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nekit [7.7K]
3 years ago
14

What is the diameter of the base of the cone below, to the nearest foot, if the volume is 314 cubic feet? Use π = 3.14.

Mathematics
1 answer:
guajiro [1.7K]3 years ago
8 0

Answer:

Step-by-step explanation:

height of cone is not given.

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Answer:

We want to find:

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Because here we are taking the limit when n tends to infinity, we can use this approximation.

Then we get.

\lim_{n \to \infty} \frac{\sqrt[n]{n!} }{n} = \lim_{n \to \infty} \frac{\sqrt[n]{\sqrt{2*\pi*n} *(\frac{n}{e} )^n} }{n} =  \lim_{n \to \infty} \frac{n}{e*n} *\sqrt[2*n]{2*\pi*n}

Now we can just simplify this, so we get:

\lim_{n \to \infty} \frac{1}{e} *\sqrt[2*n]{2*\pi*n} \\

And we can rewrite it as:

\lim_{n \to \infty} \frac{1}{e} *(2*\pi*n)^{1/2n}

The important part here is the exponent, as n tends to infinite, the exponent tends to zero.

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7 0
3 years ago
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The probability would be 6/16 or 37.5% because there are 16 coins in total and 6 of them are worth more than 5 cents. :)
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Answer:

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