1. Equations & Inequalities

Write each formula as an English phrase using the word varies or proportional. r = d/t, where r is the speed when traveling d miles in t hours.

Write each formula as an English phrase using the word varies or proportional. V = 1/3 πr²h, where V is the volume of a cone of radius r and height h

Circumference of a Circle The circumference of a circle varies directly as the radius. A circle with radius 7 in. has circumference 43.96 in. Find the circumference of the circle if the radius changes to 11 in.

Resistance of a Wire The resistance in ohms of a platinum wire temperature sensor varies directly as the temperature in kelvins (K). If the resistance is 646 ohms at a temperature of 190 K, find the resistance at a temperature of 250 K.

Distance to the Horizon The distance that a person can see to the horizon on a clear day from a point above the surface of Earth varies directly as the square root of the height at that point. If a person 144 m above the surface of Earth can see 18 km to the horizon, how far can a person see to the horizon from a point 64 m above the surface?

Fill in the blank(s) to correctly complete each sentence, or answer the question as appropriate. In the equation y = 6x, y varies directly as x. When x=5, y=30. What is the value of y when x=10?

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?