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3 years ago

AYUDAAA PORFAVOOOOOOR!!

Mathematics

2 answers:

ioda3 years ago

6 0

Answer:

La respuesta seria 3 espero que esto ayude

Step-by-step explanation:

galben [10]3 years ago

4 0

Answer:

Step-by-step explanation:

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What is x, if the volume of the cylinder is 768pi rcm3?

AVprozaik [17]

let's recall Cavalieri's Principle, <u>solids with equal altitudes and cross-sectional areas at each height have the same volume</u>, so even though this cylinder is slanted with a height = x and a radius = 8, the cross-sectional areas from the bottom to top are the same thickness and thus the same area, so its volume will be the same as a cylinder with the same height and radius that is not slanted.

$\bf \textit{volume of a cylinder}\\\\ V=\pi r^2 h~~ \begin{cases} r=radius\\ h=height\\ \cline{1-1} r=8\\ h=x\\ V=768\pi \end{cases}\implies 768\pi =\pi (8)^2(x)\implies 768\pi =64\pi x \\\\\\ \cfrac{768\pi }{64\pi }=x\implies 12=x$

5 0

3 years ago

Use the Pythagorean theorem to find the distance between the two points ANB round your answer to the nearest hundredth

jek_recluse [69]

Answer:

5.39 units

Step-by-step explanation:

Pythagorean theorem: $a^{2} + b^{2} = c^{2}$

Let point (-2,1) be C

Line segment AC would be 2 units long.

Line segment BC would be 5 units long.

Insert the length of the line segments in to the Pythagorean theorem

$2^{2} + 5^{2}$

4 + 25 = 29

$\sqrt{29}$ ≅ 5.385

6 0

3 years ago

How can you prove that csc^2(θ)tan^2(θ)-1=tan^2(θ)

Oxana [17]

Answer:

Make use of the fact that as long as $\sin(\theta) \ne 0$ and $\cos(\theta) \ne 0$ :

$\displaystyle \tan(\theta) = \frac{\sin(\theta)}{\cos(\theta)}$ .

$\displaystyle \csc(\theta) = \frac{1}{\sin(\theta)}$ .

$\sin^{2}(\theta) + \cos^{2}(\theta) = 1$ .

Step-by-step explanation:

Assume that $\sin(\theta) \ne 0$ and $\cos(\theta) \ne 0$ .

Make use of the fact that $\tan(\theta) = (\sin(\theta)) / (\cos(\theta))$ and $\csc(\theta) = (1) / (\sin(\theta))$ to rewrite the given expression as a combination of $\sin(\theta)$ and $\cos(\theta)$ .

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \left(\frac{1}{\sin(\theta)}\right)^{2} \, \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} - 1 \\ =\; & \frac{\sin^{2}(\theta)}{\sin^{2}(\theta)\, \cos^{2}(\theta)} - 1\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1\end{aligned}$ .

Since $\cos(\theta) \ne 0$ :

$\displaystyle 1 = \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)}$ .

Substitute this equality into the expression:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots\\ =\; & \frac{1}{\cos^{2}(\theta)} - 1 \\ =\; & \frac{1}{\cos^{2}(\theta)} - \frac{\cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}$ .

By the Pythagorean identity, $\sin^{2}(\theta) + \cos^{2}(\theta) = 1$ . Rearrange this identity to obtain:

$\sin^{2}(\theta) = 1 - \cos^{2}(\theta)$ .

Substitute this equality into the expression:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{1 - \cos^{2}(\theta)}{\cos^{2}(\theta)} \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\end{aligned}$ .

Again, make use of the fact that $\tan(\theta) = (\sin(\theta)) / (\cos(\theta))$ to obtain the desired result:

$\begin{aligned}& \csc^{2}(\theta) \, \tan^{2}(\theta) - 1\\ =\; & \cdots \\ =\; & \frac{\sin^{2}(\theta)}{\cos^{2}(\theta)}\\ =\; & \left(\frac{\sin(\theta)}{\cos(\theta)}\right)^{2} \\ =\; & \tan^{2}(\theta)\end{aligned}$ .

5 0

2 years ago

Sasha has some pennies nickels and dimes in her pocket the number of coins is 18 the expression 0.01 p + 0.05 n + 0.10 D represe

MAXImum [283]

A) p + n + d = 18
B) .01p + .05n + .10d = 1.14
C) 2p = d

Substituting C) into A)
A) p + n + 2p = 18 equals
A) 3p + n = 18
Substituting C) into B)
B) .01p + .05n + .10 *2p = 1.14
B) .01p + .05n + .2p = 1.14
B) .21p + .05n = 1.14
Taking equation A)
A) 3p + n = 18 and multiplying it by -.05
A) -.15p -.05n = -.90 Then adding this to B)
B) .21p + .05n = 1.14
.06p = .24
Therefore there are 4 pennies.
(I'll leave it to you to determine the nickels and dimes.)
**************************************************************************
Oh what the heck, I'll finish it for you.

Looking at equation C)
C) 2p = d
We know there are 4 pennies so there are:
2 *4 = eight dimes
Looking at Equation A)
A) p + n + d = 18 we can fill in the pennies and the dimes:
A) 4 + n + 8 = 18
Therefore, there are 6 nickels.

5 0

3 years ago

Use the following diagram to solve the problem

nordsb [41]

Answer:

Step-by-step explanation:

The exterior angle of a triangle is equal to the sum of the 2 opposite interior angles.

94° is an exterior angle of the triangle, thus

60 + 2x = 94 ( subtract 60 from both sides )

2x = 34 ( divide both sides by 2 )

x = 17 → B

7 0

3 years ago

Read 2 more answers