi>p_2</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>p_3</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>*</mo><mi>p_4</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>*</mo><mi>p_5</mi></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mn>3</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mn>4</mn></math>]]></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">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Als mil·lèsims has de deixar 3 xifres després del punt

]]> 1.1.1.22Q TruncaCentèsims Trunca les quantitats següents als centèsims:
Posa punt en lloc de coma

Quantitat

a) #a_1

b) #a_2

c) #a_3

d) #a_4

]]> 1.0000000 0.5000000 0 0 a) =#c_1b) =#c_2c) =#c_3d) =#c_4]]> <question><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mn>3</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>c</mi><mi>_</mi><mn>4</mn></math>]]></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="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Als centèsims has de deixar 2 xifres després del punt.

]]> 1.1.1.30DT ARRODONIMENT Arrodoniment

Per aproximar per arrodoniment un nombre:

Si la xifra següent a l'ordre en què volem arrodonir és més gran o igual que 5, augmentem un i trunquem.
Si és més petita, trunquem.

Exemples:

35247 s'arrodoneix a les desenes amb 35250
43661 s'arrodoneix a les desenes amb 43660

]]> 0.0000000 0.0000000 0 1.1.1.31Q ArrodonirDècims Arrodoneix les quantitats següents als dècims:
Posa punt en lloc de coma

Quantitat

a) #a_1

b) #a_2

c) #a_3

d) #a_4

]]> 1.1.1.32Q ArrodonirCentèsims Arrodoneix les quantitats següents als centèsims:
Posa punt en lloc de coma

Quantitat

a) #a_1

b) #a_2

c) #a_3

d) #a_4

]]> 1.1.1.33Q ArrodonirMil·lèsims Arrodoneix les quantitats següents als mil·lèsims:
Posa punt en lloc de coma

Quantitat

a) #a_1

b) #a_2

c) #a_3

d) #a_4

]]> 1.1.1.50DT ERROR ABSOLUT

Error absolut

És la diferència entre la quantitat i l'aproximació

EN VALOR ABSOLUT
E_A = |nombre - aproximació|

Exemple: Si s'arrodoneix 13,4276 amb 13,43, l'error absolut és de |13,4276 - 13,43 = |-1,0024| = 1,0024

]]> 0.0000000 0.0000000 0 1.1.1.51Q ErrorAbsolutArrodDècims Calcula l'error absolut (arrodonit als mil·lèsims) si s'arrodoneixen les quantitats als dècims.
Format: 0.021

Quantitat

a) #a_1

b) #a_2

c) #a_3

d) #a_4

a) #c_1

b) #c_2

c) #c_3

d) #c_4

Per trobar l'error cal fer la resta i agafar el valor absolut (positiu)

]]> 1.1.1.52Q ErrorAbsolutArrodCentèsims Calcula l'error absolut (arrodonit als cent mil·lèsims) si s'arrodoneixen les quantitats als centèsims.
Format: 0.021

Quantitat

a) #a_1

b) #a_2

c) #a_3

d) #a_4

a) #c_1

b) #c_2

c) #c_3

d) #c_4

Per trobar l'error cal fer la resta i agafar el valor absolut (positiu)

]]> 1.1.1.60DT ERROR RELATIU

Error relatiu

Es divideix l'error absolut per la quantitat

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«msub mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»E«/mi»«mi mathvariant=¨bold¨»R«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«msub»«mi mathvariant=¨bold¨»E«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mi mathvariant=¨bold¨»Nombre«/mi»«/mfrac»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1.1.1.61Q ErrorRelatiu2exercicis Calcula l'error relatiu (arrodonit als cent mil·lèsims) si s'arrodoneixen aquestes quantitats:
Posa punt en lloc de coma

Quantitat

a) #a_1 als centèsims

b) #a_2 als mil·lèsims

]]> 1.0000000 0.3333333 0 0 a) =#e_1b) =#e_2]]> <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>a_1</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>a_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mo>(</mo><mi>b_1</mi><mo>/</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>a_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mo>(</mo><mi>b_2</mi><mo>/</mo><mn>1000</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>a_3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_3</mi><mo>=</mo><mo>(</mo><mi>b_3</mi><mo>/</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>a_4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_4</mi><mo>=</mo><mo>(</mo><mi>b_4</mi><mo>/</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a_1</mi><mo>-</mo><mi>c_1</mi></mrow></mfenced><mo> </mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a_2</mi><mo>-</mo><mi>c_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_3</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a_3</mi><mo>-</mo><mi>c_3</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_4</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a_4</mi><mo>-</mo><mi>c_4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mfenced><mrow><mi>d_1</mi><mo>/</mo><mi>a_1</mi></mrow></mfenced><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mfenced><mrow><mi>d_2</mi><mo>/</mo><mi>a_2</mi></mrow></mfenced><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mfenced><mrow><mi>d_3</mi><mo>/</mo><mi>a_3</mi></mrow></mfenced><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_4</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mfenced><mrow><mi>d_4</mi><mo>/</mo><mi>a_4</mi></mrow></mfenced><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>_</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-5)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'arrodoniment és:

a) #c_1

b) #c_2

]]> L'error absolut és:

a) #d_1

b) #d_2

]]> 1.1.1.62Q ErrorRelatiuArrodonirCentèsims4exercicis Calcula l'error relatiu (arrodonit als cent mil·lèsims) si s'arrodoneix la quantitat als centèsims
Posa punt en lloc de coma

Quantitat

a) #a_1

b) #a_2

c) #a_3

d) #a_4

]]> 1.0000000 0.3333333 0 0 a) =#e_1b) =#e_2c) =#e_3d) =#e_4]]> <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>a_1</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>a_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mo>(</mo><mi>b_1</mi><mo>/</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>a_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mo>(</mo><mi>b_2</mi><mo>/</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>a_3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_3</mi><mo>=</mo><mo>(</mo><mi>b_3</mi><mo>/</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>100</mn><mo>*</mo><mi>a_4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_4</mi><mo>=</mo><mo>(</mo><mi>b_4</mi><mo>/</mo><mn>100</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a_1</mi><mo>-</mo><mi>c_1</mi></mrow></mfenced><mo> </mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a_2</mi><mo>-</mo><mi>c_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_3</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a_3</mi><mo>-</mo><mi>c_3</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_4</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a_4</mi><mo>-</mo><mi>c_4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mfenced><mrow><mi>d_1</mi><mo>/</mo><mi>a_1</mi></mrow></mfenced><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mfenced><mrow><mi>d_2</mi><mo>/</mo><mi>a_2</mi></mrow></mfenced><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mfenced><mrow><mi>d_3</mi><mo>/</mo><mi>a_3</mi></mrow></mfenced><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_4</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mfenced><mrow><mi>d_4</mi><mo>/</mo><mi>a_4</mi></mrow></mfenced><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>_</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>_</mi><mn>3</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>_</mi><mn>4</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-5)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'arrodoniment és:

a) #c_1

b) #c_2

c) #c_3

d) #c_4

]]>

L'error absolut és:

a) #d_1

b) #d_2

c) #d_3

d) #d_4

]]> 1.1.1.63Q ErrorRelatiuArrodonirCentèsims4exercicis (còpia) Calcula l'error relatiu (arrodonit als mil·lèsims) si s'arrodoneix la quantitat als dècims
Posa punt en lloc de coma

Quantitat

a) #a_1

b) #a_2

c) #a_3

d) #a_4

]]> 1.0000000 0.3333333 0 0 a) =#e_1b) =#e_2c) =#e_3d) =#e_4]]> <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>a_1</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>10</mn><mo>*</mo><mi>a_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mo>(</mo><mi>b_1</mi><mo>/</mo><mn>10</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>10</mn><mo>*</mo><mi>a_2</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mo>(</mo><mi>b_2</mi><mo>/</mo><mn>10</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>10</mn><mo>*</mo><mi>a_3</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_3</mi><mo>=</mo><mo>(</mo><mi>b_3</mi><mo>/</mo><mn>10</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>100000</mn><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>.</mo><mn>1</mn><mo>)</mo><mo>)</mo></mrow><mn>100000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_4</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>10</mn><mo>*</mo><mi>a_4</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_4</mi><mo>=</mo><mo>(</mo><mi>b_4</mi><mo>/</mo><mn>10</mn><mo>)</mo><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a_1</mi><mo>-</mo><mi>c_1</mi></mrow></mfenced><mo> </mo><mo> </mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a_2</mi><mo>-</mo><mi>c_2</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_3</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a_3</mi><mo>-</mo><mi>c_3</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_4</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>a_4</mi><mo>-</mo><mi>c_4</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mfenced><mrow><mi>d_1</mi><mo>/</mo><mi>a_1</mi></mrow></mfenced><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mfenced><mrow><mi>d_2</mi><mo>/</mo><mi>a_2</mi></mrow></mfenced><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_3</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mfenced><mrow><mi>d_3</mi><mo>/</mo><mi>a_3</mi></mrow></mfenced><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_4</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mfenced><mrow><mi>d_4</mi><mo>/</mo><mi>a_4</mi></mrow></mfenced><mo>)</mo></mrow><mn>1000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>,</mo><mi>c_1</mi><mo>,</mo><mi>d_1</mi><mo>,</mo><mi>e_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.26709</mn><mo>,</mo><mn>0.3</mn><mo>,</mo><mn>0.03291</mn><mo>,</mo><mn>0.123</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>,</mo><mi>c_2</mi><mo>,</mo><mi>d_2</mi><mo>,</mo><mi>e_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.6909</mn><mo>,</mo><mn>4.7</mn><mo>,</mo><mn>0.0091</mn><mo>,</mo><mn>0.002</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>,</mo><mi>c_3</mi><mo>,</mo><mi>d_3</mi><mo>,</mo><mi>e_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.65254</mn><mo>,</mo><mn>0.7</mn><mo>,</mo><mn>0.04746</mn><mo>,</mo><mn>0.073</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>,</mo><mi>c_4</mi><mo>,</mo><mi>d_4</mi><mo>,</mo><mi>e_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4.7285</mn><mo>,</mo><mn>4.7</mn><mo>,</mo><mn>0.02847</mn><mo>,</mo><mn>0.006</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>_</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>_</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>_</mi><mn>3</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi mathvariant="normal">e</mi><mi>_</mi><mn>4</mn></math>]]></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">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputCompound">true</data><data name="inputField">popupEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> L'arrodoniment és:

a) #c_1

b) #c_2

c) #c_3

d) #c_4

]]> L'error absolut és:

a) #d_1

b) #d_2

c) #d_3

d) #d_4

]]> 1.1.1.81PB ErrorAbsolutRelatiu AproximarGravetat

Quin error absolut i quin error relatiu cometem si aproximem l'acceleració de la gravetat g als #a? Arrodoneix als deumil·lèsims

Al nivell del mar, g és aproximadament de 9,80665 m/s².

L'acceleració de la gravetat terrestre g, genera sobre una massa m una força F = mg que fa "caure" la massa cap al terra.

