91Ó°ÊÓ

Solve each problem. For a constant area, the length of a rectangle varies inversely as the width. The length of a rectangle is \(27 \mathrm{ft}\) when the width is \(10 \mathrm{ft}\). Find the width of a rectangle with the same area if the length is \(18 \mathrm{ft}\).

Solve each problem. The force with which Earth attracts an object above Earth's surface varies inversely as the square of the distance of the object from the center of Earth. If an object 4000 mi from the center of Earth is attracted with a force of \(160 \mathrm{lb},\) find the force of attraction if the object were 6000 mi from the center of Earth.

Add or subtract as indicated. $$\frac{1}{x-1}-\frac{1}{x}$$

Solve each problem. For a given interest rate, simple interest varies jointly as principal and time. If \(\$ 2000\) left in an account for 4 yr earned interest of \(\$ 280,\) how much interest would be earned in 6 yr?

Add or subtract as indicated. $$\frac{11 x-13}{2 x-3}-\frac{3 x-1}{2 x-3}$$

Solve each problem. The force needed to keep a car from skidding on a curve varies inversely as the radius of the curve and jointly as the weight of the car and the square of the speed. If \(242 \mathrm{lb}\) of force keeps a 2000 -lb car from skidding on a curve of radius \(500 \mathrm{ft}\) at \(30 \mathrm{mph}\), what force (to the nearest tenth of a pound) would keep the same car from skidding on a curve of radius \(750 \mathrm{ft}\) at \(50 \mathrm{mph} ?\)

Multiply or divide as indicated. $$ \frac{(x+2)(x+1)}{(x+3)(x-2)} \cdot \frac{(x+3)(x+4)}{(x+2)(x+1)} $$

Add or subtract as indicated. $$\frac{3 x}{x+1}+\frac{4}{x-1}-\frac{6}{x^{2}-1}$$

Multiply or divide as indicated. $$ \frac{x^{2}-25}{x^{2}+x-20} \cdot \frac{x^{2}+7 x+12}{x^{2}-2 x-15} $$

Add or subtract as indicated. $$\frac{6 x+5 y}{6 x^{2}+5 x y-4 y^{2}}-\frac{x+2 y}{9 x^{2}-16 y^{2}}$$