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4 years ago

AP World History

1 answer:

5 0

Some good websites that will help you

http://faculty.tnstate.edu/tcorse/h1220revised/formation_of_world_systems.htm
http://www.academia.edu/9958314/What_Caused_the_Decline_of_the_Mughal_Empire_During_the_Reign_of_Aur...

if you need facts or whatever message me :>

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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.

mafiozo [28]

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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3 years ago

Which of the following best describes a species?

Airida [17]

Don’t u have to list the following?

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3 years ago

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A radio station has a contest in which contestants roll a regular 6-sided die. If he rolls a 1 or a 2, he wins $50. If he rolls

mina [271]

Answer:

0.00064300411

Explanation:

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3 years ago

Okay so im watching this video on apushreview.com and Im not sure if im suppose to be writing everything in the video or just un

Black_prince [1.1K]

So are familiar with civilization adaption?
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Google these two and read all you can in order to know the maximum of the begining of any society.

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3 years ago

How many different arrangements of the letters in the word "ALGEBRA" are there?

Dominik [7]

Answer:

2,520

Explanation:

The word ALGEBRA has 7 letters with the letter A repeated twice.

Hence we permute all 7 letters with A repeated twice

₇P₇ / 2! = 7!/ [ (2!) ( 7-7)!]

= 2,520

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3 years ago

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