]]> 1.0000000 0.5000000 0 0 error absolut=#sol1error relatiu=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>g</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>80665</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>dècims</mi><mo>,</mo><mi>centèsims</mi><mo>,</mo><mo> </mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi><mo>,</mo><mi>deumil</mi><mo>·</mo><mi>lèsims</mi></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>a</mi><mo>=</mo><mi>dècims</mi></mrow><mtable><mtr><mtd><mi>g1</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>8</mn></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>g</mi><mo>-</mo><mi>g1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mfrac><mi>e1</mi><mi>g</mi></mfrac></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mi>centèsims</mi></mrow><mtable><mtr><mtd><mi>g1</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>81</mn></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>g</mi><mo>-</mo><mi>g1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mfrac><mi>e1</mi><mi>g</mi></mfrac></mtd></mtr></mtable><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">if</csymbol><mrow><mi>a</mi><mo>=</mo><mi>mil</mi><mo>·</mo><mi>lèsims</mi></mrow><mtable><mtr><mtd><mi>g1</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>807</mn></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>g</mi><mo>-</mo><mi>g1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mfrac><mi>e1</mi><mi>g</mi></mfrac></mtd></mtr></mtable><mtable><mtr><mtd><mi>g1</mi><mo>=</mo><mn>9</mn><mo>.</mo><mn>8067</mn></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>g</mi><mo>-</mo><mi>g1</mi></mrow></mfenced></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mfrac><mi>e1</mi><mi>g</mi></mfrac></mtd></mtr></mtable></apply></apply></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mn>10000000</mn><mo>*</mo><mi>e1</mi></mrow></mfenced></mrow><mn>10000000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mrow><mi>arrodoneix</mi><mfenced><mrow><mn>10000000</mn><mo>*</mo><mi>e2</mi></mrow></mfenced></mrow><mn>10000000</mn></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><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"><mn>9.8067</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"><mi>deumil</mi><mo>*</mo><mi>lèsims</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>,</mo><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5.</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup><mo>,</mo><mn>5.</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5.0986</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>,</mo><mn>5.1</mn><mo>*</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">e</mi><mi>r</mi><mi>r</mi><mi>o</mi><mi>r</mi><mo> </mo><mi>a</mi><mi>b</mi><mi>s</mi><mi>o</mi><mi>l</mi><mi>u</mi><mi>t</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi mathvariant="normal">e</mi><mi>r</mi><mi>r</mi><mi>o</mi><mi>r</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>u</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">10</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</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="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Si arrodonim als #a, l'arrodoniment de g és #g1;

l'error absolut és el valor absolut de #g – #g1

i per trobar l'error relatiu es divideix l'error absolut per #g.

]]> 1.1.1.82PB DeterminarQtitatAmbEAiER

Si, aproximant un nombre, l'error absolut és de #e1 i l'error relatiu és de #e2, quin és el valor d'aquest nombre?

Arrodoneix als centèsims

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mrow><mi>aleatori</mi><mfenced><mrow><mn>1001</mn><mo>,</mo><mn>9999</mn></mrow></mfenced><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></mrow><mn>100</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mi>sol</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi><mo>=</mo><mfenced close="|" open="|"><mrow><mi>sol</mi><mo>-</mo><mi>a</mi></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfrac><mi>e1</mi><mi>sol</mi></mfrac><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mfrac><mi>e1</mi><mi>e2</mi></mfrac></math></input></command></group></library><group><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>94.53</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"><mn>95</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0.47</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>0.004972</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>94.53</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="precision">8</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</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> Si N és el nombre, «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«msub mathcolor=¨#0000FF¨»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»E«/mi»«mi mathvariant=¨bold¨»R«/mi»«/msub»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»E«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«mi mathvariant=¨bold¨»N«/mi»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#8658;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»N«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«msub»«mi mathvariant=¨bold¨»E«/mi»«mi mathvariant=¨bold¨»A«/mi»«/msub»«msub»«mi mathvariant=¨bold¨»E«/mi»«mi mathvariant=¨bold¨»R«/mi»«/msub»«/mfrac»«/math»

]]> 1.1.1.91PB ErrorPrestatges

En una habitació, es volen col·locar #n prestatges, l'un al costat de l'altre fins a cobrir tota l'amplada de la paret. La paret té una amplada de #a cm.
Per encarregar els prestatges es trunca la seva mida als mm. Quin espai quedarà buit?
(arrodonit en mm)

2. Multiplica aquesta mida pel nombre de prestatges i calcula la diferència amb l'amplada de la paret

]]> 1.1.1.92PB ErrorTerrat

Es volen impermeabilitzar els terrats del dos edificis rectangulars amb una pintura de cautxú que costa #a1 €/m².
S'ha mesurat la superfície total i és de #a2 m². Malauradament, s'ha comés un error mesurant i les llargades i les amplades són un #p % més grans.
Quant costarà de més l'obra per culpa de l'error?
(arrodonit als cèntims)

]]> 1rBTX 01. NOMBRES REALS/1.1.2 Nombres irracionals 1.1.2.31 Càlculs amb irracionals Quina és l'àrea d'un cercle de #a cm de diàmetre? Arrodoniu als mil·lèsims.

Format de la resposta: el nombre arrodonit (amb punt i no coma) i sense unitats de longitud.

]]> L'àrea d'un cercle es mesura amb A = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#960;«/mi»«mo»·«/mo»«msup»«mi»r«/mi»«mn»2«/mn»«/msup»«/math»«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi»§#960;«/mi»«mo»·«/mo»«msup»«mi»r«/mi»«mn»2«/mn»«/msup»«/math»

]]> 1.0000000 0.5000000 0 0 #r_12]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo> </mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfenced><mfrac><mi>a</mi><mn>2</mn></mfrac></mfenced><mo>*</mo><mfenced><mfrac><mi>a</mi><mn>2</mn></mfrac></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><mi>t</mi><mo>·</mo><pi/><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>arrodoneix</mi><mo>(</mo><mn>1000</mn><mo>*</mo><mi>r_1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi><mo>=</mo><mfrac><mi>r_2</mi><mn>1000</mn></mfrac><mo>·</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12.566</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12566</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12.566</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>12</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</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> 1.1.2.32 Càlculs amb irracionals Quina és el radi d'una circumferència de #a cm de perímetre?

Format de la resposta: nombre enter sense unitats de longitud.

]]> Es calcula pensant que el perímetre és P = «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«mi»§#960;«/mi»«mi»r«/mi»«/math»

]]> 1.0000000 0.5000000 0 0 #r <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>r</mi><mo>=</mo><mo> </mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>2</mn><mo>*</mo><pi/><mo>*</mo><mi>r</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>56.549</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"><mn>9</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">6</option><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</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> 1.1.2.33 Càlculs amb irracionals Quant mesura la diagonal d'un cub de #a cm d'aresta?

Format de la resposta: un nombre racional o irracional sense unitats de longitud; exemple: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»5«/mn»«mo»*«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/math»
]]> Tens un exercici semblant fet en el PowerPoint.
Cal que calculis primer la diagonal de la base (és la hipotenusa d'un triangle rectangle que té per costat #a i només has d'aplicar el teorema de Pitàgores.
Un cop calculada la diagonal de la base, mira com pots aplicar el teorema de Pitàgores per calcular la diagonal del cub.

]]> 1.0000000 0.5000000 0 0 #r_12 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mo> </mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><msqrt><mrow><mn>2</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi><mo>=</mo><msqrt><mrow><mn>3</mn><mo>*</mo><msup><mi>a</mi><mn>2</mn></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_12</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>7</mn><mo>*</mo><msqrt><mn>3</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 type="mathml"> #r_12 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> 1rBTX 01. NOMBRES REALS/1.1.3 Ordre, arrels i operacions 1.1.3.000DT DEFINICIÓ ARREL NÈSIMA Arrel n-èsima

S'anomena arrel n-èsima del nombre x, el nombre y que elevat a n dona x: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mrow»«mi mathvariant=¨bold¨»n«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«/math»

També es pot escriure com un exponent FRACCIONARI:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»m«/mi»«/msup»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mfrac»«mi mathvariant=¨bold¨»m«/mi»«mi mathvariant=¨bold¨»n«/mi»«/mfrac»«/msup»«/math»

]]> 0.0000000 0.0000000 0 1.1.3.00DT ORDRE EN ELS REALS

Ordre en els nombres reals

En els nombres reals, la relació "≤" o "≥" és una relació d'ordre (reflexiva, simètrica i transitiva).

Es pot definir amb «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8804;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8658;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8804;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»0«/mn»«/mrow»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1.1.3.01 Ordenar reals Ordena, de petit a gran, els nombres reals següents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/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¨»4«/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¨»5«/mn»«/mrow»«/mstyle»«/math»

Format: {1,2,3,4,5}

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a12</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a13</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a14</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a15</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>11</mn><mo>,</mo><mn>21</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><msqrt><mi>a11</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mfrac><msqrt><mrow><mi>a11</mi><mo>+</mo><mi>a12</mi></mrow></msqrt><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mfrac><mrow><msqrt><mi>a12</mi></msqrt><mo>-</mo><msqrt><mi>a13</mi></msqrt></mrow><mn>3</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mfrac><msqrt><mi>a13</mi></msqrt><msqrt><mi>a14</mi></msqrt></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a5</mi><mo>=</mo><mfrac><mrow><msqrt><mi>a11</mi></msqrt><mo>+</mo><mi>a15</mi></mrow><mn>2</mn></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>ordena</mi><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>a3</mi><mo>,</mo><mi>a4</mi><mo>,</mo><mi>a5</mi></mtd></mtr></mtable></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><mo>,</mo><mi>a3</mi><mo>,</mo><mi>a4</mi><mo>,</mo><mi>a5</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>11</mn></msqrt><mo>,</mo><mfrac><msqrt><mn>23</mn></msqrt><mn>2</mn></mfrac><mo>,</mo><mfrac><mrow><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mrow><mn>4</mn><mo>*</mo><msqrt><mn>13</mn></msqrt></mrow><mn>13</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>11</mn></msqrt><mn>2</mn></mfrac><mo>+</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mfrac><mrow><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></mrow><mn>3</mn></mfrac><mo>-</mo><mfrac><mn>4</mn><mn>3</mn></mfrac><mo>,</mo><mfrac><mrow><mn>4</mn><mo>*</mo><msqrt><mn>13</mn></msqrt></mrow><mn>13</mn></mfrac><mo>,</mo><mfrac><msqrt><mn>23</mn></msqrt><mn>2</mn></mfrac><mo>,</mo><msqrt><mn>11</mn></msqrt><mo>,</mo><mfrac><msqrt><mn>11</mn></msqrt><mn>2</mn></mfrac><mo>+</mo><mn>9</mn></mtd></mtr></mtable></mfenced></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-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> N'hi ha prou amb aproximar els nombres amb la calculadora per ordenar-los.

