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IceJOKER [234]
3 years ago
8

PLEASE HURRY I NEED HELP SOS!!!!!!!! (15 POINTS)

Mathematics
1 answer:
yaroslaw [1]3 years ago
8 0

Answer:

0, π, 7π/6, 11π/6   on the interval 0 ≤ ø <2π.

Step-by-step explanation:

sinø + 1 = cos2ø

Use the identity cos 2o = 1 - 2 sin^2 o:

sin o + 1 = 1 - 2 sin^2 o

2sin^2 o + sin o + 1 - 1 = 0

2 sin^2 o + sin o = 0

sin o (2 sin 0 + 1) = 0

Therefore sin o = 0 or sin o = -1/2.

For sin o = 0 , o = 0, π radians.

For sin o = - 1/2, o = 7π/6, 11π/6 radians.

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For funcitons f(x)=2x+3 and g(x)=-3x-2, please find (f∘g)(-1)
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Answer:

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Step-by-step explanation:

We are given the two functions:
\displaystyle f(x) = 2x + 3\text{ and } g(x) = -3x - 2

And we want to find:
\displaystyle (f\circ g)(-1)

Recall that this is equivalent to:
\displaystyle (f\circ g)(-1) = f(g(-1))

Hence, find g(-1):
\displaystyle \begin{aligned} g(x) & = -3x - 2\\ \\ g(-1) & = -3(-1) - 2\\ \\ & = (3) - 2 \\ \\ & = 1 \end{aligned}

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\displaystyle \begin{aligned} f(x) & =  2x+ 3 \\ \\ f(1) & = 2(1) + 3 \\ \\ & = 5\end{aligned}

In conclusion:
\displaystyle (f\circ g)(-1) = 5

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