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Math
CalculusSingle Variable Calculus: Early Transcendentals, Volume I8th Edition

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Chapter 4.7, Problem 16E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

Solutions

Chapter
Section
Problem 1E
Problem 2E
Problem 3E
Problem 4E
Problem 5E
Problem 6E
Problem 7E
Problem 8E
Problem 9E
Problem 10E
Problem 11E
Problem 12E
Problem 13E
Problem 14E
Problem 15E
Problem 16E
Problem 17E
Problem 18E
Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
Problem 25E
Problem 26E
Problem 27E
Problem 28E
Problem 29E
Problem 30E
Problem 31E
Problem 32E
Problem 33E
Problem 34E
Problem 35E
Problem 36E
Problem 37E
Problem 38E
Problem 39E
Problem 40E
Problem 41E
Problem 42E
Problem 43E
Problem 44E
Problem 45E
Problem 46E
Problem 47E
Problem 48E
Problem 49E
Problem 50E
Problem 51E
Problem 52E
Problem 53E
Problem 54E
Problem 55E
Problem 56E
Problem 57E
Problem 58E
Problem 59E
Problem 60E
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Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
Problem 70E
Problem 71E
Problem 72E
Problem 73E
Problem 74E
Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
Problem 80E
Problem 81E
Problem 82E
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Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

A rectangular storage container with an open top is to have a volume of 10 m3. The length of its base is twice the width. Material for the base costs $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container.

To determine

To find: The cost of materials for the cheapest open box container whose volume is 10m3

Explanation

Given:

The volume of the open box container is 10m3.

The length of base is twice the width of the box.

The cost for the base of the box is $10 per square meter.

The cost for the sides of the box is $6 per square meter.

Calculation:

Let length is denoted by L, width is denoted by W and height is denoted by H.

Volume of the box =length(L)×width(W)×height(H)

The length is twice the width, L=2W

Therefore, the volume is calculated as follows.

V=L×W×H=10

Substitute the value of L,

2W2×H=10H=102W2

Compute the cost of the materials as follows.

Cost, C=10×Area of the base+6×Area of the sides=10(L×W)+6(2×L×H+2×W×H)=10(2W×W)+6(2×2W×102W2+2×W×102W2)=20W2+120W+60W

Simplifying further,

Cost, C=20W2+180W

Differentiate C with respect to W,

dCdW=ddW(20W2+180W)=20(2W)+180(−1W2)=40W−180W2

For critical points, set dCdW=0 and solve for W

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Mathematical Applications for the Management, Life, and Social Sciences

Evaluate the integral using integration by parts with the indicated choices of u and dv. 2. xlndx;u=lnx,dv=xdx

Single Variable Calculus: Early Transcendentals

36. Let , be an arbitrary nonempty collection of subgroup of the group , and let .Prove that is subgroup of ...

Elements Of Modern Algebra

Add or subtract as indicated. (7121)+(2644)

Trigonometry (MindTap Course List)

In the figure, quadrilateral ABCD is inscribed in O. Also, CFBD. aExplain why ABEDFC. bExplain why DAB and BCD ...

Elementary Geometry For College Students, 7e

Roadway Trucking purchased and placed into service an over-the-road tractor for $135,500 in 2014. The vehicle w...

Contemporary Mathematics for Business & Consumers

Solve each equation and check: x+5=5

Elementary Technical Mathematics

Finding a Derivative In Exercises 7-26. Use the rules of differentiation to find the derivative of the function...

Calculus of a Single Variable

Volume The volume of the red right circular cylinder in figure is V=r2h. The possible errors in the radius and ...

Calculus: Early Transcendental Functions (MindTap Course List)

In Exercises 53 and 54, determine whether the statement is true or false. If it is true, explain why it is true...

Finite Mathematics for the Managerial, Life, and Social Sciences

In the figure for Exercises 21 to 24,RS is tangent to the circle at S. See Theorem 6.3.7. Given: RT=12RSandTV=9...

Elementary Geometry for College Students

Using as an estimator, find the maximum error in estimating with the Midpoint Rule and 8 subintervals. 9

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

Which is true about the series ? diverges converges absolutely converges conditionally converges, but not absol...

Study Guide for Stewart's Multivariable Calculus, 8th

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

Calculus

Mass In Exercises 25-28, find the total mass of the wire with density whose shape is modeled by r. r(t)=t2i+2t...

Multivariable Calculus

A researcher finds that college students are more anxious near final exams in December than at the beginning of...

Research Methods for the Behavioral Sciences (MindTap Course List)

The National Confectioners Association asked 1006 adults the following question: Do you set aside a personal st...

Introduction To Statistics And Data Analysis

Consider the following time series data. Month 1 2 3 4 5 6 7 Value 24 13 20 12 19 23 15 a. Compute MSE using th...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

In Figure 11.5, we show three combinations of main effects and interactions for a 2 2 factorial design. Using ...

Research Methods for the Behavioral Sciences (MindTap Course List)

Add the terms in the following expressions. 15xy+(7xy)

Mathematics For Machine Technology

The prior probabilities for events A1, A2, and A3 are P(A1) = .20, P(A2) = .50, and P(A3) = .30. The conditiona...

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

Find the probability of each event. Drawing a face card kind, queen, or jack from a card deck

College Algebra (MindTap Course List)

Mass In Exercises 25-28, find the total mass of the wire with density whose shape is modeled by r. r(t)=2costi...

Calculus (MindTap Course List)

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