]]> 1.1.3.11Q AgrupaRadicalsSemblants Agrupa els radicals semblants en l'expressió (no confonguis els símbols de restar - i de multiplicar ·):
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«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¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/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¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11 <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>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>i_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>i_1</mi><mo>≠</mo><mi>i_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>c_1</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>c_2</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>c_3</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>c_4</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>a_1</mi><mo>-</mo><mi>a_2</mi><mo>+</mo><mi>a_3</mi><mo>-</mo><mi>a_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mi>c_1</mi><mo>+</mo><mi>c_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mo>-</mo><mi>c_2</mi><mo>-</mo><mi>c_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><msqrt><mi>i_2</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>16</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>18</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>-</mo><mn>20</mn><mo>*</mo><msqrt><mn>3</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>#r_11</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Es tracta de sumar o restar els coeficients dels termes que tenen el mateix radical:

Per #e_1, el coeficient és: #d_1 = #c_1 + #c_3

Per #e_2, el coeficient és: #d_2 = -#c_2 - #c_4

]]> 1.1.3.12Q Agrupar radicals semblants_2 Agrupa els radicals semblants en l'expressió:
«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«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¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/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¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c_4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>4</mn><mo>,</mo><mn>16</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>i_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>i_1</mi><mo>≠</mo><mi>i_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>c_1</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mi>c_2</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi><mo>=</mo><mi>c_3</mi><mo>*</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi><mo>=</mo><mi>c_4</mi><mo>*</mo><msqrt><mi>i_2</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mi>a_1</mi><mo>+</mo><mi>a_2</mi><mo>-</mo><mi>a_3</mi><mo>-</mo><mi>a_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_1</mi><mo>=</mo><mi>c_1</mi><mo>-</mo><mi>c_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d_2</mi><mo>=</mo><mi>c_2</mi><mo>-</mo><mi>c_4</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_1</mi><mo>=</mo><msqrt><mi>i_1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e_2</mi><mo>=</mo><msqrt><mi>i_2</mi></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msqrt><mn>5</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>5</mn><mo>*</mo><msqrt><mn>2</mn></msqrt><mo>+</mo><mn>4</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 type="mathml"> #r_11 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Es tracta de sumar o restar els coeficients dels termes que tenen el mateix radical:

Per #e_1, el coeficient és: #d_1 = #c_1 - #c_3

Per #e_2, el coeficient és: #d_2 = #c_2 - #c_4

]]> 1.1.3.21Q SimplificaArrelQuadrada Simplifica: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«/mstyle»«/math»

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn»3«/mn»«mroot»«mn»6«/mn»«mn»4«/mn»«/mroot»«/mrow»«/mstyle»«/math»

]]> 1.1.3.22Q SimplificaArrelQuadrada Simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«msqrt mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«/msqrt»«/mstyle»«/math»

Format de resposta: semblant a «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mroot»«mn»6«/mn»«mn»4«/mn»«/mroot»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><msup><mn>2</mn><mi>a</mi></msup><mo>*</mo><msup><mn>3</mn><mi>b</mi></msup></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mn>100</mn><mo><</mo><mi>e1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>e1</mi><mo><</mo><mn>1000</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msqrt><mi>e1</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>a</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>=</mo><mi>quocient</mi><mo>(</mo><mi>b</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mi>residu</mi><mo>(</mo><mi>b</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>216</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>*</mo><msqrt><mn>6</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q1</mi><mo>,</mo><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q2</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>1</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_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> La descomposició en factors del radicand és 2^#a · 3^#b
¨Surt/en¨ #n dos/os i #n tresos i queda un dos sota l'arrel perquè:

dividim #a per 2 i ens dona #q1 de quocient i #r1 de residu.
dividim #b per 2 i ens dona #q2 de quocient i #r2 de residu.

]]> 1.1.3.25Q SimplificarArrelCúbica Simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»r_«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mstyle»«/math»

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn mathvariant=¨bold¨»3«/mn»«mroot»«mn mathvariant=¨bold¨»6«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11]]> <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>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><msup><mn>2</mn><mi>a</mi></msup><mo>·</mo><msup><mn>3</mn><mi>b</mi></msup><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mroot><mi>r_2</mi><mn>3</mn></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</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>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>240</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mroot><mn>30</mn><mn>3</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> La descomposició en factors del radicand és 2^#a · 3^#b · #c

]]> 1.1.3.26Q SimplificaArrelCúbica Simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mstyle»«/math»

Format: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»3«/mn»«mroot»«mn»6«/mn»«mn»4«/mn»«/mroot»«/math»

]]> 1.1.3.28Q SimplificarFinsIrreductible Simplifica al màxim l'arrel: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold-italic¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mroot»«/mstyle»«/math»

]]> 1.0000000 1.0000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><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>i1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>4</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>i1</mi><mo>,</mo><mi>e1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mfenced><mrow><mi>i1</mi><mo>></mo><mi>e1</mi></mrow></mfenced></mrow></apply></mtd></mtr><mtr><mtd><mi>w1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i2</mi><mo>=</mo><mi>w1</mi><mo>*</mo><mi>i1</mi></mtd></mtr><mtr><mtd><mi>e2</mi><mo>=</mo><mi>w1</mi><mo>*</mo><mi>e1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>e2</mi><mo><</mo><mn>8</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mroot><msup><mi>a1</mi><mi>e1</mi></msup><mi>i1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msup><mi>a1</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msup><mi>a1</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mroot><msup><mi>a1</mi><mi>e2</mi></msup><mi>i2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>r1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>9</mn></mroot><mo>,</mo><mroot><mn>2</mn><mn>9</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>,</mo><mi>e1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>,</mo><mi>e2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>27</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>,</mo><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>8</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"><mroot><mn>2</mn><mn>9</mn></mroot></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> Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»b«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«msup mathcolor=¨#000066¨»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mrow»«/mstyle»«/math»

cal simplificar la fracció: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 1.1.3.31Q IntroduirFactorsArQuadrada Introdueix tots els factors sota el radical: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r_«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«/mrow»«/mstyle»«/math»

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mi mathvariant=¨normal¨»a«/mi»«/msup»«mo»§#160;«/mo»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»y«/mi»«mi mathvariant=¨normal¨»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi mathvariant=¨normal¨»n«/mi»«/mroot»«/math»

]]> 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>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><msup><mi>x</mi><mi>a</mi></msup><mo>*</mo><msup><mi>y</mi><mi>b</mi></msup><mo>*</mo><msup><mi>z</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mi>c</mi></msup><mo>*</mo><msup><mi>y</mi><mi>a</mi></msup><mo>*</mo><msup><mi>z</mi><mi>b</mi></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>r_1</mi><mo>*</mo><mi>r_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mi>d</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e</mi></msup><mo>*</mo><msup><mi>z</mi><mi>f</mi></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</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>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>1</mn><mo>,</mo><mn>0</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><mi>y</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><mi>z</mi></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>3</mn></msup><mo>*</mo><mi>y</mi><mo>*</mo><msqrt><mrow><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><mi>z</mi></mrow></msqrt></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><mrow><msup><mi>x</mi><mn>6</mn></msup><mo>*</mo><msup><mi>y</mi><mn>5</mn></msup><mo>*</mo><mi>z</mi></mrow></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="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> Quan un factor entra sota l'arrel:
a) el seu exponent queda multiplicat per 2
b) un cop sota l'arrel, cal sumar aquest nou exponent amb l'exponent del mateix factor (si és que n'hi ha algun).

]]> 1.1.3.32Q IntroduirFactorsArQuadrada_2 Introdueix tots els factors sota el radical: #r_2

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mi mathvariant=¨normal¨»a«/mi»«/msup»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»y«/mi»«mi mathvariant=¨normal¨»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi mathvariant=¨normal¨»n«/mi»«/mroot»«/math»

]]>

]]> 1.0000000 0.5000000 0 0 #r <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>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><msup><mi>x</mi><mi>a</mi></msup><mo>*</mo><msup><mi>y</mi><mi>b</mi></msup><mo>*</mo><msup><mi>z</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mi>c</mi></msup><mo>*</mo><msup><mi>y</mi><mi>a</mi></msup><mo>*</mo><msup><mi>z</mi><mi>b</mi></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>r_1</mi><mo>*</mo><mi>r_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mi>d</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e</mi></msup><mo>*</mo><msup><mi>z</mi><mi>f</mi></msup></mrow></msqrt></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</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"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>1</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><msup><mi>z</mi><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mrow><msup><mi>x</mi><mn>5</mn></msup><mo>*</mo><mi>y</mi><mo>*</mo><msup><mi>z</mi><mn>3</mn></msup></mrow></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>3</mn></msup><mo>*</mo><msup><mi>z</mi><mn>5</mn></msup><mo>*</mo><msqrt><mrow><msup><mi>x</mi><mn>5</mn></msup><mo>*</mo><mi>y</mi><mo>*</mo><msup><mi>z</mi><mn>3</mn></msup></mrow></msqrt></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"><msqrt><mrow><msup><mi>x</mi><mn>7</mn></msup><mo>*</mo><msup><mi>y</mi><mn>7</mn></msup><mo>*</mo><msup><mi>z</mi><mn>13</mn></msup></mrow></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Quan un factor entra sota l'arrel quadrada:
a) el seu exponent queda multiplicat per 2
b) un cop sota l'arrel, cal sumar aquest nou exponent amb l'exponent del mateix factor (si és que n'hi ha algun).

]]> 1.1.3.33Q IntroduirFactorsArQuadrada Introdueix tots els factors sota el radical: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»z«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«msqrt mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»y«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«mo mathvariant=¨bold¨»§#183;«/mo»«msup»«mi mathvariant=¨bold¨»z«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»f«/mi»«/mrow»«/msup»«/msqrt»«/mrow»«/mstyle»«/math»

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mi mathvariant=¨normal¨»a«/mi»«/msup»«mo»§#160;«/mo»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»y«/mi»«mi mathvariant=¨normal¨»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi mathvariant=¨normal¨»n«/mi»«/mroot»«/math»

]]> 1.0000000 0.5000000 0 0 #r <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>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><msqrt><mrow><msup><mi>x</mi><mrow><mn>2</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>d</mi></mrow></msup><mo>*</mo><msup><mi>y</mi><mrow><mn>2</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>e</mi></mrow></msup><mo>*</mo><msup><mi>z</mi><mrow><mn>2</mn><mo>*</mo><mi>c</mi><mo>+</mo><mi>f</mi></mrow></msup></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>d</mi><mo>,</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>6</mn><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"><msqrt><mrow><msup><mi>x</mi><mn>9</mn></msup><mo>*</mo><msup><mi>y</mi><mn>10</mn></msup><mo>*</mo><msup><mi>z</mi><mn>11</mn></msup></mrow></msqrt></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Quan un factor entra sota l'arrel quadrada:
a) el seu exponent queda multiplicat per 2
b) un cop sota l'arrel, cal sumar aquest nou exponent amb l'exponent del mateix factor (si és que n'hi ha algun).

]]> 1.1.3.35Q IntroduirFactorsArrCúbica Introdueix tots els factors sota el radical: #r_2

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mi mathvariant=¨normal¨»a«/mi»«/msup»«mo»§#160;«/mo»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»y«/mi»«mi mathvariant=¨normal¨»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi mathvariant=¨normal¨»n«/mi»«/mroot»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><msup><mi>x</mi><mi>a</mi></msup><mo>*</mo><msup><mi>y</mi><mi>b</mi></msup><mo>*</mo><msup><mi>z</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mroot><mrow><msup><mi>x</mi><mi>c</mi></msup><mo>*</mo><msup><mi>y</mi><mi>a</mi></msup><mo>*</mo><msup><mi>z</mi><mi>b</mi></msup></mrow><mn>3</mn></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>r_1</mi><mo>*</mo><mi>r_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mroot><mrow><msup><mi>x</mi><mi>d</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e</mi></msup><mo>*</mo><msup><mi>z</mi><mi>f</mi></msup></mrow><mn>3</mn></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</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"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>2</mn></msup></mrow><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi><mo>*</mo><mroot><mrow><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>2</mn></msup></mrow><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><msup><mi>x</mi><mn>13</mn></msup><mo>*</mo><msup><mi>y</mi><mn>10</mn></msup><mo>*</mo><msup><mi>z</mi><mn>5</mn></msup></mrow><mn>3</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_11 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Quan un factor entra sota l'arrel cúbica:
a) el seu exponent queda multiplicat per 3
b) un cop sota l'arrel, cal sumar aquest nou exponent amb l'exponent del mateix factor (si és que n'hi ha algun).

