What is the volume of the cylinder below if radius is 11 and height is 15?

I dont really know how to do soh cah toah. please help me find x.

Ipatiy [6.2K]

First notice that the triangle with sides $x,y,a$ and the triangle with sides $z,a+b,x$ are similar. This is true because the angle between sides $x,y$ in the smaller triangle is clearly $30^\circ$ , while the angle between sides $y,z$ in the larger triangle is clearly $60^\circ$ . So the triangles are similar with sides $x,y,a$ corresponding to $a+b,z,x$ , respectively.

Now both triangles are $30^\circ-60^\circ-90^\circ$ , which means there's a convenient ratio between its sides. If the length of the shortest leg is $\ell_1$ , then the length of the longer leg is $\ell_2=\sqrt3\ell_1$ and the hypotenuse has length $\ell_3=\sqrt{{\ell_1}^2+{\ell_2}^2}=2\ell_1$ .

Since $x$ is the shortest leg in the larger triangle, it follows that $a+b=2x$ , so $a+b=15=2x\implies x=\dfrac{15}2$

4 0

4 years ago

BRAINIEST IF CORRECT (best to explain it will get it)

lana [24]

Answer:

C.

Step-by-step explanation:

PEMDAS

-6 x 12p = -72p

-6 x -8n = 48n

48n - 47n = n

5 0

3 years ago

At 1 pm, there were 16 seagulls on the beach. At 3 pm, there were 40 seagulls. What is the constant rate of change?

beks73 [17]

<span>The answer is (change of amount) / (change of time). For the change of amount, the numerator is 40 seagulls - 16 seagulls, leaving a total of 24 seagulls. For the change of time, the denominator is 3 pm - 1 pm, leaving a total of a 2 hour difference. The answer becomes 24 seagulls / 2 hours, or 12 seagulls per hour when simplified.</span>

4 0

3 years ago

Determine whether the following series converges or diverges using the integral test. Be sure to verify that the integral test c

Finger [1]

By using the integral test, series converges

What is an integral test for convergence and divergence?

⇒ It is used to prove the divergence or convergence of series. This test is called the integral test, which compares an infinite sum to an improper integral. It is important to note that this test can only be applied when we are considering a series whose terms are all positive.

How to know if a series is converging or diverging?

If the limit exists and is a finite number (a number less than infinity), we say the integral converges. If the limit is ±∞ or does not exist, we say the integral diverges.

let aₓ= f (x) is any function

⇒ In order for the integral test to work The function must be positive it has to be continuous and it has to be decreasing when x≥1

If the integral converges it means the series is also converging

If the integral diverges it means the series is also diverging

The sequence $k^{3} /{e^{k^{4} }$ is clearly positive and decreases for k∈N then by the integral test,

$\int\limits^\infty_1 {x^{3} /e^{x^4} dx$ $\leq\displaystyle \sum^{\infty}_{k = 1} {x^{3} /e^{x^{4}$

and

$\int\limits^\infty_1 {x^{3} /e^{x^4} dx$ $=1/4\int\limits^\infty_1 {x^{3} /e^{-u} du$

⇒ $1/4 < \infty$

So it comes with a finite value hence the series converges

Learn more about the integral tests here :

brainly.com/question/15394015

#SPJ1

4 0

1 year ago

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Audrey has .x pounds of red grapes and y pounds of

mojhsa [17]

We are looking at points in the form (x, y).

Let x = pounds of red grapes

Let y = pounds of green grapes

Audrey has less than 5 pounds of grapes. Here is where I think you made a typo. The question should indicate if Audrey has 5 pounds less of red grapes or green grapes.

Go back and check your original problem and then come back.

6 0

3 years ago

Read 2 more answers