The disk method will only involve a single integral. I've attached a sketch of the bounded region (in red) and one such disk made by revolving it around the y-axis.
Such a disk has radius x = 1/y and height/thickness ∆y, so that the volume of one such disk is
π (radius) (height) = π (1/y)² ∆y = π/y² ∆y
and the volume of a stack of n such disks is
where 
is a point sampled from the interval [1, 5].
As we refine the solid by adding increasingly more, increasingly thinner disks, so that ∆y converges to 0, the sum converges to a definite integral that gives the exact volume V,
Answer:
The second one and the fourth one :)
This problem is a multi step problem. All you have to do is break it down into parts to make it easier. We can start by finding the diameter of the inner circle.
1. circumference = πd (Since the circumference is given as 44, and we know to use 22/7 for π, divide 44 by 22/7 to get d.)
44 / 22/7 = about 14.0 when rounded
2. Now add +8 to the 14 since we know that there are 4 ft. on both sides of the small inner circle.
14 + 8 = 22
3) The last step gave us the diameter of the bigger outer circle. Now, we have to plug in the 22 for d in the formula for circumference to find the circumference of the outer circle.
c = πd → c = 22 * 22/7 = 484/7 (484/7 = about 69 when rounded as a decimal)
4) The last step now is to subtract the circumferences, since the problem was asking for how much greater the outer circle's circumference is than the inner circle.
69 - 44 = 25
Your answer should be about 25 ft.
********** Note the answer they are looking for may be slightly different depending on whether they were looking for a fraction or decimal answer and where they rounded. ********************************************************
The area of the circle is 314.16
The formula is a= pi times the radius squared
The possible values of x are 3 and 7
<h3>Solving rational expressions</h3>
Given the rational expression below;
√60-8x = x - 9
Square both sides to have:
(60-8x)² = (x-9)²
60-8x = x²-18x+81
Equate to zero to have;
x²-18x+81 - 60 + 8x = 0
x² - 10x + 21 = 0
x² -3x-7x +21 = 0
x(x-3)-7(x-3) = 0
x = 3 and 7
Hence the possible values of x are 3 and 7
Learn more on rational expression here: brainly.com/question/25292194
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