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CalculusCalculus: An Applied Approach (MindTap Course List)10th Edition

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

10th Edition
Ron Larson
ISBN: 9781305860919

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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 0≤t≤3, 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(0.568t−2.595).

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(0.568t−2.595).

Formula used:

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

Average value=1b−a∫abf(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 0≤t≤3 can be calculated as:

WFirst Quater=13−0∫03[31.184+8.447sin(0.568t−2.595)]dt=13∫03[31

(b)

To determine

To calculate: The number of scenic and sightseeing workers in second quarter 3≤t≤6, 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(0.568t−2.595).

(c)

To determine

To calculate: The number of scenic and sightseeing workers in entire year 0≤t≤12, 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(0.568t−2.595).

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Sect-8.1 P-1CPSect-8.1 P-2CPSect-8.1 P-3CPSect-8.1 P-4CPSect-8.1 P-1SWUSect-8.1 P-2SWUSect-8.1 P-3SWUSect-8.1 P-4SWUSect-8.1 P-5SWUSect-8.1 P-6SWU
Sect-8.1 P-7SWUSect-8.1 P-8SWUSect-8.1 P-9SWUSect-8.1 P-10SWUSect-8.1 P-1ESect-8.1 P-2ESect-8.1 P-3ESect-8.1 P-4ESect-8.1 P-5ESect-8.1 P-6ESect-8.1 P-7ESect-8.1 P-8ESect-8.1 P-9ESect-8.1 P-10ESect-8.1 P-11ESect-8.1 P-12ESect-8.1 P-13ESect-8.1 P-14ESect-8.1 P-15ESect-8.1 P-16ESect-8.1 P-17ESect-8.1 P-18ESect-8.1 P-19ESect-8.1 P-20ESect-8.1 P-21ESect-8.1 P-22ESect-8.1 P-23ESect-8.1 P-24ESect-8.1 P-25ESect-8.1 P-26ESect-8.1 P-27ESect-8.1 P-28ESect-8.1 P-29ESect-8.1 P-30ESect-8.1 P-31ESect-8.1 P-32ESect-8.1 P-33ESect-8.1 P-34ESect-8.1 P-35ESect-8.1 P-36ESect-8.1 P-37ESect-8.1 P-38ESect-8.1 P-39ESect-8.1 P-40ESect-8.1 P-41ESect-8.1 P-42ESect-8.1 P-43ESect-8.1 P-44ESect-8.1 P-45ESect-8.1 P-46ESect-8.1 P-47ESect-8.1 P-48ESect-8.1 P-49ESect-8.1 P-50ESect-8.1 P-51ESect-8.1 P-52ESect-8.1 P-53ESect-8.1 P-54ESect-8.1 P-55ESect-8.1 P-56ESect-8.1 P-57ESect-8.1 P-58ESect-8.2 P-1CPSect-8.2 P-2CPSect-8.2 P-3CPSect-8.2 P-4CPSect-8.2 P-5CPSect-8.2 P-6CPSect-8.2 P-7CPSect-8.2 P-1SWUSect-8.2 P-2SWUSect-8.2 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A triangular corner of a store has been roped off to be used as an area for displaying Christmas ornaments. Fin...

Elementary Geometry For College Students, 7e

Writing a Set of Parametric Equations In Exercises 4148, use the results of Exercises 3740 to find a set of par...

Calculus: Early Transcendental Functions (MindTap Course List)

Show that if x is positive, then loge(1+1x)11+x

Calculus of a Single Variable

Determine the conditions on a, b, c and d for which the system ax+by=cbx+ay=d has an infinite number of solutio...

Finite Mathematics for the Managerial, Life, and Social Sciences

Parallel lines l1 and l2 have slopes m1 and m2, respectively. Find m2 if m1 equals: a 34 b -53 c -2 d a-bc

Elementary Geometry for College Students

For f(x) = x2 and g(x) = 2x + 1, (f g)(x), = a) 2x2 + 1 b) (2x)2 + 1 c) (2x + 1)2 d) x2(2x + 1)

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

True or False: The vector function is continuous at t = 3.

Study Guide for Stewart's Multivariable Calculus, 8th

Finding the Volume of a Solid In Exercises 4148, find the volume of the solid generated by revolving the specif...

Calculus (MindTap Course List)

Area In Exercises 39-42, use the result of Exercise 34 to find the area of the region bounded by the graph of t...

Multivariable Calculus

Area Find the area of the largest rectangle that can be inscribed under the curve y=ex2 in the first and second...

Calculus

Define individual differences and explain how individual differences between groups and confounding from enviro...

Research Methods for the Behavioral Sciences (MindTap Course List)

The mean volume of a carton of milk filled by a machine is 1.0quart, with a standard deviation of 0.06quart. If...

Mathematics: A Practical Odyssey

Show that the standard form of the equation of a circle (x+2)2+(y5)2=36 is a special case of the general form o...

College Algebra (MindTap Course List)

Using PsycINFO (or a similar database), find research articles on how background music influences mood. Print o...

Research Methods for the Behavioral Sciences (MindTap Course List)

Determine the value of angle A in decimal degrees for each of the given functions. Round the answers to the nea...

Mathematics For Machine Technology

A large corporation sends many of its first-level managers to an off-site supervisory skills training course. F...

Statistics for Business & Economics, Revised (MindTap Course List)

Consider a sample with data values of 27, 25, 20, 15, 30, 34, 28, and 25. Compute the range, interquartile rang...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

Suppose that each of 935 smokers received a nicotine patch, which delivers nicotine to the bloodstream but at a...

Introduction To Statistics And Data Analysis

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