   Chapter 8.5, Problem 60E ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919

#### Solutions

Chapter
Section ### Calculus: An Applied Approach (Min...

10th Edition
Ron Larson
ISBN: 9781305860919
Textbook Problem
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# Transportation Workers The number W (In thousands) of scenic and sightseeing transportation workers employed in the United States during 2014 can be modeled by W = 31.184 + 8.447   sin ( 0.568 t − 2.595 ) Where t is the time (in months), with t = 1 corresponding to January. Find the average number of scenic and sightseeing transportation workers during the first quarter ( 0 ≤ t ≤ 3 ) . the second quarter ( 3 ≤ t ≤ 6 ) . the entire year ( 0 ≤ t ≤ 12 ) .(Source: U.S. Bureau of Labor Statistics)

(a)

To determine

To calculate: The number of scenic and sightseeing workers in first quarter 0t3, when the number of scenic and sightseeing workers in thousands that employed in United States during 2014 is given as W=31.184+8.447sin(0.568t2.595).

Explanation

Given Information:

The number of scenic and sightseeing workers in thousands that employed in United States during 2014 has given as W=31.184+8.447sin(0.568t2.595).

Formula used:

Write the formula for average value of a provided function f(x) for [a,b].

Average value=1baabf(x)dx

Write the formula for definite integral of absinnudu.

absinnudu=[cosnun]ab

Write the formula for integral of abdu.

abdu=[u]ab

Calculation:

The number of scenic and sightseeing workers in first quarter 0t3 can be calculated as:

WFirst Quater=13003[31.184+8.447sin(0.568t2.595)]dt=1303[31

(b)

To determine

To calculate: The number of scenic and sightseeing workers in second quarter 3t6, when the number of scenic and sightseeing workers in thousands that employed in United States during 2014 is given as W=31.184+8.447sin(0.568t2.595).

(c)

To determine

To calculate: The number of scenic and sightseeing workers in entire year 0t12, when the number of scenic and sightseeing workers in thousands that employed in United States during 2014 is given as W=31.184+8.447sin(0.568t2.595).

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