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2 years ago

Over the past 30 years, the number of undocumented immigrants in the United States *

Advanced Placement (AP)

1 answer:

alexandr402 [8]2 years ago

7 0

The answer is A only because immigrants have increased and so has boarder security.

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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

2 years ago

Why did Christianity take hold in some places more than in others?

zepelin [54]

- Christianity integrated most fully into regions where European colonial powers ruled, where there was an overwhelming European presence, where the established society had been defeated and disrupted, and where no literate world religion was already established.
- It had the least impact when it had to operate with the permission of non-Christian rulers, when it sought to convert in a society that was stable and well established, and when it sought to convert in a region where a literate world religion already existed.

Source: https://www.coursehero.com/file/p6tre7v/Big-Picture-Questions-1-Why-did-Christianity-take-hold-in-some-places-more-than/

5 0

2 years ago

Why would a town planner use a map at the 1:24,000 scale rather than a map at the 1:250,000 scale? The map at the 1:24,000 scale

Artemon [7]

Answer:

A The map at the 1:24,000 scale is easily converted to non-metric measurements.The map at the 1:24,000 scale shows the town close-up in more detail.

Explanation:

A scale of ration 1: 24,000 indicates that the distance on the map to the actual ground distance is large scale map and shows are a detailed close-up of the map. Also, they can be easily converted and thus a town planner decides to make use of this map for planning.

3 0

3 years ago

What does the SAT reading test requires students to do?

zhuklara [117]

Answer:

SAT Reading Passages will extract from U.S. and World Literature, History/Social Studies, and Science.

8 0

2 years ago

The corporation became a popular form of business organization during the post-Civil War period because it

Viktor [21]

The correct answer for the question that is being presented above is this one: "a. enabled corporate executives to supervise daily business activities more closely." The corporation became a popular form of business organization during the post-Civil War period because it <span>enabled corporate executives to supervise daily business activities more closely.</span>

5 0

3 years ago