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3 years ago

Why is it essential to operationally define the variables in a study?

Advanced Placement (AP)

1 answer:

Liula [17]3 years ago

3 0

Cuz you have to eat bootie

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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

7 0

3 years ago

Ano ang monsoon?o kahulugan ng monsoon

Keith_Richards [23]

Answer:

monsoon

Explanation:

5 0

3 years ago

35 points! Please help! No copy paste and no links! I will also mark you brainliest!

Sliva [168]

Answer:

I am in Iowa

Explanation:

We have hills: good for hikes.

I live 2 blocks away from the Mississippi: we get alot of floods.

Cold in the winter scalding in the summer.

I live on a mini hill so i don't get alot of floods.

I LOVE iowa sweet corn and hate every other corn.

Hope that this helped

Plz mark brainlist

4 0

3 years ago

ASAP PLEASE!!!!

prisoha [69]

Answer:

what were the answers?

Explanation:

4 0

3 years ago

Of what did the Franciscans take a vow?

Troyanec [42]

Answer:

Franciscans take the vows of poverty, chastity, and obedience.

Obedience is the vow to obey the will of God in the service of the community, the Church, and the self.

4 0

3 years ago