Precalculus: Mathematics for Calculus - 6th Edition
Precalculus: Mathematics for Calculus - 6th Edition
6th Edition
ISBN: 9780840068071
Author: Stewart, James, Redlin, Lothar, Watson, Saleem
Publisher: Cengage Learning
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Cylinders
A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.
Cones
A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is dr…
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Textbook Question
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Chapter 10.8, Problem 44E

Dimensions of a Rectangle A circular piece of sheet metal has a diameter of 20 in. The edges are to be cut off to form a rectangle of area 160 in2 (see the figure). What are the dimensions of the rectangle?

Chapter 10.8, Problem 44E, Dimensions of a Rectangle A circular piece of sheet metal has a diameter of 20 in. The edges are to

Expert Solution & Answer
Check Mark
To determine

The dimensions of given rectangle.

Answer to Problem 44E

The dimensions of given rectangle is 8.95 in_ by 17.88 in_ .

Explanation of Solution

Given:

Diameter of circular piece of sheet metal is 20 in and area of rectangle is 160 in2 .

Figure of circular piece of sheet metal and rectangle is,

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 10.8, Problem 44E , additional homework tip 1

Figure (1)

Calculation:

Let the length of rectangle is l, width of rectangle is w and diagonal of rectangle is d shows in Figure (2),

Precalculus: Mathematics for Calculus - 6th Edition, Chapter 10.8, Problem 44E , additional homework tip 2

Figure (2)

Formula of area of rectangle is,

l.w=160

Diameter of circular piece is equal to the diagonal of rectangle because rectangle form inside the circular piece and the edges of rectangle touches the perimeter of circular piece so that the value of diagonal of rectangle is,

d=20

Diagonal of rectangle divides the rectangle in right triangle, use Pythagoras theorem to get the equation,

l2+w2=d2 (1)

Solve the above equation to make complete square,

l2+w2+2.l.w−2.l.w=d2(l+w)2−2.l.w=d2

Substitute 20 for d and 160 for l.w in above equation to get the new equation,

(l+w)2−2.160=(20)2(l+w)2=400+320l+w=720l+w=26.83

Solve above equation for l,

l=26.83−w (2)

Substitute 26.83−w for l in equation (1) and solve for w,

(26.83−w)2+w2=(20)2720+w2−53.66w+w2=4002w2−53.66w+320=02(w2−26.83w+160)=0

Further, solve above equation for w,

w2−26.83w+160=0w2−17.88w−8.95w+160=0(w−17.88)(w−8.95)=0w=17.88,8.95

Substitute 17.88 for w to get the value of l,

l=26.83−17.88l=8.95

Substitute 8.95 for w to get the value of l,

l=26.83−8.95l=17.88

Thus, the dimensions of given rectangle is 8.95 in_ by 17.88 in_ .

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Chapter 10 Solutions

Precalculus: Mathematics for Calculus - 6th Edition

Ch. 10.1 - The system of equations {2x+3y=75xy=9 is a system...Ch. 10.1 - Prob. 2ECh. 10.1 - A system of two linear equations in two variables...Ch. 10.1 - The following is a system of two linear equations...Ch. 10.1 - Prob. 5ECh. 10.1 - Prob. 6ECh. 10.1 - Prob. 7ECh. 10.1 - Prob. 8ECh. 10.1 - Prob. 9ECh. 10.1 - Prob. 10E
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Admission Fees The admission fee at an amusement...Ch. 10.1 - Gas Station A gas station sells regular gas for...Ch. 10.1 - Fruit Stand A fruit stand sells two varieties of...Ch. 10.1 - Airplane Speed A man flies a small airplane from...Ch. 10.1 - Boat Speed A boat on a river travels downstream...Ch. 10.1 - Nutrition A researcher performs an experiment to...Ch. 10.1 - Coffee Blends A customer in a coffee shop...Ch. 10.1 - Mixture Problem A chemist has two large containers...Ch. 10.1 - Mixture Problem A biologist has two brine...Ch. 10.1 - Investments A woman invests a total of 20,000 in...Ch. 10.1 - Investments A man invests his savings in two...Ch. 10.1 - Prob. 71ECh. 10.1 - Prob. 72ECh. 10.1 - Prob. 73ECh. 10.1 - Area of a Triangle Find the area of the triangle...Ch. 10.1 - Prob. 75ECh. 10.2 - These exercises refer to the following system:...Ch. 10.2 - Prob. 2ECh. 10.2 - Prob. 3ECh. 10.2 - Prob. 4ECh. 10.2 - Prob. 5ECh. 10.2 - Prob. 6ECh. 10.2 - Prob. 7ECh. 10.2 - Prob. 8ECh. 10.2 - Prob. 9ECh. 10.2 - 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Publisher:PEARSON
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Author:Ron Larson, Bruce H. Edwards
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