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2 years ago

13

There is more than one answer okay!!

1 answer:

Dennis_Churaev [7]2 years ago

7 0

-3, -(-3)
-1.5, 1.5
-(-9), -9

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Find the volume of the solid formed by revolving the region bounded by the graphs of y = x^3, x = 2, and y = 1 about the y-axis.

andrezito [222]

Since the rotation is about the y-axis, I'll integrate by dy.

$\displaystyle y=x^3\\x=\sqrt[3]y\\\\V=\pi \int \limits_1^8(2^2-(\sqrt[3]y)^2)\, dy\\V=\pi \Big[4x-\dfrac{3}{5}x^{\tfrac{5}{3}}\Big]_1^8\\V=\pi \left(4\cdot8-\dfrac{3}{5}\cdot8^{\tfrac{5}{3}\right-\left(4\cdot1-\dfrac{3}{5}\cdot1^{\tfrac{5}{3}\right)\right)\\V=\pi \left(32-\dfrac{96}{5}-\left(4-\dfrac{3}{5}\right)\right)\\V=\pi \left(\dfrac{64}{5}-\dfrac{17}{5}\right)\\V=\dfrac{47\pi}{5}$

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3 years ago

Name a combination of coins that is 125% of the value of a dollar.

sweet-ann [11.9K]

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2 years ago

Read 2 more answers

What is the sum of the first 12 terms of the geometric series below 1/2+2+8+32+

Georgia [21]

∴ $\frac{1}{2} +2+8+32.......12^{th}term$ =2796202.5

Step-by-step explanation:

First term(a) = $\frac{1}{2}$ common ratio(r) = $\frac{2}{\frac{1}{2} }$ =4

n= 12

$S_{n}=\frac{a(r^n-1)}{(r-1)}$

$S_{12}=\frac{\frac{1}{2}(4^{12}-1) }{4-1}$ =2796202.5

∴ $\frac{1}{2} +2+8+32.......12^{th}term$ =2796202.5

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3 years ago

Construct a 95% confidence interval for the population mean, mu. Assume the population has a normal distribution. A sample of

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Step-by-step explanation:

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3 years ago

Rewrite using distributive property. 7(2x + 6y)

GenaCL600 [577]

Answer:

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Step-by-step explanation:

7(2x+6y)

14x+42y

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2 years ago