]]> 1.1.3.36Q IntroduirFactorsArrCúbica_2 Introdueix tots els factors sota el radical: #r_2

Format de resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot»«mrow»«msup»«mi mathvariant=¨normal¨»x«/mi»«mi mathvariant=¨normal¨»a«/mi»«/msup»«mo»§#160;«/mo»«mo»§#160;«/mo»«msup»«mi mathvariant=¨normal¨»y«/mi»«mi mathvariant=¨normal¨»b«/mi»«/msup»«mo».«/mo»«mo».«/mo»«mo».«/mo»«/mrow»«mi mathvariant=¨normal¨»n«/mi»«/mroot»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>n</mi><mo>+</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>1</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>n</mi><mo>-</mo><mn>2</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi><mo>=</mo><msup><mi>x</mi><mi>a</mi></msup><mo>*</mo><msup><mi>y</mi><mi>b</mi></msup><mo>*</mo><msup><mi>z</mi><mi>c</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi><mo>=</mo><mroot><mrow><msup><mi>x</mi><mi>c</mi></msup><mo>*</mo><msup><mi>y</mi><mi>a</mi></msup><mo>*</mo><msup><mi>z</mi><mi>b</mi></msup></mrow><mn>3</mn></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi><mo>=</mo><mi>r_1</mi><mo>*</mo><mi>r_3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>a</mi><mo>+</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>b</mi><mo>+</mo><mi>a</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mn>3</mn><mo>*</mo><mi>c</mi><mo>+</mo><mi>b</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mroot><mrow><msup><mi>x</mi><mi>d</mi></msup><mo>*</mo><msup><mi>y</mi><mi>e</mi></msup><mo>*</mo><msup><mi>z</mi><mi>f</mi></msup></mrow><mn>3</mn></mroot></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</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"><mo>(</mo><mi>a</mi><mo>,</mo><mi>b</mi><mo>,</mo><mi>c</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>1</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>2</mn></msup></mrow><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mi>x</mi><mn>4</mn></msup><mo>*</mo><msup><mi>y</mi><mn>2</mn></msup><mo>*</mo><mi>z</mi><mo>*</mo><mroot><mrow><mi>x</mi><mo>*</mo><msup><mi>y</mi><mn>4</mn></msup><mo>*</mo><msup><mi>z</mi><mn>2</mn></msup></mrow><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mrow><msup><mi>x</mi><mn>13</mn></msup><mo>*</mo><msup><mi>y</mi><mn>10</mn></msup><mo>*</mo><msup><mi>z</mi><mn>5</mn></msup></mrow><mn>3</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_11 </correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Quan un factor entra sota l'arrel cúbica:
a) el seu exponent queda multiplicat per 3
b) un cop sota l'arrel, cal sumar aquest nou exponent amb l'exponent del mateix factor (si és que n'hi ha algun).

]]> 1.1.3.40DT OPERACIONS AMB ARRELS Producte d'arrels El producte de dues arrels de mateix índex és igual a l'arrel del producte dels radicands. Quocient d'arrels

El quocient de dues arrels de mateix índex és igual a l'arrel del quocient dels radicands

Potència d'una arrel

La potència d'una arrel és igual a l'arrel de lapotència del radicand.

Arrel d'una arrel

Per calcular l'arrel d'una arrel, n'hi ha prou amb multiplicar els índex.

]]> 0.0000000 0.0000000 0 1.1.3.41Q ProducteArrelsQuad Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«msqrt mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msqrt mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«/mrow»«/mstyle»«/math»

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>9</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>9</mn></mrow></mfenced></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><msqrt><mrow><mn>6</mn><mo>*</mo><mi>a_1</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><msqrt><mrow><mn>10</mn><mo>*</mo><mi>b_1</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mn>6</mn><mo>*</mo><mi>a_1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mn>10</mn><mo>*</mo><mi>b_1</mi></mtd></mtr><mtr><mtd/></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>b_1</mi><mo>)</mo><mo>≠</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a_1</mi><mo>≠</mo><mi>b_1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>6</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>24</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>60</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>15</mn></msqrt></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>12</mn><mo>*</mo><msqrt><mn>10</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="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> Cal multiplicar els radicands entre ells i simplificar si s'escau.

]]> 1.1.3.42Q ProducteArrelsQuad_2 Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mstyle»«/math»

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #r_22 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</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</mi><mo>=</mo><msqrt><mrow><mi>d</mi><mo>*</mo><mi>a_1</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msqrt><mrow><mi>d</mi><mo>*</mo><mi>b_1</mi></mrow></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_22</mi><mo>=</mo><mi>a</mi><mo>*</mo><mi>b</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>15</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>21</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>*</mo><msqrt><mn>35</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 type="mathml">#r_22</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression" correctAnswer="0"/><assertion name="equivalent_symbolic" correctAnswer="0"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data></localData></question> Cal multiplicar els radicands entre ells i simplificar si s'escau.

]]> 1.1.3.43Q QuocientArrelsQuadrades Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/msqrt»«/mfrac»«/mstyle»«/math»

Format de la resposta: enter o «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>17</mn><mo>,</mo><mn>19</mn><mo>,</mo><mn>23</mn><mo>,</mo><mn>29</mn><mo>,</mo><mn>31</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>17</mn><mo>,</mo><mn>19</mn><mo>,</mo><mn>23</mn><mo>,</mo><mn>29</mn><mo>,</mo><mn>31</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><msqrt><mrow><mn>8</mn><mo>*</mo><mi>a_1</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><msqrt><mrow><mn>12</mn><mo>*</mo><mi>b_1</mi></mrow></msqrt></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mn>8</mn><mo>*</mo><mi>a_1</mi></mtd></mtr><mtr><mtd><mi>b2</mi><mo>=</mo><mn>12</mn><mo>*</mo><mi>b_1</mi></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>a_1</mi><mo>≠</mo><mi>b_1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><msqrt><mfrac><mrow><mn>8</mn><mo>*</mo><mi>a_1</mi></mrow><mrow><mn>12</mn><mo>*</mo><mi>b_1</mi></mrow></mfrac></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi><mo>=</mo><mfrac><mrow><mn>2</mn><mo>*</mo><mi>a_1</mi></mrow><mrow><mn>3</mn><mo>*</mo><mi>b_1</mi></mrow></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mi>numerador</mi><mo>(</mo><mi>f1</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>denominador</mi><mo>(</mo><mi>f1</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>88</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>156</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>22</mn><mn>39</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>,</mo><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>22</mn><mo>,</mo><mn>39</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"><mfrac><msqrt><mn>858</mn></msqrt><mn>39</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="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> Cal dividir els radicands entre ells i simplificar i/o racionalitzar si s'escau.

]]> 1.1.3.44Q QuocientArrelsCúbiques Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

Format de la resposta: enter o «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>14</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>17</mn><mo>,</mo><mn>18</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>10</mn><mo>,</mo><mn>11</mn><mo>,</mo><mn>13</mn><mo>,</mo><mn>14</mn><mo>,</mo><mn>15</mn><mo>,</mo><mn>17</mn><mo>,</mo><mn>18</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a</mi><mo>=</mo><mroot><mrow><mn>2</mn><mo>·</mo><mi>a_1</mi></mrow><mn>3</mn></mroot></mtd></mtr><mtr><mtd><mi>b</mi><mo>=</mo><mroot><mrow><mn>2</mn><mo>·</mo><mi>b_1</mi></mrow><mn>3</mn></mroot></mtd></mtr><mtr><mtd><mi>sol</mi><mo>=</mo><mroot><mfrac><mi>a_1</mi><mi>b_1</mi></mfrac><mn>3</mn></mroot></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mfenced><mrow><mi>a_1</mi><mo>></mo><mi>b_1</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>b_1</mi><mo>)</mo><mo>≠</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>b</mi><mo>∉</mo><naturalnumbers/></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>a_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mn>2</mn><mo>*</mo><mi>b_1</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>36</mn><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>20</mn><mn>3</mn></mroot></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><mroot><mn>225</mn><mn>3</mn></mroot><mn>5</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#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">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> És el mateix que: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#0000FF¨»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mstyle»«/math»

Cal simplificar si s'escau.

]]> 1.1.3.45 Arrel d'una arrel Calcula i simplifica «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mroot»«/mstyle»«/math»

Format de la resposta: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«/math»

]]> 1.0000000 0.5000000 0 0 #r_22]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>a</mi><mo>=</mo><msup><mfenced><mrow><mi>aleatori</mi><mfenced><mrow><mn>3</mn><mo>,</mo><mn>19</mn></mrow></mfenced></mrow></mfenced><mn>2</mn></msup></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>n</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mo>=</mo><mi>m</mi><mo>*</mo><mi>n</mi></mtd></mtr><mtr><mtd><mi>r_22</mi><mo>=</mo><mroot><mi>a</mi><mi>i</mi></mroot></mtd></mtr><mtr><mtd/></mtr></mtable><mfenced><mrow><mi>m</mi><mo>≠</mo><mi>n</mi></mrow></mfenced></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>256</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>,</mo><mi>n</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_22</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>7</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>22</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal multiplicar els índex entre ells i simplificar si s'escau.

]]> 1.1.3.50DT REDUCCIÓ A ÍNDEX COMÚ Reducció a índex comú

Per reduir a índex comú, es fa com en les fraccions:

es calcula el mcm dels índex
s'escriuen fraccions equivalents amb aquest mcm de denominador. «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»mcm«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»6«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»9«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»18«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8594;«/mo»«mroot mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»6«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mroot mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/msup»«mn mathvariant=¨bold¨»18«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mroot mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»9«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mroot mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»7«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mn mathvariant=¨bold¨»18«/mn»«/mroot»«/math»

]]> 0.0000000 0.0000000 0 1.1.3.51Q CalcularMínimComúÍndex Quin és el mínim comú índex dels radicals següents?

#b_1, #b_2, #b_3

]]> 1.0000000 0.5000000 0 0 #r_13 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><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>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a_1</mi><mo>≠</mo><mi>a_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mroot><mn>2</mn><mi>a_1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mroot><mn>2</mn><mi>a_2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><msqrt><mn>2</mn></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>r_13</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>7</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>15</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>210</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_13 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> És el mínim comú múltiple de 2, #a_1 i #a_2
Cal fer la descomposició en factors i agafar un factor de cada, amb els exponents més grans: #d

]]> 1.1.3.52 Calcular mínim comú índex_2 Quin és el mínim comú índex dels radicals següents?

#b_1, #b_2, #b_3

]]>

]]> 1.0000000 0.5000000 0 0 #r_13 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><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>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>15</mn><mo>)</mo></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>a_1</mi><mo>≠</mo><mi>a_2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi><mo>=</mo><mroot><mn>2</mn><mi>a_1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi><mo>=</mo><mroot><mn>2</mn><mi>a_2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi><mo>=</mo><msqrt><mn>2</mn></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>a_1</mi><mo>,</mo><mi>a_2</mi><mo>,</mo><mn>2</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>factoritza</mi><mo>(</mo><mi>r_13</mi><mo>)</mo></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>7</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>15</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b_3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_13</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>210</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mn>3</mn><mo>*</mo><mn>5</mn><mo>*</mo><mn>7</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_13 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> És el mínim comú múltiple de 2, #a_1 i #a_2
Cal fer la descomposició en factors i agafar un factor de cada, amb els exponents més grans: #d

]]> 1.1.3.53 Calcular radical equivalent Quin és el valor de m que fa certa la igualtat: #a_1 = #a_2?

Format de la resposta: m=4

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>b</mi></msup><mi>i_1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i_2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>i_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>m</mi></msup><mi>i_2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>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>r_11</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>b</mi><mi>i_1</mi></mfrac><mo>=</mo><mfrac><mi>m</mi><mi>i_2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>625</mn><mn>7</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><msup><mn>5</mn><mi>m</mi></msup><mn>35</mn></mroot></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>m</mi><mo>=</mo><mn>20.</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>20.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_11 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Si els dos radicals són equivalents, cal que les fraccions que representen els seus exponents siguin equivalents. S'ha de resoldre l'equació: #t.

]]> 1.1.3.54 Calcular radical equivalent_2 Quin és el valor de m que fa certa la igualtat: #a_1 = #a_2?

