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3 years ago

Refer to the figure and find the volume V generated by rotating the given region about the specified line.

Mathematics

1 answer:

ANEK [815]3 years ago

7 0

Volume generated by the areas R2 + R3 around the line OC
= (1/3) pi 1^2 * 3 = pi sq units

Volume generated by area R2 around OC is found as follows

the equation of the curve can be written as x = y^4 / 81

Integral between limits y = 0 and 3 of the curve is

pi INT x^2 dy = INT pi y^8 / 81^2 dx

= pi [3^9 / 9*81^2]

= pi/3

So the volume generated by R3 about OC = pi - pi/3 = 2pi/3

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How do i graph x+4y=8

Andrew [12]

Answer:

x = 8 y = 2

(8,2)

Step-by-step explanation:

You have to find the value of both x and y

x + 4y = 8

to find x you have to cancel out y so,

x + 4(0) = 8

x = 8

to find y you have to cancel out x

0 + 4y = 8

4y = 8

divide both sides by 4

y = 2

Hope this Helps!!!

6 0

3 years ago

Algebraically determine if the relation y = x3 − 4x is symmetric with respect to the x-axis, y-axis, the origin or has no symmet

Gala2k [10]

$\bf y=x^3-4x
\\\\\\
\textit{check for y-axis symmetry}\\\\
\stackrel{x=-x}{y=(-x)^3-4(-x)}\implies y=(-x)(-x)(-x)+4x\implies \boxed{y=-x^3+4x}
\\\\\\
\textit{checking for x-axis symmetry}\\\\
\stackrel{y=-y}{(-y)=x^3-4x}\implies -y=x^3-4x\implies \boxed{y=-x^3+4x}
\\\\\\
\textit{checking for origin symmetry}\\\\
\stackrel{x=-x\qquad y=-y}{(-y)=(-x)^3-4(-x)}\implies -y=(-x)(-x)(-x)+4x
\\\\\\
-y=-x^3+4x\implies y=\cfrac{-x^3+4x}{-1}\implies \boxed{y=x^3-4x}\quad \checkmark$

notice, if you replace x = -x and y = -y accordingly for each test for symmetry, if the resulting function, is equal to the original function, then it has that type of symmetry.

7 0

3 years ago

I will Mark Brainlist ! Help! this is a geometry Question :D<br><br> Thank you!

rewona [7]

The answer is 8, you replace the x with the 8 4x8 will give you 32 than subtract that from 10, which will give you 22, so RE is 22 and MA is 22

4 0

2 years ago

Betty paints twice as fast as Dan. Working together, Dan and Betty can paint 2, 400 square feet in 4 hours. Another employee, Su

Natalija [7]

Answer:

2670 square feet. Option e.

Step-by-step explanation:

Dan and Betty can paint 2,400 square feet in 4 hours.

They can paint in one hour $\frac{2400}{4}$ = 600 square feet.

Since given that Betty paints twice as fast as Dan. Let us take an equation:

Let Betty = B, Dan = D and Sue = S

B = 2D

4(B+D) = 2400

4B + 4D = 2400

12D = 2400

D = 200 sq. ft.

B = 2D = 400 sq. ft.

Therefore, Dan can paint 200 square feet in 1 hour and Betty paints twice 400 square feet in 1 hour.

Now given three of them can paint 3,600 square feet in 3 hours.

3( B+D+S) = 3600

3B + 3D + 3S = 3600

3(400) + 3(200) + 3(S) = 3600

1200 + 600 + 3S = 3600

S = 600 Sq. ft.

Sue can paint 600 square feet in one hour.

So sue can paint in 4 hours and 27 minutes.

$(\frac{4+27}{60})$ × 600

= 2670 square feet. Option e.

8 0

3 years ago

What is the domain of the square root function graphed below?

PolarNik [594]

A because I just did it

8 0

2 years ago