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CalculusCalculus (MindTap Course List)8th Edition

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Chapter 3.7, Problem 17E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621

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
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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
Problem 61E
Problem 62E
Problem 63E
Problem 64E
Problem 65E
Problem 66E
Problem 67E
Problem 68E
Problem 69E
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Problem 71E
Problem 72E
Problem 73E
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Problem 75E
Problem 76E
Problem 77E
Problem 78E
Problem 79E
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Calculus (MindTap Course List)

8th Edition
James Stewart
ISBN: 9781285740621
Textbook Problem

Do Exercise 16 assuming the container has a fid that is made from the same material as the sides.

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 such container

Explanation

1) Concept:

i. First derivative test for absolute extreme values- suppose that c is a critical number of a continuous function f defined on an interval.

a) If f'x>0 for all x<c and f'x<0 for all x>c, then fc is the absolute maximum value of f

b) If f'x<0 for all x<c and f'x>0 for all x>c, then fc is the absolute Minimum value of f

ii. The cost is 10 times the area of the base (x·y) plus 6 times the total area of the sides

iii. A critical number of a function f   is a number c in the domain of f s uch that either  f'c=0 or f'c does not exist.

2) Formula:

Volume of the rectangle =l·w·h

3) Given:

The rectangular container has volume 10m3 ; also its length is twice the width and the cost is $10 per square meter of the base and $6 per square meter of the sides and the lid

4) Calculation:

Let x be the length, y be the width and z be the height of a rectangle

So, volume of the rectangle is V=x·y·z

Given that V=x·y·z=10 and x=2·y

Now put x=2·y in the equation x·y·z=10

(2·y)·y·z=10

2y2·z=10

Divide by 2y2

2y2·z2y2=102y2

z=102y2

Now we have to find the cost

C=10x·y+6(2·x·z+2·y·z)

Put x=2·y, z=102y2  in the above equation  =102·y·y+62·2·y·102y2+2·y·102y2+6(2x2)

On simplifying,

=102y2+64y·102y2+2·y·102y2+6(2x2)

=32y2+240y<

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Sect-3.1 P-1ESect-3.1 P-2ESect-3.1 P-3ESect-3.1 P-4ESect-3.1 P-5ESect-3.1 P-6ESect-3.1 P-7ESect-3.1 P-8ESect-3.1 P-9ESect-3.1 P-10E
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Mathematical Applications for the Management, Life, and Social Sciences

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For Problems 1-10, answer true or false. The terms 5x2y and 6xy2 are similar terms.

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Map Coloring The following map shows six countries in the Indian subcontinent. Four colors have been used to co...

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Find a power series representation for f, and graph f and several partial sums sn(x) on the same screen. What h...

Single Variable Calculus: Early Transcendentals

Graphical, Numerical, and Analytic Analysis In Exercises 75-82, use a graphing utility to graph the function an...

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Solve the following word problems by using Table 11-1 or 11-2. When necessary, create new table factors. Round ...

Contemporary Mathematics for Business & Consumers

For Questions 1 through 8, fill in the blank with an appropriate word. Airspeed is the speed of an object relat...

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True or False Label each of the following statements as either true or false. 2. The field of real numbers is...

Elements Of Modern Algebra

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A rectangle has a perimeter 16 in. What is the limit largest possible value of the area of the rectangle?

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Finding Parametric EquationsIn Exercises 39 and 40, find a set of parametric equations of the line with the giv...

Multivariable Calculus

Rectangular-to-Polar Conversion In Exercises 15-24, the rectangular coordinates of a point are given. Plot the ...

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HOW DO YOU SEE IT? Which set of parametric equations is shown in the graph below? Explain your reasoning. (a) x...

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The following Exercises 7 through 19 involve rectangles, parallelograms, trapezoids, and triangles. Given certa...

Mathematics For Machine Technology

Summarize the major APA ethical standards concerning the care and use of animals in research.

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Graph each function. y=2x

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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)

Consider the following time series. a. Construct a time series plot. What type of pattern exists in the data? b...

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

As part of a study on transportation safety, the U.S. Department of Transportation collected data on the number...

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Suppose that 25% of the fire alarms in a large city are false alarms. Let x denote the number of false alarms i...

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