1. Equations & Inequalities

Using k as the constant of variation, write a variation equation for each situation. h varies inversely as t.

Solve each problem. If y varies directly as x, and y=20 when x=4, find y when x = -6.

Solve each problem. If m varies jointly as x and y, and m=10 when x=2 and y=14, find m when x=21 and y=8.

Solve each problem. If y varies inversely as x, and y=10 when x=3, find y when x=20.

Solve each problem. Suppose r varies directly as the square of m, and inversely as s. If r=12 when m=6 and s=4, find r when m=6 and s=20.

Solve each problem. Let a be directly proportional to m and n², and inversely proportional to y³. If a=9when m=4, n=9, and y=3, find a when m=6, n=2, and y=5.

Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as x. (y=kx)

Match each statement with its corresponding graph in choices A–D. In each case, k > 0. y varies directly as the second power of x. (y=kx²)

Hooke's Law for a Spring Hooke's law for an elastic spring states that the distance a spring stretches varies directly as the force applied. If a force of 15 lb stretches a certain spring 8 in., how much will a force of 30 lb stretch the spring?

Solve each problem. The speed of a pulley varies inversely as its diameter. One kind of pulley, with diameter 3 in., turns at 150 revolutions per minute. Find the speed of a similar pulley with diameter 5 in.

Simple Interest Simple interest varies jointly as principal and time. If \$1000 invested for 2 yr earned \$70, find the amount of interest earned by \$5000 invested for 5 yr.

Current Flow In electric current flow, it is found that the resistance offered by a fixed length of wire of a given material varies inversely as the square of the diameter of the wire. If a wire 0.01 in. in diameter has a resistance of 0.4 ohm, what is the resistance of a wire of the same length and material with diameter 0.03 in., to the nearest ten-thousandth of an ohm?

Force of Wind The force of the wind blowing on a vertical surface varies jointly as the area of the surface and the square of the velocity. If a wind of 40 mph exerts a force of 50 lb on a surface of 1/2 ft², how much force will a wind of 80 mph place on a surface of 2 ft²?

Period of a Pendulum The period of a pendulum varies directly as the square root of the length of the pendulum and inversely as the square root of the acceleration due to gravity. Find the period when the length is 121 cm and the acceleration due to gravity is 980 cm per second squared, if the period is 6π seconds when the length is 289 cm and the acceleration due to gravity is 980 cm per second squared.

Nuclear Bomb Detonation Suppose the effects of detonating a nuclear bomb will be felt over a distance from the point of detonation that is directly proportional to the cube root of the yield of the bomb. Suppose a 100-kiloton bomb has certain effects to a radius of 3 km from the point of detonation. Find, to the nearest tenth, the distance over which the effects would be felt for a 1500-kiloton bomb.