Format de la resposta: m=4

]]>

]]> 1.0000000 0.5000000 0 0 #r_11 <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>5</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>11</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>b</mi></msup><mi>i_1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i_2</mi><mo>=</mo><mi>c</mi><mo>*</mo><mi>i_1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>m</mi></msup><mi>i_2</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>R</mi><mo>=</mo><mi>resol</mi><mfenced><mrow><mi>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>r_11</mi><mo>=</mo><msub><mi>R</mi><mrow><mn>1</mn><mo>,</mo><mn>1</mn></mrow></msub></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mfrac><mi>b</mi><mi>i_1</mi></mfrac><mo>=</mo><mfrac><mi>m</mi><mi>i_2</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>625</mn><mn>7</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a_2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><msup><mn>5</mn><mi>m</mi></msup><mn>35</mn></mroot></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>m</mi><mo>=</mo><mn>20.</mn></mtd></mtr></mtable></mfenced></mtd></mtr></mtable></mfenced></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mn>20.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><correctAnswers><correctAnswer type="mathml"> #r_11 </correctAnswer></correctAnswers><localData><data name="cas">false</data><data name="inputField">textField</data></localData></question> Si els dos radicals són equivalents, cal que les fraccions que representen els seus exponents siguin equivalents. S'ha de resoldre l'equació: #t.

]]> 1.1.3.61Q Reduïr Mcíndex Multiplicar Redueix a mínim comú índex i multiplica: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»r«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«/mstyle»«/math»

Format de la resposta: arrel simplificada

Després eleva els radicands #a_1 i #a_2 per tal que els radicals siguin equivalents.

]]> 1.1.3.62Q ReduïrMcíndexMultiplica_2 Redueix a mínim comú índex i multiplica:

Format de la resposta: arrel simplificada

]]> 1.0000000 0.5000000 0 0 #r <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>i</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>5</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>j</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>6</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a_1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>a_2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>b_2</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>5</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mroot><msup><mfenced><mi>a_1</mi></mfenced><mi>b_1</mi></msup><mi>i</mi></mroot></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mroot><msup><mfenced><mi>a_1</mi></mfenced><mi>b_2</mi></msup><mi>j</mi></mroot></mtd></mtr></mtable><mrow><mfenced><mrow><mi>i</mi><mo>≠</mo><mi>j</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>b_1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>j</mi><mo>,</mo><mi>b_2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r</mi><mo>=</mo><mi>r1</mi><mo>*</mo><mi>r2</mi></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><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>3</mn><mo>,</mo><mn>9</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><mroot><mn>4</mn><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>32</mn><mn>9</mn></mroot></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"><mn>4</mn><mo>*</mo><mroot><mn>4</mn><mn>9</mn></mroot></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r</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> Primer calcula el m.c.m de #i i #j.

Després eleva els radicands #a_1 i #a_2 per tal que els radicals amb el mcm com a índex siguin equivalents als de l'enunciat; per exemple cal transformar «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»en«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mroot mathcolor=¨#0000FF¨»«msup»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»5«/mn»«/msup»«mn mathvariant=¨bold¨»15«/mn»«/mroot»«/mstyle»«/math»

]]> 1.1.3.63Q ReduïrMcíndexMultiplicar_3 Redueix a mínim comú índex i multiplica: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»r«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#007F00¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#007F00¨»r«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#007F00¨»2«/mn»«/mstyle»«/math»

Format de la resposta: arrel simplificada

]]> 1.0000000 0.3333333 0 0 #sol <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>j</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>3</mn><mo>,</mo><mn>6</mn></mtd></mtr></mtable></mfenced><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>a2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>9</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd/></mtr><mtr><mtd><mi>r1</mi><mo>=</mo><mroot><mi>a1</mi><mi>i</mi></mroot></mtd></mtr><mtr><mtd><mi>r2</mi><mo>=</mo><mroot><mi>a2</mi><mi>j</mi></mroot></mtd></mtr></mtable><mrow><mfenced><mrow><mi>i</mi><mo>≠</mo><mi>j</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcm</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo><mo>≠</mo><mi>i</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcm</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo><mo>≠</mo><mi>j</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>a1</mi><mo>≠</mo><mi>a2</mi></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>a1</mi><mo>,</mo><mi>a2</mi><mo>)</mo><mo>≠</mo><mn>1</mn></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mi>r1</mi><mo>*</mo><mi>r2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><mi>mcm</mi><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mi>m</mi><mi>i</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m2</mi><mo>=</mo><mfrac><mi>m</mi><mi>j</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msup><mi>a1</mi><mi>m1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msup><mi>a2</mi><mi>m2</mi></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>i</mi><mo>,</mo><mi>j</mi><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>4</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>6</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>2</mn><mn>4</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>6</mn><mn>3</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>,</mo><mi>m1</mi><mo>,</mo><mi>m2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>10368</mn><mn>12</mn></mroot></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">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> Primer calculo el m.c.m dels índex #i i #j que és #m. Aquest és l'índex comú.

A la primera arrel, he multiplicat l´index per #m1. Haig d'elevar el radicand #a1 a #m1

A la segon arrel, he multiplicat l´index per #m2. Haig d'elevar el radicand #a2 a #m2

]]> Les arrels ara són: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mroot mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mroot»«/math»

Només cal multiplicar els radicands

]]> 1.1.3.90DT EXPONENT FRACCIONARI

Arrel i exponent fraccionari

L'arrel n-èsima d'un nombre es defineix així:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#003300¨»«mi mathvariant=¨bold¨»x«/mi»«mi mathvariant=¨bold¨»n«/mi»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8660;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»y«/mi»«mi mathvariant=¨bold¨»n«/mi»«/msup»«/math»

Qualsevol arrel es pot escriure com un exponent fraccionari

i viceversa:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»3«/mn»«mn mathvariant=¨bold¨»5«/mn»«/msup»«mn mathvariant=¨bold¨»7«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»3«/mn»«mfrac bevelled=¨true¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»7«/mn»«/mfrac»«/msup»«/math»

]]> 0.0000000 0.0000000 0 1.1.3.91Q D'arrel a fracció Escriu els exponents que corresponen a les arrels següents:

«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»«mroot mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»x«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mroot mathcolor=¨#003300¨»«msup»«mi mathvariant=¨bold¨»y«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mroot»«/mrow»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 Exponent de x=#sol1Exponent de y=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mfrac><mi>n1</mi><mi>d1</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mfrac><mi>n2</mi><mi>d2</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>,</mo><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>,</mo><mn>7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>8</mn><mn>7</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>,</mo><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>5</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"><mfrac><mn>2</mn><mn>5</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>E</mi><mi>x</mi><mi>p</mi><mi>o</mi><mi>n</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>x</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>E</mi><mi>x</mi><mi>p</mi><mi>o</mi><mi>n</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>y</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_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> L'exponent de x, #n1, és el numerador de la fracció.

L'índex de l'arrel, #d1 és el denominador de la fracció.

L'exponent de y, #n2, és el numerador de la fracció.

L'índex de l'arrel, #d2 és el denominador de la fracció.

]]> 1.1.3.92Q De fracció a arrel Escriu les arrels que corresponen a les potències següents:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»A«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»x«/mi»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»B«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«msup mathcolor=¨#003300¨»«mi mathvariant=¨bold-italic¨ mathcolor=¨#003300¨»y«/mi»«mfrac»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/msup»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 A=#sol1B=#sol2]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n1</mi><mo>,</mo><mi>d1</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n1</mi><mo><</mo><mi>d1</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msup><mi>x</mi><mfrac><mi>n1</mi><mi>d1</mi></mfrac></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>d2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></mtd></mtr></mtable><mrow><mfenced><mrow><mi>mcd</mi><mo>(</mo><mi>n2</mi><mo>,</mo><mi>d2</mi><mo>)</mo><mo>=</mo><mn>1</mn></mrow></mfenced><mo>∧</mo><mfenced><mrow><mi>n2</mi><mo><</mo><mi>d2</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msup><mi>y</mi><mfrac><mi>n2</mi><mi>d2</mi></mfrac></msup></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi><mo>,</mo><mi>d1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn><mo>,</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mroot><mi>x</mi><mn>9</mn></mroot><mn>5</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi><mo>,</mo><mi>d2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>,</mo><mn>7</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"><msup><mroot><mi>y</mi><mn>7</mn></mroot><mn>2</mn></msup></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>A</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>B</mi><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></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 numerador de la fracció, #n1 és la potència de x. El denominador de la fracció, #d1 és l'índex de l'arrel.

El numerador de la fracció, #n2 és la potència de y. El denominador de la fracció, #d2 és l'índex de l'arrel.

]]> 1.1.3.95DT RADICALS EQUIVALENTS Radicals equivalents

Dos radicals són equivalents si els seus exponents fraccionaris són equivalents.

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mroot mathcolor=¨#003300¨»«msup»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mn»6«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mroot mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»5«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»perqu§#232;«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mfrac mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»6«/mn»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»=«/mo»«mfrac mathcolor=¨#003300¨»«mn mathvariant=¨bold¨»1«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mfrac»«/math»

]]> 0.0000000 0.0000000 0 1.1.3.96Q RadicalsEquivalents? Els radicals següents són equivalents?

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

]]> 1.0000000 1.0000000 0 Vertader Fals Els radicands són «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«msup mathcolor=¨#000066¨»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»a«/mi»«msup mathcolor=¨#000066¨»«mn mathvariant=¨bold¨ mathcolor=¨#000066¨»1«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mstyle»«/math»

Cal comparar les fraccions: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»i«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>i1</mi><mo>,</mo><mi>e1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mfenced><mrow><mi>i1</mi><mo>></mo><mi>e1</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mroot><msup><mi>a1</mi><mi>e1</mi></msup><mi>i1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msup><mi>a1</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msup><mi>a1</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>w1</mi><mo>*</mo><mi>i1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfenced><mrow><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w1</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mrow></mfenced><mo>*</mo><mi>e1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mroot><msup><mi>a1</mi><mi>e2</mi></msup><mi>i2</mi></mroot></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><mfrac><mi>e2</mi><mi>e1</mi></mfrac><mo>=</mo><mi>w1</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>cert</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>fals</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>,</mo><mi>e1</mi><mo>,</mo><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>,</mo><mn>5</mn><mo>,</mo><mroot><mn>16807</mn><mn>12</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>,</mo><mi>i2</mi><mo>,</mo><mi>e2</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>72</mn><mo>,</mo><mn>30</mn><mo>,</mo><mroot><mn>16807</mn><mn>12</mn></mroot></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>cert</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 1.1.3.97Q RadicalsEquivalents?_2 Els radicals següents són equivalents?

]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mtable><mtr><mtd><mi>i1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>12</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>e1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>1</mn><mo>,</mo><mn>6</mn><mo>)</mo></mtd></mtr><mtr><mtd><mi>a1</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>,</mo><mn>7</mn></mtd></mtr></mtable></mfenced></mfenced></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>mcd</mi><mo>(</mo><mi>i1</mi><mo>,</mo><mi>e1</mi><mo>)</mo><mo>=</mo><mn>1</mn><mo>∧</mo><mfenced><mrow><mi>i1</mi><mo>></mo><mi>e1</mi></mrow></mfenced></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r1</mi><mo>=</mo><mroot><msup><mi>a1</mi><mi>e1</mi></msup><mi>i1</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><msup><mi>a1</mi><mi>e1</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><msup><mi>a1</mi><mi>e2</mi></msup></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>3</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i2</mi><mo>=</mo><mi>w1</mi><mo>*</mo><mi>i1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>e2</mi><mo>=</mo><mfenced><mrow><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>w1</mi><mo>,</mo><mi>w1</mi><mo>+</mo><mn>1</mn></mtd></mtr></mtable></mfenced></mfenced></mrow></mfenced><mo>*</mo><mi>e1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r2</mi><mo>=</mo><mroot><msup><mi>a1</mi><mi>e2</mi></msup><mi>i2</mi></mroot></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><mfrac><mi>e2</mi><mi>e1</mi></mfrac><mo>=</mo><mi>w1</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>cert</mi></mrow><mrow><mi>sol</mi><mo>=</mo><mi>fals</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>i1</mi><mo>,</mo><mi>e1</mi><mo>,</mo><mi>r1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>12</mn><mo>,</mo><mn>5</mn><mo>,</mo><mroot><mn>16807</mn><mn>12</mn></mroot></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>w1</mi><mo>,</mo><mi>i2</mi><mo>,</mo><mi>e2</mi><mo>,</mo><mi>r2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>72</mn><mo>,</mo><mn>30</mn><mo>,</mo><mroot><mn>16807</mn><mn>12</mn></mroot></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>cert</mi></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><options><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="casSession"/></localData></question> 1rBTX 01. NOMBRES REALS/1.1.4 Racionalització 1.1.4.10DT RACIONALITZAR 1

Racionalitzar 1

Racionalitzar és eliminar les arrels del denominador.

