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professor190 [17]
2 years ago
12

What angle is vertical to angle 2?

Mathematics
1 answer:
suter [353]2 years ago
8 0

Answer:

Answer: a = 140°, b = 40° and c = 140°

Step-by-step explanation:

Angles a° and c° are also vertical angles, so must be equal, which means they are 140° each. Answer: a = 140°, b = 40° and c = 140°. Note: They are also called Vertically Opposite Angles, which is just a more exact way of saying the same thing.

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Precal help if you could could you answer both. Me finishing this helps me graduate.
oee [108]

Exercise 1:

The easiest way to compute powers of complex numbers is to write them in the form

z = \rho e^{i\theta} = \rho(\cos(\theta)+i\sin(\theta))

In this form, you have

z^n = \rho^n e^{in\theta} = \rho^n(\cos(n\theta)+i\sin(n\theta))

The magnitude of the number is given by

z=a+bi \implies \rho = \sqrt{a^2+b^2}

So, we have

z=-1+\sqrt{3}i \implies \rho = \sqrt{1+3}=2

As for the angle, we have

z=a+bi \implies \theta = \text{atan2}\dfrac{b}{a}

So, we have

z=-1+\sqrt{3}i \implies \theta = \text{atan2}\left(\dfrac{-\sqrt{3}}{-1}\right) = -\dfrac{2\pi}{3}

Finally,

z=-1-\sqrt{3}i = 2\left(\cos\left( -\dfrac{2\pi}{3}\right) + i\sin\left( -\dfrac{2\pi}{3}\right)\right) \implies z^6 = 2^6\left(\cos\left( -4\pi\right) + i\sin\left(-4\pi\right)\right) = 64

Exercise 2:

You simply have to compute the trigonometric function:

\cos\left(-\dfrac{\pi}{4}\right) = \dfrac{\sqrt{2}}{2},\quad \sin\left(-\dfrac{\pi}{4}\right) = -\dfrac{\sqrt{2}}{2}

So, we have

z = \sqrt{2}\left(\dfrac{\sqrt{2}}{2} - i\dfrac{\sqrt{2}}{2}\right) = 1-i

7 0
3 years ago
I need to get this done for tomorrow
Nikolay [14]
I think its d but you cant see all of the question.<span />
4 0
3 years ago
Read 2 more answers
Write the direct variation function given that y varies directly with x, and y = 6 when x = 10.
ivolga24 [154]
0.6=k
This is your answer because the equation is for direct variation is y=kx
You substitute the numbers
4 0
3 years ago
Andrew sold $50 less than sarah did and evan sold $25 more than Sarah. these quantities can be communicated symbolically. if x=
aliya0001 [1]
The answer is I think b because it has x-50 and it said Andrew sold less that Sarah so its subtracting
8 0
3 years ago
Can someone help quick
9966 [12]

Step-by-step explanation:

22+2x+8= x+20

2x+30=x+20

x+30=20

x=-10

answer is -10

3 0
2 years ago
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