91Ó°ÊÓ

If \(A\) is inversely proportional to the cube of \(B,\) and \(A=20.5\) when \(B=-4,\) write \(A\) as a power function of \(B\)

In Exercises \(1-21,\) solve the equation for the variable. $$ 2 b^{4}-11=81 $$

Suppose \(c\) is directly proportional to the square of \(d\). If \(c=50\) when \(d=5,\) find the constant of proportionality and write the formula for \(c\) in terms of \(d\). Use your formula to find \(c\) when \(d=7\).

In Exercises \(1-21,\) solve the equation for the variable. $$ \sqrt{a}-2=7 $$

In Exercises \(7-16\), write the expression as a constant times a power of a variable. Identify the coefficient and the exponent. $$ 3 \sqrt{p} $$

The volume, \(V\), of a cylinder whose radius is 5 times its height is given by \(V=\frac{1}{5} \pi r^{3}\), where \(r\) is the radius. (a) Identify the coefficient and exponent of this power function. (b) If the radius is \(2 \mathrm{~cm},\) what is the volume? (c) If the height is \(0.8 \mathrm{~cm}\), what is the volume?

Write the expression as a constant times a power of a variable. Identify the coefficient and the exponent. $$ \sqrt{2 b} $$

In Exercises \(1-21,\) solve the equation for the variable. $$ 3 \sqrt[3]{x}+1=16 $$

Suppose \(c\) is inversely proportional to the square of \(d\). If \(c=50\) when \(d=5\), find the constant of proportion-ality and write the formula for \(c\) in terms of \(d\). Use your formula to find \(c\) when \(d=7\).

Write the expression as a constant times a power of a variable. Identify the coefficient and the exponent. $$ \frac{4}{\sqrt[4]{z}} $$