2 years ago

Given that f(x) = x^2+ 11x + 30 and g(x) = x + 6, find

Mathematics

1 answer:

kaheart [24]2 years ago

6 0

Answer:

X^3+17x^2+96x+180

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

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3 years ago

Help!!!! 20 points!!!!!!’

Gnoma [55]

Answer:

option c is the correct answer

first take y raised to the power 4 common then cancel its power by y raised to the power 3

you get your answer

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3 years ago

Hiba grew up in Great Britain, where she learned metric measurements. Now she lives in the U.S., and at the doctors office, she

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120 pounds is 54.4 kilograms

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3 years ago

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A bottle of grape juice costs 6.50$ of you buy 6 bottles you can get 10%discount workout how much you save if you buy 6 bottles

Neporo4naja [7]

Answer:

$2.6

Step-by-step explanation:

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2 years ago

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dean counted 10 red cards, 10 black catds, and 20 blue cards in a deck of cards. what is the ratio of red cards to all cards?

miv72 [106K]

Answer:

10:40

Step-by-step explanation:

10+10+20=40

10 red cards

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2 years ago