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Maurinko [17]
3 years ago
10

What is the difference between x-12=y and y=x-12?

Mathematics
1 answer:
ANEK [815]3 years ago
8 0
There no difference between x-12=y and y=x-12
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Faces: <br> Edges: <br> Vertices:
sesenic [268]

Answer:

Below.

Step-by-step explanation:

This is a square based pyramid.

There are:

5 Faces (one on the base and 4 side faces)

8 edges.   ( 4 on base and 4 on side)

5 vertices   (4 on the base and one on the top)

5 0
1 year ago
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Look at image please
Kay [80]

Answer:

a

Step-by-step explanation:

It begins at the point (0, -1200). 0 tickets sold, $1200 spent.

$5 for a ticket means that slope =5.

(600, 1800) and (0,-1200)

m= (1800-(-1200))/(600-0)=3000/600=5

slope=5

Answer is a.

8 0
3 years ago
14. A triangle ABC is drawn on a coordinate plane. Find the length of the side BC.
Sveta_85 [38]
My best guess would be A
3 0
3 years ago
Calculus Problem
Roman55 [17]

The two parabolas intersect for

8-x^2 = x^2 \implies 2x^2 = 8 \implies x^2 = 4 \implies x=\pm2

and so the base of each solid is the set

B = \left\{(x,y) \,:\, -2\le x\le2 \text{ and } x^2 \le y \le 8-x^2\right\}

The side length of each cross section that coincides with B is equal to the vertical distance between the two parabolas, |x^2-(8-x^2)| = 2|x^2-4|. But since -2 ≤ x ≤ 2, this reduces to 2(x^2-4).

a. Square cross sections will contribute a volume of

\left(2(x^2-4)\right)^2 \, \Delta x = 4(x^2-4)^2 \, \Delta x

where ∆x is the thickness of the section. Then the volume would be

\displaystyle \int_{-2}^2 4(x^2-4)^2 \, dx = 8 \int_0^2 (x^2-4)^2 \, dx \\\\ = 8 \int_0^2 (x^4-8x^2+16) \, dx \\\\ = 8 \left(\frac{2^5}5 - \frac{8\times2^3}3 + 16\times2\right) = \boxed{\frac{2048}{15}}

where we take advantage of symmetry in the first line.

b. For a semicircle, the side length we found earlier corresponds to diameter. Each semicircular cross section will contribute a volume of

\dfrac\pi8 \left(2(x^2-4)\right)^2 \, \Delta x = \dfrac\pi2 (x^2-4)^2 \, \Delta x

We end up with the same integral as before except for the leading constant:

\displaystyle \int_{-2}^2 \frac\pi2 (x^2-4)^2 \, dx = \pi \int_0^2 (x^2-4)^2 \, dx

Using the result of part (a), the volume is

\displaystyle \frac\pi8 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{256\pi}{15}}}

c. An equilateral triangle with side length s has area √3/4 s², hence the volume of a given section is

\dfrac{\sqrt3}4 \left(2(x^2-4)\right)^2 \, \Delta x = \sqrt3 (x^2-4)^2 \, \Delta x

and using the result of part (a) again, the volume is

\displaystyle \int_{-2}^2 \sqrt 3(x^2-4)^2 \, dx = \frac{\sqrt3}4 \times 8 \int_0^2 (x^2-4)^2 \, dx = \boxed{\frac{512}{5\sqrt3}}

7 0
2 years ago
HELP PLEASE I DON'T UNDERSTAND
liraira [26]
If I counted correctly, the answer would be 52/150. You just need to simplify the fraction. I'll recount soon, and update if it changes.
3 0
3 years ago
Read 2 more answers
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