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Katyanochek1 [597]
3 years ago
13

NEED HELP RIGHT NOW PLEASE HELP!!!!!!

Mathematics
2 answers:
Gekata [30.6K]3 years ago
3 0
The rule is to subtract 6
Vesna [10]3 years ago
3 0
The rule for the sequence subtract 6 or add -6
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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
After distributing, which equation is equivalent to -4(3x + 2) = 10a.-12x -8 = 10b.-12x + 8 = 10c.-12x -6 = 10d.-12x + 6 = 1
rodikova [14]

Answer:

Option A: -12x-8=10 is the correct answer.

Step-by-step explanation:

Given equation is:

-4 (3x+2) = 10

We will distribute the equation by multiplying the terms inside the brackets with -4.

Therefore,

-4*3x + 2*-4 = 10

-12x +(-8) = 10

-12x - 8 = 10

The equation -4 (3x+2) = 10 will become -12x-8=10 after distributing.

Hence,

Option A: -12x-8=10 is the correct answer.

5 0
3 years ago
the difference between a number and two times a number is seven the number is greater than zero what is the number
bagirrra123 [75]
7 is the answer

2x - x = 7
x = 7

3 0
3 years ago
0.31 repeating as a fraction
sukhopar [10]
I believe its 31/100! <span>To write 0.3111 as a fraction you have to write 0.3111 as numerator and put 1 as the denominator. Now you multiply numerator and denominator by 10 as long as you get in numerator the whole number.</span>

7 0
3 years ago
Read 2 more answers
Will give 25 points pleaseee help
Sonja [21]

Answer:

i don't understand anything what grade are you in

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
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