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1 answer:
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Cross sections of the volume are washers or annuli with outer radii <em>x(y)</em> + 1, where
<em>y</em> = <em>x(y) </em>² - 1 ==> <em>x(y)</em> = √(<em>y</em> + 1)
and inner radii 1. The distance between the outermost edge of each shell to the axis of revolution is then 1 + √(<em>y</em> + 1), and the distance between the innermost edge of <em>R</em> on the <em>y</em>-axis to the axis of revolution is 1.
For each value of <em>y</em> in the interval [-1, 3], the corresponding cross section has an area of
<em>π</em> (1 + √(<em>y</em> + 1))² - <em>π</em> (1)² = <em>π</em> (2√(<em>y</em> + 1) + <em>y</em> + 1)
Then the volume of the solid is the integral of this area over [-1, 3]:
Answer:
x = 6; ∠ONP = 24°
Step-by-step explanation:
1. Find the value of x
2. Find the measures of the angles
(a) x = 2
∠ ONP = x² - 2x = 2² - 2(2) = 4 - 4 = 0
This answer does not make sense because O lies in the interior of ∠MNP.
We disregard x = 2.
(b) x = 6
∠ ONP = x² - 2x = 6² - 2(6) = 36 - 12 = 24
