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3 years ago

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A triangular prism is shown. A cylinder is cut out of the center of the prism. The triangular base has side lengths of 14 and 10

units. The heights of both the cylinder and prism are 8 units. The cylinder has a diameter of 5 units. Which expression represents the volume, in cubic units, of the shaded region of the composite figure?

2 answers:

Anuta_ua [19.1K]3 years ago

8 0

Answer:

Step-by-step explanation:

bogdanovich [222]3 years ago

8 0

Answer:

One-half(14)(10)(8) – π(2.52)(8)

Step-by-step explanation:

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Rewrite with only sin x and cos x.

Annette [7]

Option A

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

<em><u>Solution:</u></em>

Given that we have to rewrite with only sin x and cos x

Given is cos 3x

$cos 3x = cos(x + 2x)$

We know that,

$\cos (a+b)=\cos a \cos b-\sin a \sin b$

Therefore,

$\cos (x+2 x)=\cos x \cos 2 x-\sin x \sin 2 x$ ---- eqn 1

We know that,

$\sin 2 x=2 \sin x \cos x$

$\cos 2 x=\cos ^{2} x-\sin ^{2} x$

Substituting these values in eqn 1

$\cos (x+2 x)=\cos x\left(\cos ^{2} x-\sin ^{2} x\right)-\sin x(2 \sin x \cos x)$ -------- eqn 2

We know that,

$\cos ^{2} x-\sin ^{2} x=1-2 \sin ^{2} x$

Applying this in above eqn 2, we get

$\cos (x+2 x)=\cos x\left(1-2 \sin ^{2} x\right)-\sin x(2 \sin x \cos x)$

$\begin{aligned}&\cos (x+2 x)=\cos x-2 \sin ^{2} x \cos x-2 \sin ^{2} x \cos x\\\\&\cos (x+2 x)=\cos x-4 \sin ^{2} x \cos x\end{aligned}$

$\cos (x+2 x)=\cos x-4 \cos x \sin ^{2} x$

Therefore,

$\cos 3 x=\cos x-4 \cos x \sin ^{2} x$

Option A is correct

7 0

3 years ago

What is -2=-5t+10+2t

frutty [35]

Answer: T is 4

Step-by-step explanation:

7 0

3 years ago

Read 2 more answers

Line AB contains points A(-6,1) and B(1,4).

Free_Kalibri [48]

To solve this problem you must apply the proccedure shown below:

1- You have that the equation of the line is:

$y=mx+b$

Where $m$ is the slope and $b$ is the y-intercept.

2- Based on the information given in the problem, the lines $AB$ and $CD$ are parallel, which means that both have the same slope. Therefore, you can calculate the slope of $AB$ :

$m=\frac{y2-y1}{x2-x1}$

$m=\frac{4-1}{1-(-6)}=\frac{3}{7}$

3- Use the coordinates of the point $D(7,2)$ to calculate the y-intercept:

$2=\frac{3}{7}(7)+b$

4. Solve for $b$ :

$b=2-3=-1$

5. The equation of the line $CD$ is:

$y=\frac{3}{7}x-1$

The answer is: $y=\frac{3}{7}x-1$

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3 years ago

There are 70 students in the school band. 40% of them are sixth graders, 20% are seventh graders, and the rest are eighth grader

Anon25 [30]

Answer:

The number of students in the school band = 70

40% of students in the school band are sixth graders.

20% of students in the school band are seventh graders.

We have to find the number of band members that are sixth graders.

The number of sixth graders in school band are:

$40\% of 70$

$0.40 \times 70$

$28$

Therefore, there are 28 band members that are sixth graders.

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4 years ago

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VMariaS [17]

For the answer to the question above asking w<span>hat is the conditional probability that exactly two of the children will be allergic to peanuts, given that at least one of the three children suffers from this allergy?
The answer to the question above is 0.0012. I hope this helps</span>

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3 years ago