1. Equations & Inequalities

In Exercises 11–20, 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.

In Exercises 11–20, 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.

In Exercises 11–20, 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.

In Exercises 11–20, 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.

In Exercises 11–20, 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.

In Exercises 11–20, 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.

In Exercises 11–20, 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.

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.