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2 years ago

Whats the answer? ( Khan Academy ) Also Ill give branliest if its correct!

Mathematics

2 answers:

vagabundo [1.1K]2 years ago

7 0

Answer:

option (a) is the answer in think

S_A_V [24]2 years ago

4 0

Answer:

A is the equavelent expression

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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,

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

7 0

2 years ago

You are given the parametric equations x=2cos(θ),y=sin(2θ). (a) List all of the points (x,y) where the tangent line is horizonta

vladimir1956 [14]

Answer:

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

Step-by-step explanation:

The slope of the tangent line at a point of the curve is:

$m = \frac{\frac{dy}{dt} }{\frac{dx}{dt} }$

$m = -\frac{\cos 2\theta}{\sin \theta}$

The tangent line is horizontal when $m = 0$ . Then:

$\cos 2\theta = 0$

$2\theta = \cos^{-1}0$

$\theta = \frac{1}{2}\cdot \cos^{-1} 0$

$\theta = \frac{1}{2}\cdot \left(\frac{\pi}{2}+i\cdot \pi \right)$ , for all $i \in \mathbb{N}_{O}$

$\theta = \frac{\pi}{4} + i\cdot \frac{\pi}{2}$ , for all $i \in \mathbb{N}_{O}$

The first four solutions are:

x: $\sqrt{2}$ $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$

y: 1 -1 1 -1

The solutions listed from the smallest to the greatest are:

x: $-\sqrt{2}$ $-\sqrt{2}$ $\sqrt{2}$ $\sqrt{2}$

y: -1 1 -1 1

6 0

2 years ago

How to find the base of a triangle if your height is 6 inches.

AnnyKZ [126]

Answer:

Use this to find your answer.

Step-by-step explanation:

Triangle Area = 1/2 x Base Length x Height Example: The area of a triangle with a base length of 5 inches and height of 6 inches is:

5 0

1 year ago

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How can you use the quadratic formula to complete a square?

Marina86 [1]

It has become somewhat fashionable to have students derive the Quadratic Formula themselves; this is done by completing the square for the generic quadratic equation ax2 + bx + c = 0. While I can understand the impulse (showing students how the Formula was invented, and thereby providing a concrete example of the usefulness of abstract symbolic manipulation), the computations involved are often a bit beyond the average student at this point.

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2 years ago

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In a fruit salad, there are 12 strawberries, 14 grapes, 6 kiwis, and 4 papayas. Find the ratio of kiwis to the total number of p

KonstantinChe [14]

Answer:

1:6

this is because 6 kiwis + 30 fruits = 36 fruits. Then you have 6 kiwis and 36 fruits. therefore the ratio is 6:36. when you simplify , it becomes 1:6

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2 years ago

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