Write an equation that expresses the following relationship: \( x \) varies jointly as \( y \) and \( p \) and inversely as the square root of \( z \). Then solve the equation for \( y \). Write an equation that expresses the given relationship. Use k as the constant of variation. \( x=\square \)

ANIMATION A computer graphics animator would like to make a realistic simulation of a tossed ball. The animator wants the ball to follow the parabolic trajectory represented by \( f(x)=-0.2(x+5)(x-5) \). a. What are the solutions of \( f(x)=0 \) ? List the solutions from least to greatest.

h) \( \left[(1,2)^{4}:(1,2)^{-3}\right] \cdot(1,2)^{-5}= \)

Simplify the expression. Write the answer without using negative exponents. All variables represent positive real numbers. \[ \left(\mathrm{mn}^{-2 / 3}\right)^{-3 / 5} \]

The volume \( V \) of a rectangular solid is equal to the product of its length \( l \), width \( w \), and height \( h \). Solve for \( l \); for \( w \); for \( h \).

Use synthetic division to find the result when \( x^{3}+x^{2}+2 x+9 \) is divided by \( x+2 \). If there is a remainder, express the result in the form \( q(x)+\frac{r(x)}{b(x)} \).