91Ó°ÊÓ

Solve each equation involving "nested" radicals for all real solutions analytically. Support your solutions with a graph. $$\sqrt[3]{\sqrt{x+63}}=\sqrt[3]{2 x+6}$$

Sketch a graph of rational function. Your graph should include all asymptotes. Do not use a calculator. $$f(x)=\frac{x^{2}-x}{x+2}$$

Determine the domain of each function. $$f(x)=\sqrt[3]{8 x-24}$$

Sketch a graph of rational function. Your graph should include all asymptotes. Do not use a calculator. $$f(x)=\frac{x^{2}-9}{x+3}$$

Construction Find possible dimensions for a closed box with volume 196 cubic inches, surface area 280 square inches, and length that is twice the width.

The velocity \(v\) of a meteorite approaching Earth is given by $$v=\frac{k}{\sqrt{d}}$$ measured in kilometers per second, where \(d\) is its distance from the center of Earth and \(k\) is a constant. If \(k=350\) what is the velocity of a meteorite that is 6000 kilometers away from the center of Earth? Round to the nearest tenth.

Determine the domain of each function. $$f(x)=\sqrt[5]{x+32}$$

Sketch a graph of rational function. Your graph should include all asymptotes. Do not use a calculator. $$f(x)=\frac{x^{2}-16}{x+4}$$

The illumination \(I\) in foot-candles produced by a light source is related to the distance \(d\) in feet from the light source by the equation $$d=\sqrt{\frac{k}{I}},$$ where \(k\) is a constant. If \(k=400,\) how far from the source will the illumination be 14 foot-candles? Round to the nearest hundredth of a foot.

Period of a Pendulum The period \(P\) of a pendulum in seconds depends on its length \(L\) in feet and is given by $$P=2 \pi \sqrt{\frac{L}{32}}$$ If the length of a pendulum is 5 feet, what is its period? Round to the nearest tenth.