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DaniilM [7]
3 years ago
12

Please I need this asap, my answer is wrong

Mathematics
1 answer:
zavuch27 [327]3 years ago
7 0

Answer: 512\pi

Step-by-step explanation:

Given

Equation of curve is x=\sqrt{8+y}

When this curve is rotated about the y-axis, then volume generated is given by

V=\int_{a}^{b}\pi x^2dy

When x=0, y=-8

Put the limits and solve the integral

\Rightarrow V=\int_{-8}^{24}\pi (8+y)dy\\\\\Rightarrow V=\pi\left (  8y+\dfrac{y^2}{2}\right )_{-8}^{24}\\\\\Rightarrow V=\pi \left (  8\times 32+\dfrac{24^2-8^2}{2}\right )\\\\\Rightarrow V=512\pi

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Since the intersection is - by definition - common to both sets, we can work out the number of people that use only the fitness suite or the swimming pool.

We know that 57 people use the fitness suite, but 36 of those are already counted in the intersection. So, 57-36=21 people use only the fitness suite.

The same goes for the swimming pool: 49-36=13 people use only the swimming pool.

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