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4 years ago

The solution of f(x)=x^3-2x^2- 9x + 18 is

Mathematics

1 answer:

Tom [10]4 years ago

5 0

Answer:

x = -3, 2, 3.

Step-by-step explanation:

f(x )= x^3 - 2x^2 - 9x + 18 We factor this by grouping:

f(x) = x^2(x - 2) - 9(x - 2)

f(x) = (x ^2- 9)(x - 2)

f(x) = (x - 3)(x + 3)(x - 2).

The zeroes of the function are:

x = -3, 2, 3.

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(50 points)There are x ducks in a pond. The number of swans in the pond is equal to the square root of the number of ducks. If t

RoseWind [281]

there are nine ducks and 3 swans

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6 0

3 years ago

Read 2 more answers

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

The ratio of red cars to blue cars in a parking lot was 5:3 . If there was 40 red cars , how many blue cars were there ?

Bas_tet [7]

The answer is x equals 24
you set up a proportion new over old
so for red cars 40 over 5
since we don’t know the new for blue cars we’ll use x
so x over 3
we then make them equal to each other
40 x
—- = —-
5 3
cross multiply, then we get
120=5x
isolate the x by dividing 5 from both sides to get 24

5 0

3 years ago

How do I solve (3x2y) (10x5y3)

dmitriy555 [2]

Answer:

30x^7y^4

Step-by-step explanation:

Hope this helps!

Please Mark Brainliest!

4 0

3 years ago

Write in simplest radical form.

ipn [44]

Step-by-step explanation:

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3 years ago