Si hi ha una sola arrel quadrada, es multiplica numerador i denominador per aquesta arrel:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac»«mn»3«/mn»«msqrt»«mn»15«/mn»«/msqrt»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»§#183;«/mo»«msqrt mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»15«/mn»«/msqrt»«/mrow»«mrow»«msqrt»«mn»15«/mn»«/msqrt»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«msqrt mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»15«/mn»«/msqrt»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»3«/mn»«mo»§#183;«/mo»«msqrt»«mn»15«/mn»«/msqrt»«/mrow»«mn»15«/mn»«/mfrac»«mo»=«/mo»«mfrac»«msqrt»«mn»15«/mn»«/msqrt»«mn»5«/mn»«/mfrac»«/mrow»«/mstyle»«/math»

i es SIMPLIFICA

]]> 0.0000000 0.0000000 0 1.1.4.11Q a/√b Racionalitza: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/msqrt»«/mfrac»«/mstyle»«/math»

]]> 1.1.4.12Q a/√b (a múltiple de b) Racionalitza: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/msqrt»«/mfrac»«/mstyle»«/math»

]]> 1.1.4.12Q a/√b (simplificable) Racionalitza: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«msqrt»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/msqrt»«/mfrac»«/mstyle»«/math»

]]> 1.1.4.20DT RACIONALITZAR 2

Racionalitzar 2

Racionalitzar és eliminar les arrels del denominador.

Si hi ha una arrel d'índex i superior a 2, es multiplica el numerador i el denominador per una arrel d'índex i i de radicand tal que permeti simplificar el denominador:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»12«/mn»«mroot»«mn»4«/mn»«mn»3«/mn»«/mroot»«/mfrac»«mo»=«/mo»«mfrac»«mn»12«/mn»«mroot»«msup»«mn»2«/mn»«mn»2«/mn»«/msup»«mn»3«/mn»«/mroot»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»12«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mroot mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mrow»«mrow»«mroot»«msup»«mn»2«/mn»«mn»2«/mn»«/msup»«mn»3«/mn»«/mroot»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mroot mathcolor=¨#0000FF¨»«mn mathvariant=¨bold¨»2«/mn»«mn mathvariant=¨bold¨»3«/mn»«/mroot»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»12«/mn»«mo»§#183;«/mo»«mroot»«mn»2«/mn»«mn»3«/mn»«/mroot»«/mrow»«mroot»«msup»«mn»2«/mn»«mn»3«/mn»«/msup»«mn»3«/mn»«/mroot»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»12«/mn»«mo»§#183;«/mo»«mroot»«mn»2«/mn»«mn»3«/mn»«/mroot»«/mrow»«mn»2«/mn»«/mfrac»«mo»=«/mo»«mn»6«/mn»«mo»§#183;«/mo»«mroot»«mn»2«/mn»«mn»3«/mn»«/mroot»«/math»

i es simplifica

]]> 0.0000000 0.0000000 0 1.1.4.21Q Racionalitza 2 Racionalitza: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

Format: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac»«mrow»«mn»8«/mn»«mroot»«mn»2«/mn»«mn»5«/mn»«/mroot»«/mrow»«mn»2«/mn»«/mfrac»«/mstyle»«/math»

]]> La solució és: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#0000FF¨»m«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#0000FF¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mroot mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mstyle»«/math»

]]> 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>i</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>j</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>i</mi><mo>-</mo><mi>j</mi></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><msup><mi>c</mi><mi>e</mi></msup></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>residu</mi><mfenced><mrow><mi>i</mi><mo>,</mo><mi>e</mi></mrow></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>e</mi></msup><mi>i</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>i</mi><mo>-</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mi>a</mi><mi>c</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>8</mn><mn>5</mn></mroot></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><msup><mroot><mn>8</mn><mn>5</mn></mroot><mn>4</mn></msup><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Factoritzo el radicand del denominador «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«msup mathcolor=¨#000066¨»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math» i la fracció és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«/mstyle»«/math»

Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»e«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»k«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold-italic¨ mathcolor=¨#000066¨»i«/mi»«/mstyle»«/math» cal multiplicar el numerador i el denominador per «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mroot mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mstyle»«/math»:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#FF0000¨»§#160;«/mo»«mroot mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«mo»§#183;«/mo»«mo»§#160;«/mo»«mroot mathcolor=¨#FF0000¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»§#183;«/mo»«mo mathvariant=¨bold¨»§#160;«/mo»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»k«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

Només falta simplifica si s'escau.

]]> 1.1.4.22Q Racionalitza 2_2 Racionalitza: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 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>i</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>j</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>i</mi><mo>-</mo><mi>j</mi></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><msup><mi>c</mi><mi>e</mi></msup></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>residu</mi><mfenced><mrow><mi>i</mi><mo>,</mo><mi>e</mi></mrow></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>e</mi></msup><mi>i</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>i</mi><mo>-</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mi>a</mi><mi>c</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>8</mn><mn>5</mn></mroot></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><msup><mroot><mn>8</mn><mn>5</mn></mroot><mn>4</mn></msup><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Factoritzo el radicand del denominador «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«msup mathcolor=¨#000066¨»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math» i la fracció és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«/mstyle»«/math»

Només falta simplifica si s'escau.

]]> 1.1.4.23Q Racionalitza 2_3 Racionalitza: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 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>i</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>3</mn><mo>,</mo><mn>4</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>j</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>1</mn><mo>,</mo><mn>2</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>e</mi><mo>=</mo><mi>i</mi><mo>-</mo><mi>j</mi></mtd></mtr><mtr><mtd><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></mtd></mtr><mtr><mtd><mi>m</mi><mo>=</mo><msup><mi>c</mi><mi>e</mi></msup></mtd></mtr><mtr><mtd/></mtr></mtable><mrow><mi>residu</mi><mfenced><mrow><mi>i</mi><mo>,</mo><mi>e</mi></mrow></mfenced><mo>≠</mo><mn>0</mn></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>)</mo><mo>*</mo><mi>c</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mroot><msup><mi>c</mi><mi>e</mi></msup><mi>i</mi></mroot></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi><mo>=</mo><mi>i</mi><mo>-</mo><mi>e</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m1</mi><mo>=</mo><mfrac><mi>a</mi><mi>c</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mroot><mn>8</mn><mn>5</mn></mroot></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><msup><mroot><mn>8</mn><mn>5</mn></mroot><mn>4</mn></msup><mn>2</mn></mfrac></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>k</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#sol</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Factoritzo el radicand del denominador «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»m«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«msup mathcolor=¨#000066¨»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mrow»«/mstyle»«/math» i la fracció és «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mroot»«mrow»«mo mathvariant=¨bold¨»#«/mo»«msup»«mi mathvariant=¨bold¨»c«/mi»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»e«/mi»«/mrow»«/msup»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»i«/mi»«/mrow»«/mroot»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«/mstyle»«/math»

Només falta simplifica si s'escau.

]]> 1.1.4.30DT RACIONALITZAR 3

Racionalitzar 3

Racionalitzar és eliminar les arrels del denominador.

Si hi ha una suma o una diferència d'arrels al denominador, es multiplica el numerador i el denominador pel conjugat per aplicar

(a+b)(a-b)=a²-b²

Si no hi ha arrels al numerador:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mn»26«/mn»«mrow»«msqrt»«mn»7«/mn»«/msqrt»«mo»-«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»26«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«msqrt»«mn mathvariant=¨bold¨»7«/mn»«/msqrt»«mo mathvariant=¨bold¨»+«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«msqrt»«mn»7«/mn»«/msqrt»«mo»-«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«msqrt»«mn mathvariant=¨bold¨»7«/mn»«/msqrt»«mo mathvariant=¨bold¨»+«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»26«/mn»«mo»§#183;«/mo»«mfenced»«mrow»«msqrt»«mn»7«/mn»«/msqrt»«mo»+«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«mrow»«mn mathcolor=¨#7F0000¨»7«/mn»«mo mathcolor=¨#7F0000¨»-«/mo»«mn mathcolor=¨#7F0000¨»3«/mn»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mo»=«/mo»«mfrac»«mrow»«mn»26«/mn»«mo»§#183;«/mo»«mfenced»«mrow»«msqrt»«mn»7«/mn»«/msqrt»«mo»+«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«mn»4«/mn»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»13«/mn»«mo»§#183;«/mo»«mfenced»«mrow»«msqrt»«mn»7«/mn»«/msqrt»«mo»+«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«mn»2«/mn»«/mfrac»«/math»

i es simplifica

]]> 0.0000000 0.0000000 0 1.1.4.31Q Racionalitzar3- Racionalitza: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #r_11]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msqrt><mi>c</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msqrt><mi>c</mi></msqrt><mo>-</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>10</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>7</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>5</mn><mo>*</mo><msqrt><mn>3</mn></msqrt></mrow><mn>2</mn></mfrac><mo>+</mo><mfrac><mrow><mn>5</mn><mo>*</mo><msqrt><mn>7</mn></msqrt></mrow><mn>2</mn></mfrac></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mo>#</mo><mi>r</mi><mo>_</mo><mn>11</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="tolerance">10^(-4)</option><option name="relative_tolerance">false</option><option name="precision">4</option><option name="implicit_times_operator">false</option><option name="times_operator">·</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">inlineEditor</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> Cal multiplicar el numerador i el denominador pel conjugat: #m + #n:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math» perquè «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»-«/mo»«msup mathcolor=¨#0000FF¨»«mfenced mathcolor=¨#0000FF¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mn mathvariant=¨bold¨»2«/mn»«/msup»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#160;«/mo»«/mrow»«/mstyle»«/math»

i s'eliminen les arrels.

]]> Tenim «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»d«/mi»«/mrow»«/mstyle»«/math», ens queda

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«/mstyle»«/math» per simplificar, si es pot.

]]> 1.1.4.32Q Racionalitzar3-_2 Racionalitza: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

i s'eliminen les arrels.

]]> 1.1.4.35Q Racionalitzar3+ Racionalitza: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #r_11 <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>15</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msqrt><mi>c</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msqrt><mi>c</mi></msqrt><mo>+</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>a</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>3</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>2</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>6</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mfrac><mrow><mn>3</mn><mo>*</mo><msqrt><mn>2</mn></msqrt></mrow><mn>4</mn></mfrac><mo>+</mo><mfrac><mrow><mn>3</mn><mo>*</mo><msqrt><mn>6</mn></msqrt></mrow><mn>4</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>#r_11</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Multiplica i divideix pel conjugat: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

]]> Tens «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

Com que «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mfenced mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»=«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»-«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#000066¨»d«/mi»«/mstyle»«/math», et queda

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«/mstyle»«/math» per simplificar, si es pot.

]]> 1.1.4.36Q Racionalitzar3+_2 Racionalitza: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«/mstyle»«/math» per simplificar, si es pot.

]]> 1.1.4.40DT RACIONALITZAR 4

Racionalitzar 4

Racionalitzar és eliminar les arrels del denominador.

