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2 years ago

Need help simplifying please.

Mathematics

1 answer:

qwelly [4]2 years ago

7 0

Answer:

14x² + 7y - 22

Step-by-step explanation:

Combine like terms.

5x² - 6y - 22 + 13y + 9x²

5x² + 9x² = 14x²

-6y + 13y = 7y

Reorder the terms.

14x² + 7y - 22

Hope that helps.

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The curves y = √x and y=(2-x) and the Cartesian axes form two distinct regions in the first quadrant. Find the volumes of rotati

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Answer:

Step-by-step explanation:

If you graph there would be two different regions. The first one would be

$y = \sqrt{x} \,\,\,\,, 0\leq x \leq 1 \\$

And the second one would be

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And if you rotate the second region around the "y" axis you get that

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If you revolve just the outer curve you get

If you rotate the first region around the x axis you get that

$A_1 =\pi \int\limits_{0}^{1} ( \sqrt{x})^2 dx = \frac{\pi}{2} = 1.5708$

And if you rotate the second region around the x axis you get that

$A_2 = \pi \int\limits_{1}^{2} (2-x)^2 dx = \frac{\pi}{3} = 1.0472$

And the sum would be 1.5708+1.0472 = 2.618

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