Mathematics Questions & Answers

\( \int_{0}^{\pi / 6} 9 \sec ^{2} x d x=\square \) (Type an exact answer.)

The roots of the equation \( 2 x^{2}+(p+1) x+q=0 \) are 1 and 3 , where \( p \) and \( q \) are constants. Find the values of \( p \) and \( q . \quad \) [WAEC]

e. \( 0.5 x+1=\frac{4}{3}-\left(x-\frac{7}{3}\right) \)

Problema 2: Ana es 23 ahlos mayor que su hija Vicioria. Hace 10 antos, el cuadrado ee la edad de Victoria aum antos era igual a la edad de Ans. ¿Cual es la edad de Ana y la de su hija actualmente?

Use the price-demand equation to find the values of \( p \) for which demand is elastic and the values for which demand is inelastic. Assume that price and demand are both positive. \[ x=f(p)=2704-4 p^{2} \] The values of \( p \) for which demand is elastic are \( \square \) . (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.) The values of \( p \) for which demand is inelastic are \( \square \) \( \square \). (Simplify your answer. Type your answer in interval notation. Type an exact answer, using radicals as needed. Use integers or fractions for any numbers in the expression.)

\( \frac{\sqrt{3}}{2} \) \( \int_{0}^{2} \frac{7 d x}{\sqrt{1-x^{2}}}=\square \) (Type an exact answer)

\( \left.\begin{array}{l}\frac{10}{y}=x \\ \text { Direct variation } \\ \text { Constant of variation: } k=\square \\ \text { Inverse vartation } \\ \text { Constant of variation: } k=\square\end{array}\right] \)

(8) \( \frac{16^{-a}}{16^{3 a+2}}=\frac{1}{64} \)

L (Valor \( 40 \% \) ) Si se sabe que la dureza Rockwell de pernos de cierto tipo tiene un valor medio de 50 y varianza de 16.44 . 1. Si la distribución es normal, écuál es la probabilidad de que la dureza muestral media para una muestra aleatoria de 9 pernos sea por lo menos 51 ? 2. ¿Cuál es la probabilidad de que la dureza muestral media para una muestra aleatoria de 40 pernos sea no mayor a 52 ?

\( \int _ { 1 / 2 } ^ { 2 } ( 1 - \frac { 1 } { x ^ { 2 } } ) d x = \square \)