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3 years ago

On a number line, what is two-thirds of the distance from one-half to 2.25

1 answer:

7 0

The distance is .5 2.25-1.5--->Distance .75/3---->divide by 3 ----> .25 + .25 two thirds .25 is one thirds .5 is the distance, while on the number line, it would be the number 2

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Use DeMoivre's theorem to evaluate the expression

natima [27]

Answer:

B. $\dfrac{9}{2}-i\dfrac{9\sqrt{3}}{2}$

Step-by-step explanation:

DeMoivre's theorem:

If the complex number $z=r(\cos \alpha+i\sin\alpha),$ then for natural number n

$z^n=r^n(\cos n\alpha+i\sin n\alpha).$

In your case,

$z=\sqrt{3}\left(\cos\dfrac{5\pi}{12}+i\sin\dfrac{5\pi}{12}\right)$

and you have to evaluate $z^4.$

By DeMoivre's theorem,

$z^4=(\sqrt{3})^4\left(\cos 4\cdot \dfrac{5\pi}{12}+i\sin 4\cdot \dfrac{5\pi}{12}\right)=9\left(\cos \dfrac{5\pi}{3}+i\sin\dfrac{5\pi}{3}\right)=9\left(\dfrac{1}{2}-i\dfrac{\sqrt{3}}{2}\right)=\dfrac{9}{2}-i\dfrac{9\sqrt{3}}{2}.$

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2 years ago

Solve log x=2. A. 2 B. 20 C. 100 D. 1,000

Ber [7]

Answer:

100

Step-by-step explanation:

5 0

3 years ago

Read 2 more answers

The variable z is directly proportional to x, and inversely proportional to y. When x is 4 and y is 13, z has the value 1.230769

Talja [164]

Answer:

Step-by-step explanation:

1.2307692307692.

The first step is to find the proportionality constant.

The formula is

z = kx/y

1.2307692307692 = k * 4/13 Multiply both sides by 13

1.2307692307692 * 13 = 4k

16 = 4*k Divide by 4

k = 16/4

k = 4

=================================

z = k*x/y

x = 9

y = 20

k = 4

z = 4 *9/20

z = 36/20

z = 1.8

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2 years ago

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Brainliest if correct

Bad White [126]

Answer:

(-2,11) (0,3) (2,-5) (4,-13)

Step-by-step explanation:

used desmos calculator

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2 years ago

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Dima020 [189]

Answer:

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3 years ago