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3 years ago

The height of a cylinder is twice the radius of its base.

Mathematics

1 answer:

Ber [7]3 years ago

6 0

Let x represent radius of circle.

We have been given that the height of a cylinder is twice the radius of its base. So height of cylinder would be $2x$ .

Now we will use volume of cylinder formula to our given problem.

$V=\pi r^2h$ , where,

r = Radius of base of cylinder,

h = Height of cylinder.

Upon substituting our given values, we will get:

$V=\pi\cdot x^2\cdot 2x$

$V=2x^3\pi$

Therefore, our required volume expression would be $2x^3\pi$ .

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Find the radius of convergence, r, of the series. ? n2xn 7 · 14 · 21 · ? · (7n) n = 1

defon

I'm guessing the series is supposed to be

$\displaystyle\sum_{n=1}^\infty\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}$

By the ratio test, the series converges if the following limit is less than 1.

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7\cdot14\cdot21\cdot\cdots\cdot(7n)\cdot(7(n+1))}}{\frac{n^2x^n}{7\cdot14\cdot21\cdot\cdots\cdot(7n)}}\right|$

The first $n$ terms in the numerator's denominator cancel with the denominator's denominator:

$\displaystyle\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2x^{n+1}}{7(n+1)}}{n^2x^n}\right|$

$|x^n|$ also cancels out and the remaining factor of $|x|$ can be pulled out of the limit (as it doesn't depend on $n$ ).

$\displaystyle|x|\lim_{n\to\infty}\left|\frac{\frac{(n+1)^2}{7(n+1)}}{n^2}\right|=|x|\lim_{n\to\infty}\frac{|n+1|}{7n^2}=0$

which means the series converges everywhere (independently of $x$ ), and so the radius of convergence is infinite.

3 0

3 years ago

On Roberto's shelf there are:

Sergio039 [100]

Answer:

he would have a 20% chance he will pick a history book, so in decimal form it would be .2

Step-by-step explanation:

7+6+4+3=20

20*5=100

5*4=20

5 0

3 years ago

Write down the bearing of: (a) Henly from Dinder (b) Dinder from Weare (c) Weare from Dinder (d) Weare from Henly (e) Dinder fro

Neko [114]

The bearing of the individuals from each other are as indicated below;

S45°E
N25°E
S65°E
S15°E
N45°E
N75°E

<h3>What is bearing of Henley from Dinder?</h3>

It follows from the task content that the bearing of the individuals from each other are expected to be determined.

a) For Henley from Dinder; it follows from observation that Henley is; S45°E of Dinder's position.

b) For Dinder from Weare; it follows from observation that Dinder is; N25°E of Weare's position.

c) For Weare from Dinder; it follows from observation that Weare is; S65°E of Dinder's position.

d) For Weare from Henly; it follows from observation that Weare is; S15°E of Dinder's position.

e) For Dinder from Henly; it follows from observation that Dinder is; N45°E of Henly's position.

f) For Henly from Weare; it follows from observation that Henly is; N75°E of Weare's position.