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3 years ago

Write the equation of a line that is horizontal and contains the point (-4, 1)

Mathematics

1 answer:

olga nikolaevna [1]3 years ago

6 0

Answer:

y = 1

Step-by-step explanation:

The slope of a horizontal line is 0 which leaves you with only the y-intercept

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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

What is the area of this shape?

m_a_m_a [10]

Step-by-step explanation:

idk the answer but find the area of a circle with the radius of 45 m and then find the area of the rectangle then add them together.

5 0

3 years ago

5. PLEASE HELP

lana66690 [7]

Answer:

The potential energy of the ball having 2kg mass would be $392$ J

Step-by-step explanation:

I am assuming the ball has a mass of 2 kg, as you have not mentioned the mass of a ball.

Considering the formula for calculating the gravitational potential energy

$G.P.E\:=\:m.g.h$

$m = 2$ kg

Acceleration of gravity = g = 9.8 $ms^{-2}$

As the ball is on the height = h = 20 meters

So,

$G.P.E\:=\:(2)(9.8)(20)$

$G.P.E\:=392$ J

Therefore, the potential energy of the ball = $392$ J

Keywords: potential energy, Gravitation potential energy

Learn more potential energy from brainly.com/question/14022793

#learnwithBrainly

5 0

3 years ago

Which number line shows a fraction equivalent to 4.5?

Alchen [17]

The forth picture is the one that represents 4.5

3 0

3 years ago

Read 2 more answers

approximately 30,400 citizens of a country died in automobile accident in 2015. express this toll in deaths per day

sertanlavr [38]

If you divide 30,400 by the amount of days in a year 365 you should get 83.3 but because you cant have part of a person lets leave it at 83 death per day

6 0

3 years ago