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2 years ago

The volume of a rectangular prism is

Mathematics

1 answer:

Feliz [49]2 years ago

6 0

Answer:

h = v/lw .

Step-by-step explanation:

v=lwh

Divide both sides by lw:

v / lw = h.

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Rewrite with only sin x and cos x.

Annette [7]

Option A

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

Solution:

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

2 years ago

Sole the system by elimination -4x+9y=9 x-3y=-6

Natalka [10]

Answer:

A) -4x + 9y = 9

B) x -3y = -6

We multiply B) by 3

B) 3x -9y = -18 Then add it to A)

A) -4x + 9y = 9

-x = -9

x = 9

9 -3y = -6

3y = 15

y = 5

Step-by-step explanation:

5 0

2 years ago

What is the volume of this cylinder?

tatiyna

Answer:

The volume of the cylinder is 792

Step-by-step explanation:

3.14*6^2*7= 791.68 then when you round it up to the nearest whole number it's 792

4 0

2 years ago

Please help or i am grounded

Dahasolnce [82]

Answer:

$x=140$

Step-by-step explanation:

Do not get grounded.

An angle at a point is 360°.

So, $x+120+70+30=360$

$x+220=360$

$x=140$

3 0

3 years ago

Remove the parentheses and simplify 3a^2-6ab+3b^2-5(-6a^2+7ab-7b^2)

Oksi-84 [34.3K]

$3a^2-6ab+3b^2-5(-6a^2+7ab-7b^2)=\\\\3a^2-6ab+3b^2+30a^2-35ab+35b^2=\\\\33a^2-41ab+38b^2$

4 0

2 years ago