MATHEMATICS HIGH SCHOOL

The base of a solid in the xy-plane is a circle with a radius of 3. cross sections of the solid perpendicular to the x-axis are squares. set up the integral to arrive at the volume of the solid and solve.

Answers

Answer 1
Answer:

Answer:

\large \boxed{144}

Step-by-step explanation:

1. Set up the integral.

The equation for the circle is

x² + y² = 9

The bottom corners of the square are at  

(x, \sqrt{9 - x^(2)})\text{ and } (x, -\sqrt{9 - x^(2)})

The length (a) of a side is

a = 2\sqrt{9 - x^(2)}

and the area (A) of the square cross-section is

A = a² = 4(9 - x²)

The volume (V) of the solid is

V = \displaystyle \int_(-3)^(3) {4(9 - x^(2))} dx

2. Solve the integral

\displaystyle \int_(-3)^(3) {4(9 - x^(2))} dx = 4\begin{bmatrix}9x - (1)/(3)x^(3)\end{bmatrix}_(-3)^(3)= 4[(27 - 9) - (-27 +9)] = 4[18 - (-18)]\n= 4[18 + 18] = 4 *36 = \mathbf{144}\n\n\text{The volume of the solid is $\large \boxed{\mathbf{144}}$}

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Which can be represented by the expression 17 – 2x?
At a concert 2/5 of the people were men, there were 3 times as many women as children. If there were 45 more men than children, how many people were there at the concert.
Need help ASAP! Anyone know?
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In 36 days a girl spent 18 dollars. On average, what did she spend daily?

Answers

On average, she spent 18/36 = 0.5$

Tai resized a photograph that was 8 inches by 10 inches so that it would fit on a 4 inch by 4 inch page. Find the maximum dimensions of the reduced photograph. An explanation wold be great, please. Thank you so much!

Answers

ok so it has to be max 4 inches when resized since the max size is 4 inches

10 is max of original so
they have to be shrunk in same ratio so find ratio of shrink
10 times ratio=4
divide both sides by 10
ratio=4/10=2/5
so multiply the measuremet by 2/5 to find new dimention

8 times 2/5=16/5=3 and 1/5=3.2


new dimentions is 4 by 3.2 inches

in a circle graph, what is the measure of the central angle of a sector that represents 24% of the whole?

Answers

0.24*360=86.4 degrees
24/100 =x/360

100x=8640
x=86.4

Question 13 (Multiple Choice Worth 1 points)(03.01 MC)

Which expression is equivalent to 32 + 16?

8(4 + 2)
8(24 + 8)
7(4 + 2)
7(24 + 8)

Answers

8(4+2) This is so because 8x 4= 32 8x2= 16 Therefore 32+16
8(4+2) = 8x4 + 8x2 = 32 + 16

What percent of 55 is 34

Answers

So,

To what percent 34 is of 55, we first need to find the fraction equivalent.

34 out of 55 parts or 34/55

Divide 34 by 55.

34/55 = 0.61818...

Now, we move the decimal point 2 places to the right in order to convert it to a percent.

6.1818...
61.81818...

Rounded to the nearest hundredth: 61.82%
Rounded to the nearest tenth: 61.8%
Rounded to the nearest percent: 62%

(8n+10) divided by 2, for n=5

Answers

Answer: 25

Step-by-step explanation:

(8(5) + 10) / 2

40 + 10 / 2

50 / 2

25
The answer would be 25. (8(5)+10 = 50 50/2 = 25. Hope that helped!
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