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quester [9]
3 years ago
14

Analyze the graph and I would like some help.

Advanced Placement (AP)
1 answer:
elixir [45]3 years ago
3 0

Answer:

A (As the x-values go to positive infinity, the functions values go to positive infinity)

Explanation:

As the x-values go to positive infinity, that means they are going to the right, and as they go further to the right the y-values decrease but then increase and don’t stop increasing

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Surface Area of a can is 517.8 cm^2. Maximize the volume of this can using the measured surface area.
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Answer:

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Explanation:

Given

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Substitute 517.8 for S.A

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258.9 = \pi r(r + h)

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h = \frac{258.9}{\pi r} - r --- (1)

Volume (V) is calculated as:

V = \pi r^2h

Substitute (1) for h

V = \pi r^2(\frac{258.9}{\pi r} - r)

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V = 258.9r - \pi r^3

Differentiate V

V' = 258.9 - 3\pi r^2

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3\pi r^2 = 258.9

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\pi r^2 = 86.3

Divide through by \pi

r^2 = \frac{86.3}{\pi}

r^2 = \frac{86.3*7}{22}

r^2 = \frac{604.1}{22}

Take square root of both sides

r = \sqrt{\frac{604.1}{22}

r = 5.24

Recall that:

h = \frac{258.9}{\pi r} - r

Substitute 5.24 for r

h = \frac{258.9}{\pi * 5.24} - 5.24

h = \frac{258.9*7}{22 * 5.24} - 5.24

h = \frac{1812.3}{115.28} - 5.24

h = 15.72 - 5.24

h = 10.48

Hence, the dimension that maximize the volume is:

r = 5.24 --- Radius

h = 10.48 --- Height

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