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3 years ago

A measure of the degree of relatedness between two variables is

Advanced Placement (AP)

1 answer:

ivann1987 [24]3 years ago

3 0

Correlation- a measure of association between two variable.

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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

Giving 50 points for one question PLZ help fast for a test due in 20 min and this is the only one I don't know!

Salsk061 [2.6K]

I think it is planet a orbits faster than planet b so sorry if I get it wrong but I’m pretty sure that’s what it is good luck!

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2 years ago

How many solutions exist for the given equation? 3x + 13 = 3(x + 6) + 1

Deffense [45]

Answer:

There is no solutions to this problem.

Because when you solve it you get an untrue statement. When this happens, it means that there is nothing that can make it true.

Explanation:

3x + 13 = 3(x + 6) + 1 use distribute property

3x + 13 = 3x + 18 + 1 combine like terms

3x + 13 = 3x + 19 subtract 3x from both sides

13 = 19

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2 years ago

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Which best describes how changes in air pressure can affect the development of a hurricane?

Vadim26 [7]

Hurricanes are formed in tropical places. And hurricanes and thunderstorms are two totally different things! And so the best answer is C. I hope this helped u!

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3 years ago

Which of the following characteristics of populations are associated with highly developed countries?

Oksana_A [137]

It’s a higher fertility rate high rate of industrialization and longer life expectancy

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2 years ago