91Ó°ÊÓ

In the following exercises, solve. The distance an object falls varies directly to the square of the time it falls. A ball falls 45 feet in 3 seconds. (a) Write the equation that relates the distance to the time. (b) How far will the ball fall in 7 seconds?

In the following exercises, solve. The maximum load a beam will support varies directly with the square of the diagonal of the beam's cross-section. A beam with diagonal 6 inch will support a maximum load of 108 pounds. (a) Write the equation that relates the load to the diagonal of the cross- section. (b) What load will a beam with a 10 inch diagonal support?

In the following exercises, solve. The area of a circle varies directly as the square of the radius. A circular pizza with a radius of 6 inches has an area of 113.04 square inches. (a) Write the equation that relates the area to the radius. (b) What is the area of a personal pizza with a radius 4 inches?

In the following exercises, solve. The distance an object falls varies directly to the square of the time it falls. A ball falls 72 feet in 3 seconds, (a) Write the equation that relates the distance to the time. (b) How far will the ball have fallen in 8 seconds?

In the following exercises, solve. If \(y\) varies inversely with \(x\) and \(y=5\) when \(x=4\) find the equation that relates \(x\) and \(y\).

In the following exercises, solve. If \(p\) varies inversely with \(q\) and \(p=2\) when \(q=1\) find the equation that relates \(p\) and \(q\).

In the following exercises, solve. If \(v\) varies inversely with \(w\) and \(v=6\) when \(w=\frac{1}{2}\) find the equation that relates \(v\) and \(w\).

In the following exercises, solve. If \(a\) varies inversely with \(b\) and \(a=12\) when \(b=\frac{1}{3}\) find the equation that relates \(a\) and \(b\).

The fuel consumption (mpg) of a car varies inversely with its weight. A Toyota Corolla weighs 2800 pounds and gets \(33 \mathrm{mpg}\) on the highway. (a) Write the equation that relates the mpg to the car's weight. (b) What would the fuel consumption be for a Toyota Sequoia that weighs 5500 pounds?

Write an inverse variation equation to solve the following problems. A car's value varies inversely with its age. Jackie bought a 10 year old car for \(\$ 2,400\). (a) Write the equation that relates the car's value to its age. (b) What will be the value of Jackie's car when it is 15 years old ?