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

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Chapter 8, Problem 24TYS
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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
1 views

The sales S (in thousands of dollars) of a company that produces insect repellent can be modeled by

S = 20.3 − 17.2   cos   π t 6 where t is the time (in months), with t = 1 corresponding to January.

(a) Find the total sales during the year (0 ≤ t ≤ 12).

(b) Find the average monthly sales from April through October (3 ≤ t ≤ 10).

(a)

To determine

To calculate: The total sales in thousands of dollars during the year 0≤t≤12, when sales S is given by expression S=20.3−17.2cosπt6.

Explanation

Given Information:

The sales S is given by expression S=20.3−17.2cosπt6.

Formula used:

Write the formula for definite integral of ∫abcosnudu.

∫abcosnudu=[sinnun]ab

Here, n is the any number.

Write the formula for integral of ∫abdu.

∫abdu=[u]ab

Calculation:

Consider the sales S.

S=20.3−17.2cosπt6

The total sales in thousands of dollars during the year 0≤t≤12 can be calculated by integrating the expression of sales S over the interval [0,12], which can be mathematically written as:

∫012S=∫012(20.3−17.2cosπt6)dt

Rewrite.

∫012S=∫01220.3dt−∫012(17.2cosπt6)dt=∫01220

(b)

To determine

To calculate: The average monthly sales S from April to October in thousands of dollars, when sales S is given by expression S=20.3−17.2cosπt6.

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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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Contemporary Mathematics for Business & Consumers

Solve each equation and check: 62=13y3

Elementary Technical Mathematics

For Questions 1 through 6, fill in the blank with an appropriate word. The ________ ______ test can be used to ...

Trigonometry (MindTap Course List)

Pumping Water A hemispherical tank of radius 6 feet is positioned so that its base is circular. How much work i...

Calculus of a Single Variable

WRITING ABOUT CONCEPTS Tangent Plane Discuss the relationship between the tangent plane to a surface and approx...

Calculus: Early Transcendental Functions (MindTap Course List)

Use the result from Exercise 25 to find m1 if mAB=104. Exercises 25, 26

Elementary Geometry for College Students

In Exercise 1-8, determine whether the matrix is an absorbing schematic matrix. [10.5000100.50]

Finite Mathematics for the Managerial, Life, and Social Sciences

is a(n): ellipsoid elliptic cone elliptic paraboloid elliptic cylinder

Study Guide for Stewart's Multivariable Calculus, 8th

Finding CurvatureIn Exercises 2936, find the curvature of the curve. r(t)=4cos2ti+4sin2tj

Multivariable Calculus

Precalculus or Calculus In Exercises 3-6.decide whether the problem can be solved using precalculus or whether ...

Calculus

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

Make a list of some of the factors in your life that change from one day to the next. Possible examples include...

Research Methods for the Behavioral Sciences (MindTap Course List)

A survey question for a sample of 150 individuals yielded 75 Yes responses, 55 No responses, and 20 No Opinions...

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

A hole is cut in a rectangular metal plate as shown in Figure 4-8. To find the area of a rectangle, multiply th...

Mathematics For Machine Technology

In a study of memory recall, eight students from a large psychology class were selected at random and given 10 ...

Introduction To Statistics And Data Analysis

Determine whether each series is an alternating infinite series. a+a2+a3+....+an+....;a=2

College Algebra (MindTap Course List)

At Western University the historical mean of scholarship examination scores for freshman applications is 900. A...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

How is the descriptive strategy different from the other four research strategies?

Research Methods for the Behavioral Sciences (MindTap Course List)

Electric Force Two electrons repel each other with a force that varies inversely as the square of the distance ...

Calculus (MindTap Course List)

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