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ludmilkaskok [199]
3 years ago
7

I need help please ..

Mathematics
1 answer:
koban [17]3 years ago
4 0

A is 18

B is 162

C is 18

D is 162

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A solid lies between planes perpendicular to the x-axis at x tox=. The cross sections perpendicular to the x-axis are circular d
cluponka [151]

It's unclear what the planes are supposed to be, so I'll take x=a and x=b with 0\le a.

The cross sections are disks with diameter \csc x-\cot x, so each disk of thickness \Delta x has a volume of

\dfrac{\pi(\csc x-\cot x)^2}4\Delta x

Then taking infinitesimally thin disks, we find the solid has a volume of

\displaystyle\frac\pi4\int_a^b(\csc x-\cot x)^2\,\mathrm dx

Since

(\csc x-\cot x)^2=2\csc^2x-2\csc x\cot x-1

and

\dfrac{\mathrm d(\csc x)}{\mathrm dx}=-\csc x\cot x

\dfrac{\mathrm d(\cot x)}{\mathrm dx}=-\csc^2x

it follows that the volume is

\displaystyle\frac\pi4\left(-2\cot x+2\csc x-x\right)\bigg|_a^b

=\dfrac\pi4(2(\cot a-\cot b)+2(\csc b-\csc a)+a-b)

=\dfrac\pi4\left(2\tan\dfrac b2-2\tan\dfrac a2+a-b\right)

3 0
3 years ago
What is the answer to this: X3 + Y3 = Z3 why is the answer Z3
Yuki888 [10]
Because x+y = z like a+b= c
6 0
2 years ago
It looks easy i just dont know how to do it can someone help me out
Arada [10]

Answer:

16

Step-by-step explanation:

16+4x = 10 +14

-16             -16

4x = 8

/4      /4

x=2

8x=8(2)

=16

3 0
2 years ago
What is i^30?<br>0A. -i<br>0B. -1<br>0C. 1<br>0D. i​
kozerog [31]

Answer:   B

Step-by-step explanation:

-1 will be your answer. (B)

6 0
3 years ago
y = c1 cos(5x) + c2 sin(5x) is a two-parameter family of solutions of the second-order DE y'' + 25y = 0. If possible, find a sol
TEA [102]

Answer:

y = 2cos5x-9/5sin5x

Step-by-step explanation:

Given the solution to the differential equation y'' + 25y = 0 to be

y = c1 cos(5x) + c2 sin(5x). In order to find the solution to the differential equation given the boundary conditions y(0) = 1, y'(π) = 9, we need to first get the constant c1 and c2 and substitute the values back into the original solution.

According to the boundary condition y(0) = 2, it means when x = 0, y = 2

On substituting;

2 = c1cos(5(0)) + c2sin(5(0))

2 = c1cos0+c2sin0

2 = c1 + 0

c1 = 2

Substituting the other boundary condition y'(π) = 9, to do that we need to first get the first differential of y(x) i.e y'(x). Given

y(x) = c1cos5x + c2sin5x

y'(x) = -5c1sin5x + 5c2cos5x

If y'(π) = 9, this means when x = π, y'(x) = 9

On substituting;

9 = -5c1sin5π + 5c2cos5π

9 = -5c1(0) + 5c2(-1)

9 = 0-5c2

-5c2 = 9

c2 = -9/5

Substituting c1 = 2 and c2 = -9/5 into the solution to the general differential equation

y = c1 cos(5x) + c2 sin(5x) will give

y = 2cos5x-9/5sin5x

The final expression gives the required solution to the differential equation.

3 0
3 years ago
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