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3 years ago

How do you figure these out?

Mathematics

1 answer:

Andreyy893 years ago

7 0

I know that angle 2 and 10 are corresponding. That is question 2 I'll keep looking and comment as I figure them out.

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Find the length of the short leg of a 30-60-90 triangle if the long leg is 3cm

antoniya [11.8K]

Answer:

Short leg = √3 cm

Step-by-step explanation:

the opposite angle of long leg is 60°

hypotenuse : x

sin 60° = 3/x = √3 / 2

x = (3 x 2) / √3 = 2√3

short leg length (s)

Cos 60° = 1/2 = s / x = s / 2√3

s = √3

7 0

3 years ago

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

If an area can be washed at a rate of 3,600 cm2/minute, how many square inches can be washed per hour? Enter your answer with th

r-ruslan [8.4K]

Answer:

276923 square inches

Step-by-step explanation:

I probably got it wrong to be honest

4 0

3 years ago

Please help me!! I need help

Setler [38]

Answer:

c=l/--a^2+b^2=l/--45^2+20^2≈49.24429

Step-by-step explanation:

l/-- mean square root

^ means squared/ exponent

7 0

3 years ago

Read 2 more answers

Select the correct answer.

maks197457 [2]

The answer to this question has to be D. 42.75 square inches.

7 0

2 years ago