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2 years ago

PLEASE HELP ASAP 25 POINTS

Mathematics

1 answer:

motikmotik2 years ago

6 0

Answer:

it's b

Step-by-step explanation:

If you can use your phone in class, I highly suggest the desmos app because you can just put the equations in and it shows you everything

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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

I need help please #19

o-na [289]

Answer:

Step-by-step explanation:

5 0

2 years ago

Would you rather buy 18 eggs 2/8.00 or 18 eggs for 97c each

Vesnalui [34]

Answer:

18 eggs for 97 cents.

Step-by-step explanation:

.97/18 = 5 cents

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2 years ago

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Help Me Please! I will give you 5 stars if your answer is correct!

lys-0071 [83]

Answer:

......................

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2 years ago

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Help pls ill love you forever

Nesterboy [21]

Answer:

$y-4=\frac{1}{5}(x-7)$

Step-by-step explanation:

The point-slope form of a line is given by:

$y-y_1=m(x-x_1)$

Where

(x_1,y_1) is the coordinate pair (any of the points given)

m is the slope. The ratio of change in y coordinates by x coordinates

Let's calculate the slope:

$m=\frac{4-3}{7-2}\\m=\frac{1}{5}$

Now, it is given "y - 4", so y_1 is 4, so they are using the coordinate pair (7,4). So we can say x_1 = 7

Now we have all the values, lets write the equation:

$y-y_1=m(x-x_1)\\y-4=\frac{1}{5}(x-7)$

This is the point-slope form.

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3 years ago