Please do these, I am so confused. :(

A cone-shaped container has a height of 9 inches and diameter of 2 inches. It is filled with a liquid that is worth $2 per cubic

Vesnalui [34]

Volume liquid = volume of the cone = 1/3 * pi * r^2 * h = 1/3 *3.14 * 1^2 * 9

= 9.42 in^3

so total value = 2 * 9.42 = $18.84

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3 years ago

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(1 point) Each of the following statements is an attempt to show that a given series is convergent or divergent not using the Co

kvv77 [185]

Answer:

I.

CORRECT.

II.

CORRECT.

III.

CORRECT.

IV.

CORRECT.

V.

INCORRECT.

VI.

CORRECT

Step-by-step explanation:

To understand let us restate the comparison test in simple terms.

Comparison test :

Given $\text{Series}_A$ and $\text{Series}_B$ such that $\text{Series}_A < \text{Series}_B$ , then

1. If $\text{Series}_B$ converges then $\text{Series}_A$ converges as well.

2. If $\text{Series}_A$ diverges then $\text{Series}_B$ diverges as well.

Now to give you a more intuitive idea of what is going on, think about it like this. When the series on top converges it is like an "upper bound" for what you have on the bottom, therefore what you have on the bottom has to converge as well.

Similarly if what you have on the bottom explotes, then what you have on top will explote as well.

That's how I like to think about that intuitively.

Now, using those results let us examine the statements.

I.

$\frac{1}{n} < \frac{ln(n)}{n}$

Since the infinite sum of 1/n diverges in fact the infinite sum of ln(n)/n does not converge.

Therefore, CORRECT.

II.

$\frac{\arctan(n)}{n^3} < \frac{\pi}{2}\frac{1}{n^3}$

Since the infinite sum of $\frac{\pi}{2}\frac{1}{n^3}$ is in fact convergent then $\frac{\arctan(n)}{n^3}$ converges as well using the comparison theorem. Therefore