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Mathematics Questions & Answers

Q:
La enésima suma parcial de la serie \( \sum_{n=1}^{\infty} a_{n} \) está dada por \( S_{n}=\frac{n+1}{n^{2}+1} \) \( \sum_{n}^{5} a_{n}= \)
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Question Use Newton's method to approximate the solution to the equation \( \frac{4}{x-8}=x+3 \). Use \( x_{0}=-2 \) as your starting value to find the approximation \( x_{2} \) rounded to the nearest thousandth. Sorry, that's incorrect. Try again? \( x_{2} \approx \square \)
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\( 2.1 \quad \) Solve for \( p \) and \( q \) simultaneously. \[ q+2 p=2 \text { and } q^{2}+2 p^{2}=3 q p \]
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10. Use any method to solve the system: \( \left\{\begin{array}{l}x^{2}+y^{2}=9 \\ y=3-x^{2}\end{array}\right. \)
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EJERCICIO 7 -1 Se muestran las tallas de calzado de los últimos 20 clientes que han entrado a una zapatería \[ \begin{array}{l}25,22.5,26,26.5,27,25,23,24,24,23,24,24.5,24.5,24,23.5,24.5 \\ 23.5,24.5,25,23.5\end{array} \] Ordena las tallas y elabora una gráfica de columnas para representar los datos
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Given: \( \frac{2 m-3}{3}-3 \geq \frac{2 m}{6} \)
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Question Use Newton's method with the specified initial approximation \( x_{0} \) to find \( x_{2} \), the third approximation to the root of the equation given below. Round your answer to the nearest thousandth. \[ f(x)=x^{3}-10 x-2, \quad x_{0}=1 \] Sorry, that's incorrect. Try again? \[ x_{2} \approx \square \]
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QUESTION 4 Given: \( f(x)=2\left(x^{2}-1\right) \) Sketch function \( f \) on the diagram sheet. Clearly show all intercepts with the axes.
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Solve the equation for exact solutions over the interval \( [0,2 \pi) \) \( 2 \tan 3 x=2 \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is \( \left\{\frac{\pi}{12}, \frac{5 \pi}{12}, \frac{3 \pi}{4}, \frac{13 \pi}{12}, \frac{17 \pi}{12}, \frac{7 \pi}{4}\right\} \). (Type an exact answer, using \( \pi \) as needed. Type your answer in radians. Use integers or fractions for any numbers in the expression. Use a com B. The solution is the empty set.
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Simplify the following: \( \begin{array}{ll}\text { 2.1.1 } & \left(-2 x^{3} y^{3}\right)^{4} \\ \text { 2.1.2 } & -2\left(-4 x^{2}\right)^{2}+2\left(3 x^{2}\right)^{2} \\ \text { 2.1.3 } & \sqrt{49 x^{8}}+(2 x)^{4} \\ \text { 2.1.4 } & \frac{\left(3 x^{3}+2 x^{3}\right)^{2}}{5 x^{2} .5 x^{2} x}\end{array} \)
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