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valina [46]
4 years ago
6

Renee is a social worker in an urban community mental health center. She has just seen a new client who has depression, which sh

e codes on
A) Axis I.
B) Axis II.
C) Axis III.
D) Axis IV.
Advanced Placement (AP)
1 answer:
steposvetlana [31]4 years ago
3 0
The correct answer for the question that is being presented above is this one: "A) Axis I." Renee is a social worker in an urban community mental health center. She has just seen a new client who has depression, which she codes on <span>Axis I.</span>
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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:

r = 5.24 --- Radius

h = 10.48 --- Height

Explanation:

Given

Object: Can (Cylinder)

Surface\ Area = 517.8cm^2

Required

Maximize the volume

The surface area is:

S.A = 2\pi r^2 + 2\pi rh

Substitute 517.8 for S.A

517.8 = 2\pi r^2 + 2\pi rh

Divide through by 2

258.9 = \pi r^2 + \pi rh

Factorize:

258.9 = \pi r(r + h)

Divide through by \pi r

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

Make h the subject

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)

Open Bracket

V = 258.9r - \pi r^3

Differentiate V

V' = 258.9 - 3\pi r^2

Set V' to 0

0 = 258.9 - 3\pi r^2

Collect Like Terms

3\pi r^2 = 258.9

Divide through by 3

\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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