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harkovskaia [24]
3 years ago
9

HELP ASAP WORTH 20 POINTS!!!​

Mathematics
1 answer:
AlekseyPX3 years ago
4 0

Answer:

what is the full question to this??

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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
3 years ago
The type of transformation PQRS undergoes is a . If vertex Q is at (-4, -5), then vertex Q′ is at ?
MissTica

Answer:

(-4, -5) it gives the answer in the question

Step-by-step explanation:

8 0
3 years ago
The tiles on the left contain functions written using function notation. Match each function with its input.
Degger [83]

Answer:

1. The input is f

2. The input is g

3. The input is h

Step-by-step explanation:

The value inside the bracket of the function is the input given to the function.

1. g(f) = 2f

The input is f

2. h(g) = -4+g

The input is g

3. f(h) = h - 7

The input is h

3 0
3 years ago
Read 2 more answers
Find the most important variable in the problem.
natali 33 [55]

Answer:

A

Step-by-step explanation:

Let

x = the number of phone available

If it would require 8 more phones, then the total number of phones will be x + 8.

A company hired an additional 12 employees, and every employee needed a phone, then

x + 8 = 12

x = 4

This means 4 phones were available (and 8 more needed to total in 12 phones for 12 new employees)

Hence, correct option is option A.

3 0
3 years ago
40 fifth graders went to a school trip 25%of the students went to see the space exhibit how many students is that
Zielflug [23.3K]
The answer would A. 20 students
3 0
3 years ago
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