Mathematics Questions & Answers

Simplify: \( \sqrt[3]{135 a^{13}} \) \( 3 \sqrt[3]{5 a^{13}} \) \( 3 a^{6} \sqrt{15 a} \) \( 3 a^{4} \sqrt[3]{5 a} \) \( 9 a^{6} \sqrt{15 a} \)

Which is the rationalized form of the expression \( \frac{\sqrt{x}}{\sqrt{x}+\sqrt{7}} \) ? \( \begin{array}{ll}\frac{x-\sqrt{7 x}}{x-7} & \text { c. } \frac{x+\sqrt{7 x}}{x-7} \\ \text { b. } \frac{\sqrt{7 x}}{7} & \text { d. } \frac{x}{x+7}\end{array} \)

How many cups of milk can be served from a storage of 200 L ? (round your answer to two decimal places) cups of milk can be served from a storage of 200 L .

0) \( 65^{\circ} 53^{\prime} 19^{\prime \prime}+39^{\circ} 24^{\prime} 17^{\prime \prime} \)

Al redefinir la función \( f(x)=\frac{\text { sin } x}{3 x^{2}+2 x} \) para que sea continua en \( x=0 \), se obtiene a. \( f(x)=\left\{\begin{array}{ll}\frac{\sin x}{3 x^{2}+2 x} & \text { si } x \neq 0 \\ 1 & \text { si } x=0\end{array}\right. \) b. \( f(x)=\left\{\begin{array}{ll}\frac{\min x}{3 x^{2}+2 x} & \text { si } x \neq 0 \\ 0 & \text { si } x=0\end{array}\right. \) o. c. \( f(x)=\left\{\begin{array}{ll}\frac{\sin x}{3 x^{2}+2 x} & \text { si } x \neq 0 \\ \frac{1}{2} & \text { si } x=0\end{array}\right. \) d. \( f(x)=\left\{\begin{array}{ll}\frac{\sin x}{3 x^{2}+2 x} & \text { si } x \neq 0 \\ \frac{1}{3} & \text { si } x=0\end{array}\right. \)

69 Résoudre dans \( \mathbb{R} \) les inéquations suivantes. a. \( x^{2}+1>(x+1)^{2} \) b. \( 3-4 x \leqslant 6(x-2)-10 x \) c. \( 3(1-2 x) \geqslant-6 x+2 \)

The square of a whole number is between 1,500 and 1,600 . The number must be between 30 and 35 35 and 40 40 and 45 45 and 50

\( 16 \begin{array}{l}\text { Solve the inequality and express the solution set in set-builder notation and interval notation, if possible. Graph the solution set on a real number line. } \\ -3 z-(2+4 z)>3-7 z\end{array} \)

Simplify \( \sqrt{3^{15}} \). \( \begin{array}{ll}\text { a. } 3^{5} \sqrt{3} & \text { c. } 3^{3} \sqrt{5} \\ \text { b. } 3^{3} \sqrt{3} & \text { d. } 3^{7} \sqrt{3}\end{array} \)

(3) \( \int_{-3}^{2}\left(2 x^{2}+1\right)^{3 / 2}|4 x| d x \)