EBK PRECALCULUS W/LIMITS

4th Edition

ISBN: 9781337516853

Author: Larson

Publisher: CENGAGE CO

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Question

Chapter 5, Problem 12PS

To determine

Use a graphing utility to graph the heights of these pistons in the same viewing window for 0≤t≤1 .

Expert Solution

Answer to Problem 12PS

EBK PRECALCULUS W/LIMITS, Chapter 5, Problem 12PS , additional homework tip 1

Explanation of Solution

Given information:

The heights h (in inches) of pistons 1 and 2 in an automobile engine can be modelled by

h1=3.75sin733t+7.5 and h2=3.75sin733(t+4π3)+7.5

respectively, where t is measured in seconds.

Calculation:

The heights h (in inches) of pistons 1 and 2 in an automobile engine can be modelled by

h1=3.75sin733t+7.5

h2=3.75sin733(t+4π3)+7.5

The graph of the expressions of the heights of pistons 1 and 2 is shown below,

EBK PRECALCULUS W/LIMITS, Chapter 5, Problem 12PS , additional homework tip 2

Hence, the graph is shown above.

To determine

How often are the pistons at the same height?

Expert Solution

Answer to Problem 12PS

t=(n−56)π1466

Explanation of Solution

Given information: The heights h (in inches) of pistons 1 and 2 in an automobile engine can be modelled by

h1=3.75sin733t+7.5 and h2=3.75sin733(t+4π3)+7.5

respectively, where t is measured in seconds.

How often are the pistons at the same height?

Calculation:

The heights of the given heights will be equal at certain points in time domain. Those points can be determined by keeping the expressions of both the heights equal and simplifying then as below,

3.75sin733t+7.5=3.75sin(733t+4π3)+7.53.75sin733t=3.75sin(733t+4π3)3.75(sin733t−sin(733t+4π3))=02cos(733t+733t+4π3)sin(733t−(733t+4π3))=0cos(1466t+4π3)sin(−4π3)=0cos(1466t+4π3)=0

The relation obtained above has been obtained incosine form. The above formcan be simplified further to obtain values of t at which the heights of the pistons will be equal.

cos(1466t+4π3)=cos((2n+1)π2)1466t+4π3=(2n+1)π21466t=(n+12−43)πt=(n−56)π1466

Hence, t=(n−56)π1466

Chapter 5, Problem 11PS

Chapter 5, Problem 13PS

Chapter 5 Solutions

EBK PRECALCULUS W/LIMITS

Ch. 5.1 - Prob. 1E Ch. 5.1 - Prob. 2E Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Prob. 5E Ch. 5.1 - Prob. 6E Ch. 5.1 - Prob. 7E Ch. 5.1 - Prob. 8E Ch. 5.1 - Prob. 9E Ch. 5.1 - Prob. 10E

Ch. 5.1 - Prob. 11E Ch. 5.1 - Prob. 12E Ch. 5.1 - Prob. 13E Ch. 5.1 - Prob. 14E Ch. 5.1 - Prob. 15E Ch. 5.1 - Prob. 16E Ch. 5.1 - Prob. 17E Ch. 5.1 - Prob. 18E Ch. 5.1 - Prob. 19E Ch. 5.1 - Prob. 20E Ch. 5.1 - Prob. 21E Ch. 5.1 - Prob. 22E Ch. 5.1 - Prob. 23E Ch. 5.1 - Prob. 24E Ch. 5.1 - Prob. 25E Ch. 5.1 - Prob. 26E Ch. 5.1 - Prob. 27E Ch. 5.1 - Prob. 28E Ch. 5.1 - Prob. 29E Ch. 5.1 - Prob. 30E Ch. 5.1 - Prob. 31E Ch. 5.1 - Prob. 32E Ch. 5.1 - Prob. 33E Ch. 5.1 - Prob. 34E Ch. 5.1 - Prob. 35E Ch. 5.1 - Prob. 36E Ch. 5.1 - Prob. 37E Ch. 5.1 - Prob. 38E Ch. 5.1 - Prob. 39E Ch. 5.1 - Prob. 40E Ch. 5.1 - Prob. 41E Ch. 5.1 - Prob. 42E Ch. 5.1 - Prob. 43E Ch. 5.1 - Prob. 44E Ch. 5.1 - Prob. 45E Ch. 5.1 - Prob. 46E Ch. 5.1 - Prob. 47E Ch. 5.1 - Prob. 48E Ch. 5.1 - Prob. 49E Ch. 5.1 - Prob. 50E Ch. 5.1 - Prob. 51E Ch. 5.1 - Prob. 52E Ch. 5.1 - Prob. 53E Ch. 5.1 - Prob. 54E Ch. 5.1 - Prob. 55E Ch. 5.1 - Prob. 56E Ch. 5.1 - Prob. 57E Ch. 5.1 - Prob. 58E Ch. 5.1 - Prob. 59E Ch. 5.1 - Prob. 60E Ch. 5.1 - 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