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Electric charge is distributed over the disk x2 + y2 ≤ 16 so that the charge density at (x, y) is rho(x, y) = 2x + 2y + 2x2 + 2y

professor190 [17]

Answer:

Required total charge is $256\pi$ coulombs per square meter.

Step-by-step explanation:

Given electric charge is dristributed over the disk,

$x^2=y^2\leq 16$ so that the charge density at (x,y) is,

$\rho (x,y)=2x+2y+2x^2+2y^2$

To find total charge on the disk let Q be the total charge and $x=r\cos\theta,y=r\sin\theta$ so that,

$Q={\int\int}_Q\rho(x,y) dA$ where A is the surface of disk.

$=\int_{0}^{2\pi}\int_{0}^{4}(2x+2y+2x^2+2y^2)dA$

$=\int_{0}^{2\pi}\int_{0}^{4}(2r\cos\theta+2r\sin\theta+2r^2 \cos^{2}\theta+2r^2\sin^2\theta)rdrd\theta$

$=2\int_{0}^{2\pi}\int_{0}^{4}r^2(\cos\theta+\sin\theta)drd\theta+2\int_{0}^{2\pi}\int_{0}^{4}r^3drd\theta$

$=\frac{2}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)\Big[r^3\Big]_{0}^{4}d\theta+2\int_{0}^{2\pi}\Big[\frac{r^4}{4}\Big]d\theta$

$=\frac{128}{3}\int_{0}^{2\pi}(\sin\theta+\cos\theta)d\theta+128\int_{0}^{2\pi}d\theta$

$=\frac{128}{3}\Big[\sin\theta-\cos\theta\Big]_{0}^{2\pi}+128\times 2\pi$

$=\frac{128}{3}\Big[\sin 2\pi-\cos 2\pi-\sin 0+\cos 0\Big]+256\pi$

$=256\pi$

Hence total charge is $256\pi$ coulombs per square meter.

3 0

2 years ago

PLEASE HELP 13 INSTEAD OF FIVE POINTS!!!! I REALLY NEED HELP

devlian [24]

A is what the answer is

6 0

3 years ago

Read 2 more answers

Please tell me how much it would be for 1

Monica [59]

Answer:

small

per Oz

0.269 dollars

medium

per Oz

0.227 dollars

large

per Oz

0.1845 dollars

3 0

2 years ago

Read 2 more answers

Factor 15z^2+17z-18 please show work

siniylev [52]

There is no common factor between 15, 17 and 18 because 17 is prime.

15z² +17z - 18 =

d = 17² - 4.15.-18

d = 289 + 1080

d = 1369

z = (-17 +/- \/1369) : 2 * 15

z = (-17 + 37) : 30

z' = 20 : 30 = 2/3

z" = (-17 - 37) : 30

z" = -54 : 30 = -1.8

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7 0

3 years ago

the elephants at the norfolk zoo are fed 1/2 a barrel of corn each day. the buffalo are fed 7/10 as much corn as the elephants.

maksim [4K]

7/20 barrels of corn are the buffalo fed each day.

How to solve word problems?

It's actually fairly easy to solve word problems using a tried-and-true step-by-step approach.

Aloud to yourself, read the issue.
Make a Drawing.
Ask yourself, "What am I looking for?"
List the items that have been provided.
Locate the key phrases.
Solve.
Verify your work.

Here are some actions to take:

Recognize the issue, including all the terminology used to describe it. Recognize what you need to look for, Recognize the issue's context.
Convert the issue into an equation. Give the unknown a variable (or variables) to symbolize, Indicate exactly what the variable stands for.
Put the strategy into action and find a solution.

Given:

Elephants at the Norfolk zoo are fed = 1/2

Buffalo are fed 7/10 as much corn as the elephants = 7/10 * Elephants fed

= 7/10 * 1/2

= 7/20

Hence, 7/20 barrels of corn are the buffalo fed each day.

To know more about word problems check the below link:

brainly.com/question/13818690

#SPJ4

4 0

1 year ago