91Ó°ÊÓ

Two airplanes leave an airport at the same time and at a \(90^{\circ}\) angle from each other. After an hour of flying at the same altitude, one plane is 160 miles from the airport, and the other is 180 miles from the airport. To the nearest tenth of a mile, how far are the planes from each other?

Two boats leave a dock at the same time and at a \(90^{\circ}\) angle from each other. After 3 hours one boat is 30 miles from the dock, while the other is 50 miles from the dock. To the nearest tenth of a mile, how far are the boats from each other?

Answers should be rounded to the nearest tenth unless otherwise indicated. How much water is needed to fill a cylindrical swimming pool of diameter \(4 \mathrm{m}\) to a height of \(1.4 \mathrm{m} ?\)

Consider a cube of side \(x\) (a) Show that the surface area of a cube of side \(x\) is \(S=6 x^{2}\) (b) If the edge of a cube is doubled in length, what happens to the surface area? To the volume? [Hint: Consider the ratio of the original surface area to the new surface area, and similarly for the volumes.] (c) If the edge of a cube is tripled in length, what happens to the surface area? To the volume? [Hint: Consider the ratio of the original surface area to the new surface area, and similarly for the volumes.] (d) Can you generalize the results of parts (b) and (c) to describe what happens to the surface area and volume of a cube if the length of its edge is multiplied by \(k ?\)

A side of one rectangle is \(25 \mathrm{ft}\) and the corresponding side of a second similar rectangle is \(10 \mathrm{ft}\). If the perimeter of the first rectangle is \(150 \mathrm{ft}\) and its area is 1250 sq ft, find the perimeter and area of the similar rectangle.

A scale drawing uses a scale of \(\frac{1}{30}\) for the floor plan of a house. If the perimeter of the house on the scale drawing is 62 in., what is the actual perimeter of the house in ft?