1. Equations & Inequalities

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as z and inversely as the difference between y and w.

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as z and the difference between y and w.

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as z and the sum of y and w.

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z and inversely as the square of w.

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z and inversely as the square root of w.

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as the cube root of z and inversely as y.

Write an equation that expresses each relationship. Then solve the equation for y. x varies directly as the cube of z and inversely as y.

Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z.

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies jointly as a and b and inversely as the square root of c. y = 12 when a = 3, b = 2, and c = 25. Find y when a = 5, b = 3 and c = 9.

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies jointly as x and z. y = 25 when x = 2 and z = 5. Find y when x = 8 and z = 12.

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies directly as x and inversely as the square of z. y = 20 when x = 50 and z = 5. Find y when x = 3 and z = 6.

Use the four-step procedure for solving variation problems given on page 447 to solve Exercises 1–10. y varies inversely as x. y = 12 when x = 5. Find y when x = 2.

Solve the variation problems in Exercises 77–82. The pitch of a musical tone varies inversely as its wavelength. A tone has a pitch of 660 vibrations per second and a wavelength of 1.6 feet. What is the pitch of a tone that has a wavelength of 2.4 feet?

Solve the variation problems in Exercises 77–82. The distance that a body falls from rest is directly proportional to the square of the time of the fall. If skydivers fall 144 feet in 3 seconds, how far will they fall in 10 seconds?

Write each formula as an English phrase using the word varies or proportional. C=2πr, where C is the circumference of a circle of radius r.