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Nesterboy [21]
3 years ago
7

Convert 6cis5π/6 to rectangular form.

Mathematics
1 answer:
kati45 [8]3 years ago
3 0

Answer:

-3 sqrt(3) + 3 i

Step-by-step explanation:

6  cis ( 5 * pi / 6)

cis  is (cos + i sin)

6 ( cos ( 5 pi /6)  +i sin ( 5 * pi /6))

6 (-sqrt(3)/2 + i (1/2))

distribute

-3 sqrt(3) + 3 i

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Find the value of x.<br> 128<br> (6x + 20
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What is the 128 for ?
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3 years ago
Let f(x) = x+2/x+6 <br> f^-1(-6) =
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We can explicitly find the inverse. If f^{-1}(x) is the inverse of f(x), then

f\left(f^{-1}(x)\right) = \dfrac{f^{-1}(x)+2}{f^{-1}(x)+6} = x

Solve for the inverse :

\dfrac{f^{-1}(x) + 2}{f^{-1}(x) + 6} = x

\dfrac{f^{-1}(x) + 6 - 4}{f^{-1}(x) + 6} = x

1 - \dfrac4{f^{-1}(x) + 6} = x

1 - x = \dfrac4{f^{-1}(x) + 6}

f^{-1}(x) + 6 = \dfrac4{1-x}

\implies f^{-1}(x) = \dfrac4{1-x} - 6

Then when x = -6, we have

f^{-1}(-6) = \dfrac4{1-(-6)} - 6 = \dfrac47-6 = \boxed{-\dfrac{38}7}

Alternatively, we can first solve for x such that f(x) = -6. Then taking the inverse of both sides, x = f^{-1}(-6). (The difference in this method is that we don't compute the inverse for all x.)

We have

\dfrac{x+2}{x+6} = -6

x + 2 = -6 (x + 6)

x + 2 = -6x - 36

7x = -38

\implies x = \boxed{-\dfrac{38}7}

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