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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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Answer:

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General Formulas and Concepts:

<u>Pre-Algebra</u>

Order of Operations: BPEMDAS

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Equality Properties

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<u>Step 1: Define</u>

<u />\displaystyle \frac{6}{19} = \frac{x - 12}{2x - 2}<u />

<u />

<u>Step 2: Solve for </u><em><u>x</u></em>

  1. Cross-multiply:                     \displaystyle 6(2x - 2) = 19(x - 12)
  2. Distribute:                             \displaystyle 12x - 12 = 19x - 228
  3. Isolate <em>x</em> terms:                     \displaystyle -12 = 7x - 228
  4. Isolate <em>x</em> term:                      \displaystyle 216 = 7x
  5. Isolate <em>x</em>:                               \displaystyle \frac{216}{7} = x
  6. Rewrite:                                \displaystyle x = \frac{216}{7}
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