Skip to main content
Ch. 3 - Polynomial and Rational Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
All textbooksLial 13th EditionCh. 3 - Polynomial and Rational FunctionsProblem 35
Chapter 4, Problem 35

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.

Verified step by step guidance
1
Identify the type of variation described: the speed \( S \) varies inversely as the diameter \( D \). This means the relationship can be written as \( S = \frac{k}{D} \), where \( k \) is a constant.
Use the given values to find the constant \( k \). Substitute \( S = 150 \) revolutions per minute and \( D = 3 \) inches into the equation \( 150 = \frac{k}{3} \).
Solve for \( k \) by multiplying both sides of the equation by 3, giving \( k = 150 \times 3 \).
Write the general formula for speed using the constant \( k \): \( S = \frac{k}{D} \).
Find the speed of the pulley with diameter 5 inches by substituting \( D = 5 \) into the formula: \( S = \frac{k}{5} \).

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
4m
Was this helpful?

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Inverse Variation

Inverse variation describes a relationship where one quantity increases as the other decreases, such that their product is constant. In this problem, speed varies inversely with diameter, meaning speed × diameter = constant.
Recommended video:
4:30
Graphing Logarithmic Functions

Setting up the Variation Equation

To solve inverse variation problems, express the relationship as speed × diameter = k, where k is a constant. Use known values to find k, then apply it to find the unknown speed for the new diameter.
Recommended video:
06:00
Categorizing Linear Equations

Solving for Unknowns in Variation Problems

After determining the constant of variation, substitute the new diameter into the equation and solve for the unknown speed. This step involves basic algebraic manipulation to isolate and calculate the desired value.
Recommended video:
Guided course
6:54
Cramer's Rule - 2 Equations with 2 Unknowns
Related Practice
Textbook Question

Solve each problem. Is x+1 a factor of ƒ(x)=x3+2x2+3x+2?

Textbook Question

For each polynomial function, one zero is given. Find all other zeros. ƒ(x)=4x3+6x2−2x−1; 12ƒ(x)=4x^3+6x^2-2x-1;\(\text{ }\]\frac\)12

Textbook Question

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=(4x+3)(x+2)2

3
views
Textbook Question

Graph each polynomial function. Factor first if the polynomial is not in factored form. ƒ(x)=(3x-1)(x+2)2

Textbook Question

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = - x3 + 8x2 + 63; k=4

Textbook Question

For each polynomial function, use the remainder theorem to find ƒ(k). ƒ(x) = 2x2 - 3x-3; k = 2

2
views