a. Answer The value of θ is 1.47 radians . Explanation Given information: The equation is L = π D + ( d − D ) θ + 2 C sin θ . Calculation: Consider the equation. θ = cos − 1 ( D − d 2 C ) = cos − 1 ( 6 − 4 2 ( 10 ) ) = cos − 1 ( 1 10 ) = 1.47 radians Thus, the value of θ is 1.47 radians . b. To determine To find: The length of the belt needed to go around the two pulleys. Answer The length of the belt needed to go around the two pulleysis 35.81 inches . Explanation Given information: The equation is L = π D + ( d − D ) θ + 2 C sin θ . Calculation: Consider the equation. L = π D + ( d − D ) θ + 2 C sin θ L = π ( 6 ) + ( 4 − 6 ) ( 1.47 ) + 2 ( 10 ) sin 1.47 = 6 π − 2.94 + 20 ( 0.995 ) = 35.81 inches Thus, the length of the belt needed to go around the two pulleys is 35.81 inches .

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

1st Edition

ISBN: 9780078682278

Author: McGraw-Hill, Berchie Holliday

Publisher: Glencoe/McGraw-Hill

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Concept explainers

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.

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Question

Chapter 6.8, Problem 45E

To determine

To find: The value of θ .

Expert Solution

Answer to Problem 45E

The value of θ is 1.47radians .

Explanation of Solution

Given information: The equation is L=πD+(d−D)θ+2Csinθ .

Calculation:

Consider the equation.

θ=cos−1(D−d2C)=cos−1(6−42(10))=cos−1(110)=1.47radians

Thus, the value of θ is 1.47radians .

To determine

To find: The length of the belt needed to go around the two pulleys.

Expert Solution

Answer to Problem 45E

The length of the belt needed to go around the two pulleysis 35.81 inches .

Explanation of Solution

Given information: The equation is L=πD+(d−D)θ+2Csinθ .

Calculation:

Consider the equation.

L=πD+(d−D)θ+2CsinθL=π(6)+(4−6)(1.47)+2(10)sin1.47=6π−2.94+20(0.995)=35.81 inches

Thus, the length of the belt needed to go around the two pulleys is 35.81 inches .

Chapter 6.8, Problem 44E

Chapter 6.8, Problem 46E

Chapter 6 Solutions

Advanced Mathematical Concepts: Precalculus with Applications, Student Edition

Ch. 6.1 - Prob. 1CFU Ch. 6.1 - Prob. 2CFU Ch. 6.1 - Prob. 3CFU Ch. 6.1 - Prob. 4CFU Ch. 6.1 - Prob. 5CFU Ch. 6.1 - Prob. 6CFU Ch. 6.1 - Prob. 7CFU Ch. 6.1 - Prob. 8CFU Ch. 6.1 - Prob. 9CFU Ch. 6.1 - Prob. 10CFU

Ch. 6.1 - Prob. 11CFU Ch. 6.1 - Prob. 12CFU Ch. 6.1 - Prob. 13CFU Ch. 6.1 - Prob. 14CFU Ch. 6.1 - Prob. 15CFU Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Prob. 31E Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Prob. 34E Ch. 6.1 - Prob. 35E Ch. 6.1 - Prob. 36E Ch. 6.1 - Prob. 37E Ch. 6.1 - Prob. 38E Ch. 6.1 - Prob. 39E Ch. 6.1 - Prob. 40E Ch. 6.1 - Prob. 41E Ch. 6.1 - Prob. 42E Ch. 6.1 - Prob. 43E Ch. 6.1 - Prob. 44E Ch. 6.1 - Prob. 45E Ch. 6.1 - Prob. 46E Ch. 6.1 - Prob. 47E Ch. 6.1 - Prob. 48E Ch. 6.1 - Prob. 49E Ch. 6.1 - Prob. 50E Ch. 6.1 - Prob. 51E Ch. 6.1 - Prob. 52E Ch. 6.1 - Prob. 53E Ch. 6.1 - Prob. 54E Ch. 6.1 - Prob. 55E Ch. 6.1 - Prob. 56E Ch. 6.1 - Prob. 57E Ch. 6.1 - Prob. 58E Ch. 6.1 - Prob. 59E Ch. 6.1 - 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