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anygoal [31]
3 years ago
12

Here's an experiment you can try. Start by folding an ordinary sheet of typing paper exactly in half. Then fold it in half over

and over again. You will find that, try as you might, you can't fold it more than 6 times. If a single sheet of paper is .0125 cm thick, how thick is the last, 6-fold wad of paper?
Mathematics
1 answer:
poizon [28]3 years ago
8 0
Well, you simply just multiply! 0.125 X 64 = 8 CM
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3 years ago
Use the method of cylindrical shells to find the volume V of the solid obtained by rotating the region bounded by the given curv
harkovskaia [24]

Answer:

Step-by-step explanation:

Let's give this a go here.  The volume formula for the shell method while rotating about a horizontal line is

V=2\pi \int\limits^a_b {p(y)h(y)} \, dy

where p(y) is the distance from the axis of rotation (the x-axis) to the center of the solid.  This is a positive distance and it is just y.

h(y) is the horizontal height of the function.  Our function starts at x = 0 and ends at the function itself, so h(y) = 3 + y^2.

In the shell method when rotating about a horizontal line, we need to use x = y equations, and y-intervals.  Setting up our integral then:

V=2\pi \int\limits^3_2 {y(3+y^2)} \, dy

We can simplify this a bit by distributing the y into the parenthesis:

V=2\pi \int\limits^3_2 {3y+y^3} \, dy

Integrating gives us

V=2\pi|\frac{3y^2}{2}+\frac{y^4}{4}| from 2 to 3

Using the First Fundamental Theorem of Calculus:

V=2\pi[\frac{135}{4}-\frac{40}{4}] which simplifies down to

V=\frac{95\pi}{2}

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Negative one

Step-by-step explanation:

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