PRECALCULUS:GRAPHICAL,...-NASTA ED.
PRECALCULUS:GRAPHICAL,...-NASTA ED.
10th Edition
ISBN: 9780134672090
Author: Demana
Publisher: PEARSON
Expert Solution & Answer
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Chapter 5, Problem 68RE
Solution

a.

To graph: The function y=Sθ .

Given information: The given function is Sθ=6ab+32ab2−cotθ+3sinθ . The values are a=1.75 in. and b=0.65 in. .

Graph:

Substitute 1.75 for a and 0.65 for b in the given function.

  Sθ=61.750.65+321.750.652−cotθ+3sinθ=6.825+0.63375−cotθ+3sinθ

Draw the graph of the function y=Sθ as shown below.

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 5, Problem 68RE , additional homework tip 1

Figure (1)

Thus, the graph of the function is shown in Figure (1).

b.

To calculate: The value of θ that provides the minimum surface area.

The value of θ that provides the minimum surface area is 54.7° .

Given information: The given function is Sθ=6ab+32ab2−cotθ+3sinθ . The values are a=1.75 in. and b=0.65 in. .

Calculation:

From part (a), consider the graph of the function y=Sθ .

  PRECALCULUS:GRAPHICAL,...-NASTA ED., Chapter 5, Problem 68RE , additional homework tip 2

Figure (2)

From the graph, it can be observed that the graph reaches its minimum value for θ=0.955 .

Convert the values of θ into degrees.

  θ=0.955⋅180°π=54.7°

Thus, the value of θ that provides the minimum surface area is 54.7° .

c.

To calculate: The minimum surface area of the cell.

The minimum surface area of the cell is 7.721 .

Given information: The given function is Sθ=6ab+32ab2−cotθ+3sinθ . The values are a=1.75 in. and b=0.65 in. .

Calculation:

From the figure (2) in part (b), it can be observed that the minimum value θ=0.955 corresponds to the value 7.721 .

Thus, the minimum surface area of the cell is 7.721 .

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Chapter 5, Problem 67RE
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Chapter 5, Problem 69RE

Chapter 5 Solutions

PRECALCULUS:GRAPHICAL,...-NASTA ED.

Ch. 5.1 - Prob. 1QRCh. 5.1 - Prob. 2QRCh. 5.1 - Prob. 3QRCh. 5.1 - Prob. 4QRCh. 5.1 - Prob. 5QRCh. 5.1 - Prob. 6QRCh. 5.1 - Prob. 7QRCh. 5.1 - Prob. 8QRCh. 5.1 - Prob. 9QRCh. 5.1 - Prob. 10QR
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