Si hi ha una suma o una diferència d'arrels al denominador, es multiplica el numerador i el denominador pel conjugat per aplicar

(a+b)(a-b)=a²-b²

Si hi ha arrels al numerador:

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mfrac»«mrow»«mn»2«/mn»«mo»+«/mo»«msqrt»«mn»5«/mn»«/msqrt»«/mrow»«mrow»«msqrt»«mn»5«/mn»«/msqrt»«mo»+«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mfenced mathcolor=¨#191919¨»«mrow»«mn»2«/mn»«mo»+«/mo»«msqrt»«mn»5«/mn»«/msqrt»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«msqrt»«mn mathvariant=¨bold¨»5«/mn»«/msqrt»«mo mathvariant=¨bold¨»-«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«mrow»«mfenced»«mrow»«msqrt»«mn»5«/mn»«/msqrt»«mo»+«/mo»«msqrt»«mn»3«/mn»«/msqrt»«/mrow»«/mfenced»«mo mathvariant=¨bold¨ mathcolor=¨#0000FF¨»§#183;«/mo»«mfenced mathcolor=¨#0000FF¨»«mrow»«msqrt»«mn mathvariant=¨bold¨»5«/mn»«/msqrt»«mo mathvariant=¨bold¨»-«/mo»«msqrt»«mn mathvariant=¨bold¨»3«/mn»«/msqrt»«/mrow»«/mfenced»«/mrow»«/mfrac»«mo»=«/mo»«mfrac»«mrow»«mn»5«/mn»«mo»-«/mo»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«mo»+«/mo»«mn»2«/mn»«msqrt»«mn»5«/mn»«/msqrt»«mo»-«/mo»«msqrt»«mn»15«/mn»«/msqrt»«/mrow»«mrow»«mn mathcolor=¨#7F0000¨»5«/mn»«mo mathcolor=¨#7F0000¨»-«/mo»«mn mathcolor=¨#7F0000¨»3«/mn»«/mrow»«/mfrac»«mspace linebreak=¨newline¨/»«mo»=«/mo»«mfrac»«mrow»«mn»5«/mn»«mo»-«/mo»«mn»2«/mn»«msqrt»«mn»3«/mn»«/msqrt»«mo»+«/mo»«mn»2«/mn»«msqrt»«mn»5«/mn»«/msqrt»«mo»-«/mo»«msqrt»«mn»15«/mn»«/msqrt»«/mrow»«mn»2«/mn»«/mfrac»«/math»

i es simplifica

]]> 0.0000000 0.0000000 0 1.1.4.41 Racionalitzar va+vb/vb-vc Racionalitza: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 1.0000000 0.5000000 0 0 #r_11 <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>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msqrt><mi>c</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msqrt><mi>c</mi></msqrt><mo>-</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msqrt><mi>e</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msqrt><mi>f</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>p</mi><mo>+</mo><mi>q</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>6</mn></msqrt><mo>,</mo><msqrt><mn>5</mn></msqrt><mo>,</mo><msqrt><mn>6</mn></msqrt><mo>,</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><msqrt><mn>6</mn></msqrt></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"><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>6</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>10</mn></msqrt><mo>+</mo><msqrt><mn>30</mn></msqrt><mo>+</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r_11</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Multiplica i divideix pel conjugat «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mrow»«/mstyle»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»)«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«/mstyle»«/math» per simplificar, si es pot.

]]> 1.1.4.45 Racionalitzar va+vb/vb+vc Racionalitza: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#003300¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

]]> 1.0000000 0.3333333 0 0 #r_11 <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>e</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>f</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>6</mn><mo>,</mo><mn>7</mn><mo>,</mo><mn>11</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>{</mo><mn>2</mn><mo>,</mo><mn>3</mn><mo>,</mo><mn>5</mn><mo>}</mo><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>m</mi><mo>=</mo><msqrt><mi>c</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n</mi><mo>=</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><msqrt><mi>c</mi></msqrt><mo>+</mo><msqrt><mi>d</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>p</mi><mo>=</mo><msqrt><mi>e</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>q</mi><mo>=</mo><msqrt><mi>f</mi></msqrt></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>p</mi><mo>+</mo><mi>q</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi><mo>=</mo><mfrac><mi>a</mi><mi>b</mi></mfrac></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>e</mi><mo>,</mo><mi>f</mi><mo>,</mo><mi>c</mi><mo>,</mo><mi>d</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>,</mo><mn>2</mn><mo>,</mo><mn>6</mn><mo>,</mo><mn>5</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mi>m</mi><mo>,</mo><mi>n</mi><mo>,</mo><mi>p</mi><mo>,</mo><mi>q</mi><mo>)</mo></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><msqrt><mn>6</mn></msqrt><mo>,</mo><msqrt><mn>5</mn></msqrt><mo>,</mo><msqrt><mn>6</mn></msqrt><mo>,</mo><msqrt><mn>2</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><msqrt><mn>5</mn></msqrt><mo>+</mo><msqrt><mn>6</mn></msqrt></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"><msqrt><mn>2</mn></msqrt><mo>+</mo><msqrt><mn>6</mn></msqrt></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>r_11</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>2</mn><mo>*</mo><msqrt><mn>3</mn></msqrt><mo>+</mo><msqrt><mn>10</mn></msqrt><mo>+</mo><msqrt><mn>30</mn></msqrt><mo>+</mo><mn>6</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer>#r_11</correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><localData><data name="inputField">inlineEditor</data><data name="inputCompound">false</data><data name="cas">false</data></localData></question> Multiplica i divideix pel conjugat «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

]]> Tenim «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«mo mathvariant=¨bold¨ mathcolor=¨#000066¨»§#183;«/mo»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfrac»«/mstyle»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mfrac mathcolor=¨#000066¨»«mrow»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»)«/mo»«mfenced»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»m«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»n«/mi»«/mrow»«/mfenced»«/mrow»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»c«/mi»«mo mathvariant=¨bold¨»§#160;«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»d«/mi»«/mrow»«/mfrac»«/mstyle»«/math» per simplificar, si es pot.

]]> 1rBTX 01. NOMBRES REALS/1.1.5 Intervals i not. científica 1.1.5.10DT INTERVALS Definició d'interval Un interval és un conjunt de nombres reals que correspon un segment sobre la recta real. Vores

Hi ha dos tipus de vora:

tancada: indica que el nombre que hi figura està inclòs: s'escriu "[a" o "a]"
oberta: indica que el nombre que hi figura no està inclòs. S'escriu "(a" o "a)"

Exemples:

[2, 7) són tots els nombres més grans o iguals que 2 i més petits que 7: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mn»2«/mn»«mo»§#160;«/mo»«mo»§#10877;«/mo»«mo»§#160;«/mo»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#60;«/mo»«mo»§#160;«/mo»«mn»7«/mn»«/mrow»«/mstyle»«/math»

«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo»(«/mo»«mo»-«/mo»«mo»§#8734;«/mo»«mo»,«/mo»«mo»-«/mo»«mn»3«/mn»«mo»]«/mo»«/mrow»«/mstyle»«/math» són tots els nombres més petits o iguals que -3: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mi»x«/mi»«mo»§#160;«/mo»«mo»§#10877;«/mo»«mo»§#160;«/mo»«mo»-«/mo»«mn»3«/mn»«/mrow»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1.1.5.10DT2 TEORIA: INEQUACIO INTERVAL

Interval → Inequació
Expressió	interval	inequació
Nombres més petits o iguals que 4	(-∞,4]	x≤4
Nombres més grans que -2	(-2,+∞)	x>-2
Nombres entre -2 (inclòs) i 4	[-2,4)	«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8805;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8743;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#60;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«/mstyle»«/math»
Nombres més petits que -2 i més grans que 4	(-∞,-2)U(4,+∞)	«math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#60;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»-«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8744;«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»x«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#62;«/mo»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»4«/mn»«/mstyle»«/math»

]]> 0.0000000 0.0000000 0 1.1.5.11 Pertinença a un interval Dels nombres següents, quins pertanyen a la intersecció dels intervals: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mrow»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»[«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8745;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»[«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»c«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»d«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mrow»«/mstyle»«/math»?

]]> 1.0000000 0.5000000 0 false true none #s1

]]> #s2

]]> #s3

]]> #n1

]]> #n2

]]> <question><wirisCasSession><session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="es">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>10</mn><mo>)</mo><mo>*</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mi>a</mi><mo>+</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>5</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mi>a</mi><mo>.</mo><mo>.</mo><mi>b</mi><mo>-</mo><mn>1</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mi>c</mi><mo>+</mo><mn>2</mn><mo>.</mo><mo>.</mo><mn>12</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>s1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>200</mn><mo>.</mo><mo>.</mo><mn>200</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo></mrow><mrow><mi>c</mi><mo>&les;</mo><mi>s1</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>s1</mi><mo>&lt;</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>s2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>200</mn><mo>.</mo><mo>.</mo><mn>200</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo></mrow><mrow><mi>c</mi><mo>&les;</mo><mi>s2</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>s2</mi><mo>&lt;</mo><mi>b</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>s2</mi><mo>≠</mo><mi>s1</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>s3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>200</mn><mo>.</mo><mo>.</mo><mn>200</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo></mrow><mrow><mi>c</mi><mo>&les;</mo><mi>s3</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>s3</mi><mo>&lt;</mo><mi>b</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>s3</mi><mo>≠</mo><mi>s1</mi><mo> </mo><mo>∧</mo><mo> </mo><mi>s3</mi><mo>≠</mo><mi>s2</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>n1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>200</mn><mo>.</mo><mo>.</mo><mn>200</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo></mrow><mrow><mi>c</mi><mo>&gt;</mo><mi>n1</mi><mo> </mo><mo>∨</mo><mo> </mo><mi>n1</mi><mo>&ges;</mo><mi>b</mi></mrow></apply></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><apply><csymbol definitionURL="http://www.wiris.com/XML/csymbol">repeat</csymbol><mrow><mi>n2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mo>-</mo><mn>200</mn><mo>.</mo><mo>.</mo><mn>200</mn><mo>)</mo><mo>/</mo><mn>10</mn><mo>.</mo></mrow><mrow><mo>(</mo><mi>c</mi><mo>&gt;</mo><mi>n2</mi><mo> </mo><mo>∨</mo><mo> </mo><mi>n2</mi><mo>&ges;</mo><mi>b</mi><mo>)</mo><mo> </mo><mo>∧</mo><mo> </mo><mi>n2</mi><mo>≠</mo><mi>n1</mi></mrow></apply></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn></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>8</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d</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>s1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>7.7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>4.7</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>s3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>6.9</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9.3</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>n2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>1.</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session></wirisCasSession><localData><data name="cas">false</data></localData></question> 1.1.5.21Q [ ] → inequació Escriu en forma d'inequació l'interval: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»[«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mstyle»«/math»

]]> 1.1.5.22Q [ ) → inequació Escriu en forma d'inequació l'interval: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»[«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math»

Com que la vora de #b és oberta, s'escriu <#b

]]> 1.1.5.23Q ( ] → inequació Escriu en forma d'inequació l'interval: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mstyle»«/math»

Com que la vora de #b és tancada, s'escriu ≤ #b

]]> 1.1.5.24Q ( ) → inequació Escriu en forma d'inequació l'interval: «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»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»b«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»]«/mo»«/mstyle»«/math»

Com que la vora de #b és oberta, s'escriu <#b

]]> 1.1.5.31Q (-∞,b] → inequació Escriu en forma d'inequació l'interval: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»]«/mo»«/mrow»«/mstyle»«/math»

]]> 1.1.5.32Q (-∞,b) → inequació Escriu en forma d'inequació l'interval: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»(«/mo»«mo mathvariant=¨bold¨»-«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math»

]]> 1.1.5.35Q (a,+∞] → inequació Escriu en forma d'inequació l'interval: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»(«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»,«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»+«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#8734;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»)«/mo»«/mstyle»«/math»

]]> 1.1.5.36Q [a,+∞] → inequació Escriu en forma d'inequació l'interval: «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨14px¨»«mrow mathcolor=¨#003300¨»«mo mathvariant=¨bold¨»[«/mo»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»a«/mi»«mo mathvariant=¨bold¨»,«/mo»«mo mathvariant=¨bold¨»+«/mo»«mo mathvariant=¨bold¨»§#8734;«/mo»«mo mathvariant=¨bold¨»)«/mo»«/mrow»«/mstyle»«/math»

]]> 1.1.5.50DT NOTACIÓ CIENTÍFICA

Notació científica

^{Un nombre en notació científica s'escriu}

351 000 = 3,51·10⁵si és més gran que 1

i 0,0426 = 4,26 · 10^-2 si és més petit que 1.

La part entera és la primera xifra diferent de zero del nombre. L'exponent indica el nombre de POSICIONS que s'ha mogut la coma; positiu si es mou cap a la dreta, negatiu si es mou cap a l'esquerra

]]> 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 0.0000000 0.0000000 0 1.1.5.51Q NotCientífica→Decimal(±) Escriu els nombres decimals que corresponen a:

a) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»1«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»10«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»1«/mn»«/mrow»«/msup»«/mstyle»«/math»

b) «math xmlns=¨http://www.w3.org/1998/Math/MathML¨»«mstyle mathsize=¨12px¨»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»#«/mo»«mi mathvariant=¨bold¨ mathcolor=¨#003300¨»a«/mi»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»2«/mn»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#183;«/mo»«mo mathvariant=¨bold¨ mathcolor=¨#003300¨»§#160;«/mo»«msup mathcolor=¨#003300¨»«mn mathvariant=¨bold¨ mathcolor=¨#003300¨»10«/mn»«mrow»«mo mathvariant=¨bold¨»#«/mo»«mi mathvariant=¨bold¨»b«/mi»«mn mathvariant=¨bold¨»2«/mn»«/mrow»«/msup»«/mstyle»«/math»

Atenció: es fan servir punts i no comes!

]]> 1.0000000 0.5000000 0 0 a) =#sol1b) =#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>c1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>c1</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>c2</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>*</mo><mi>c3</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>001</mn><mo>*</mo><mi>c4</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>0001</mn><mo>*</mo><mi>c5</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><msup><mn>10</mn><mi>b1</mi></msup><mo>*</mo><mi>a1</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d1</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d2</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d3</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d4</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d5</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5</mn><mo>,</mo><mn>9</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>=</mo><mo>(</mo><mo>-</mo><mn>1</mn><mo>)</mo><mo>*</mo><mi>aleatori</mi><mo>(</mo><mn>2</mn><mo>,</mo><mn>4</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>d1</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>1</mn><mo>*</mo><mi>d2</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>01</mn><mo>*</mo><mi>d3</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><msup><mn>10</mn><mi>b2</mi></msup><mo>*</mo><mi>a2</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b3</mi><mo>=</mo><mfenced close="|" open="|"><mi>b2</mi></mfenced></math></input></command></group></library><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b1</mi><mo>,</mo><mi>a1</mi><mo>,</mo><mi>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo>,</mo><mn>4.8867</mn><mo>,</mo><mn>48867.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>b2</mi><mo>,</mo><mi>a2</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>-</mo><mn>3</mn><mo>,</mo><mn>3.89</mn><mo>,</mo><mn>0.00389</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/></assertions><options><option name="precision">8</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="times_operator">·</option><option name="implicit_times_operator">false</option><option name="imaginary_unit">i</option></options><localData><data name="inputField">popupEditor</data><data name="inputCompound">true</data><data name="gradeCompound">and</data><data name="gradeCompoundDistribution"></data><data name="casSession"/></localData></question> a) Cal moure la coma #b1 posicions cap a la dreta, perquè l'exponent és positiu

a) Cal moure la coma #b3 posicions cap a l'esquerra, perquè l'exponent és negatiu

]]> 1.1.5.51Q NotCientífica→Decimal(±)_2 Escriu els nombres decimals que corresponen a:

Atenció: es fan servir punts i no comes!

a) Cal moure la coma #b3 posicions cap a l'esquerra, perquè l'exponent és negatiu

]]> )]]> Escriu els nombres en notació científica:

a) #a1

b) #a2

c) #a3

d) #a4

Atenció: es fan servir punts i no comes!

]]> 1.0000000 0.5000000 0 0 a) =#sol1b) =#sol2c) =#sol3d) =#sol4]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5001</mn><mo>.</mo><mo>.</mo><mn>9999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>10000</mn><mo>,</mo><mn>100000</mn><mo>,</mo><mn>1000000</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mfrac><mi>a11</mi><mi>d11</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>cadena</mi><mfenced><mrow><mi>sol1</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>float_format</mi><mo>=</mo><mo>"</mo><mo>.</mo><mn>10</mn><mi>mr</mi><mo>"</mo></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5001</mn><mo>.</mo><mo>.</mo><mn>9999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d21</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>10000</mn><mo>,</mo><mn>100000</mn><mo>,</mo><mn>1000000</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><mfrac><mi>a21</mi><mi>d21</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>cadena</mi><mfenced><mrow><mi>sol2</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>float_format</mi><mo>=</mo><mo>"</mo><mo>.</mo><mn>10</mn><mi>mr</mi><mo>"</mo></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a31</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5001</mn><mo>.</mo><mo>.</mo><mn>9999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d31</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>10000</mn><mo>,</mo><mn>100000</mn><mo>,</mo><mn>1000000</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mfrac><mi>a31</mi><mi>d31</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>a3</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>cadena</mi><mfenced><mrow><mi>sol3</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>float_format</mi><mo>=</mo><mo>"</mo><mo>.</mo><mn>10</mn><mi>mr</mi><mo>"</mo></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a41</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5001</mn><mo>.</mo><mo>.</mo><mn>9999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d41</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>10000</mn><mo>,</mo><mn>100000</mn><mo>,</mo><mn>1000000</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mfrac><mi>a41</mi><mi>d41</mi></mfrac></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>a4</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>cadena</mi><mfenced><mrow><mi>sol4</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>float_format</mi><mo>=</mo><mo>"</mo><mo>.</mo><mn>10</mn><mi>mr</mi><mo>"</mo></mtd></mtr></mtable></mfenced></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>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0.008858</ms><mo>,</mo><mn>0.008858</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0.062</ms><mo>,</mo><mn>0.062</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>,</mo><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0.009163</ms><mo>,</mo><mn>0.009163</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>,</mo><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>0.05576</ms><mo>,</mo><mn>0.05576</mn></math></output></command></group><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command></group></session>]]></wirisCasSession><correctAnswers><correctAnswer type="mathml"><![CDATA[<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>3</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>4</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_scientific_notation"/></assertions><options><option name="float_format">me</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</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> Mou la coma fins després de la primera xifra no nul·la.

Per l'exponent negatiu, compta quantes posicions has mogut la coma cap a la dreta.

]]> 1)]]> Escriu els nombres en notació científica:

a) #a1

b) #a2

c) #a3

d) #a4

Atenció: es fan servir punts i no comes!

]]> 1.0000000 0.5000000 0 0 a) =#sol1b) =#sol2c) =#sol3d) =#sol4]]> <question><wirisCasSession><![CDATA[<session lang="ca" version="2.0"><library closed="false"><mtext style="color:#ffc800" xml:lang="ca">variables</mtext><group><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a11</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5001</mn><mo>.</mo><mo>.</mo><mn>9999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d11</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>10</mn><mo>,</mo><mn>100</mn><mo>,</mo><mn>1000</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>a11</mi><mo>*</mo><mi>d11</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol1</mi><mo>=</mo><mi>a1</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a1</mi><mo>=</mo><mi>cadena</mi><mfenced><mrow><mi>sol1</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>float_format</mi><mo>=</mo><mo>"</mo><mo>.</mo><mn>10</mn><mi>mr</mi><mo>"</mo></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a21</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5001</mn><mo>.</mo><mo>.</mo><mn>9999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d21</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>1000</mn><mo>,</mo><mn>10000</mn><mo>,</mo><mn>100000</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>a21</mi><mo>*</mo><mi>d21</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol2</mi><mo>=</mo><mi>a2</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>=</mo><mi>cadena</mi><mfenced><mrow><mi>sol2</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>float_format</mi><mo>=</mo><mo>"</mo><mo>.</mo><mn>10</mn><mi>mr</mi><mo>"</mo></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a31</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5001</mn><mo>.</mo><mo>.</mo><mn>9999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d31</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>10</mn><mo>,</mo><mn>100</mn><mo>,</mo><mn>1000</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>a31</mi><mo>*</mo><mi>d31</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol3</mi><mo>=</mo><mi>a3</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>=</mo><mi>cadena</mi><mfenced><mrow><mi>sol3</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>float_format</mi><mo>=</mo><mo>"</mo><mo>.</mo><mn>10</mn><mi>mr</mi><mo>"</mo></mtd></mtr></mtable></mfenced></mrow></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"/></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a41</mi><mo>=</mo><mi>aleatori</mi><mo>(</mo><mn>5001</mn><mo>.</mo><mo>.</mo><mn>9999</mn><mo>)</mo></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>d41</mi><mo>=</mo><mi>aleatori</mi><mfenced><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mn>100</mn><mo>,</mo><mn>1000</mn><mo>,</mo><mn>10000</mn></mtd></mtr></mtable></mfenced></mfenced></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>a41</mi><mo>*</mo><mi>d41</mi></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>sol4</mi><mo>=</mo><mi>a4</mi><mo>*</mo><mn>1</mn><mo>.</mo><mn>0</mn></math></input></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>=</mo><mi>cadena</mi><mfenced><mrow><mi>sol4</mi><mo>,</mo><mfenced close="}" open="{"><mtable align="center"><mtr><mtd><mi>float_format</mi><mo>=</mo><mo>"</mo><mo>.</mo><mn>10</mn><mi>mr</mi><mo>"</mo></mtd></mtr></mtable></mfenced></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>sol1</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>75340.</ms><mo>,</mo><mn>75340.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a2</mi><mo>,</mo><mi>sol2</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>9268000.</ms><mo>,</mo><mn>9.268</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a3</mi><mo>,</mo><mi>sol3</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>80790.</ms><mo>,</mo><mn>80790.</mn></math></output></command><command><input><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>a4</mi><mo>,</mo><mi>sol4</mi></math></input><output><math xmlns="http://www.w3.org/1998/Math/MathML"><ms>9557000.</ms><mo>,</mo><mn>9.557</mn><mo>*</mo><msup><mn>10</mn><mn>6</mn></msup></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><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>1</mn><mspace linebreak="newline"/><mi>b</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>2</mn><mspace linebreak="newline"/><mi>c</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>3</mn><mspace linebreak="newline"/><mi mathvariant="normal">d</mi><mo>)</mo><mo> </mo><mo>=</mo><mo>#</mo><mi>s</mi><mi>o</mi><mi>l</mi><mn>4</mn></math>]]></correctAnswer></correctAnswers><assertions><assertion name="syntax_expression"/><assertion name="equivalent_symbolic"/><assertion name="check_scientific_notation"/></assertions><options><option name="float_format">me</option><option name="tolerance">10^(-3)</option><option name="relative_tolerance">true</option><option name="precision">8</option><option name="times_operator">·</option><option name="implicit_times_operator">false</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> Mou la coma fins després de la primera xifra no nul·la.

Per l'exponent positiu, compta quantes posicions has mogut la coma cap a l'esquerra.

]]>