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Nonamiya [84]
3 years ago
12

Question 6

Mathematics
1 answer:
inn [45]3 years ago
7 0

Answer:

c

Step-by-step explanation:

4 times 2 is 8. 3 and 3 times -4 is -12

8 minus -12 is negative 4

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vesna_86 [32]

Answer:  Choice D

15(cos85° + i sin85°)

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

Explanation:

Let's say we had these two general complex numbers, which are in polar form.

z_1 = r_1*\left(\cos(\theta_1)+i*\sin(\theta_1)\right)\\\\z_2 = r_2*\left(\cos(\theta_2)+i*\sin(\theta_2)\right)\\\\

We can abbreviate them into the shorthand form

z_1 = r_1*\text{cis}(\theta_1)\\\\z_2 = r_2*\text{cis}(\theta_2)\\\\

The notation "cis" stands for "cosine i sine".

Now that we have those complex numbers set up, multiplying them is as simple as saying this:

z_1*z_2 = (r_1*r_2)*\text{cis}(\theta_1+\theta_2)

We do two basic things:

  1. Multiply the r values out front
  2. Add the theta values inside the the cis function

---------------------------------------

With all that in mind, let's tackle the problem your teacher gave you.

The given complex numbers

z_1 = 5*\left(\cos(15^{\circ})+i*\sin(15^{\circ})\right)\\\\z_2 = 3*\left(\cos(70^{\circ})+i*\sin(70^{\circ})\right)\\\\

abbreviate into

z_1 = 5*\text{cis}(15^{\circ})\\\\z_2 = 3*\text{cis}(70^{\circ})\\\\

then those multiply to

z_1*z_2 = (r_1*r_2)*\text{cis}(\theta_1+\theta_2)\\\\z_1*z_2 = (5*3)*\text{cis}(15+70)\\\\z_1*z_2 = 15\text{cis}(85^{\circ})\\\\z_1*z_2 = 15\left(\cos(85^{\circ})+i\sin(85^{\circ})\right)\\\\

which is why choice D is the final answer.

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3 years ago
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Answer:

The midpoint of AB is (0.5,0)

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What is the solution set of 4x = y and 2x^2− y = 0?
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Answer:{0,2}

Step-by-step explanation:

Substitute 4x in for the y

2x^2-4x=0

Factor out GCF 2x

2x(x-2)=0

Set each factor = 0 and solve

2x=0 x=0 x-2=0 x=2

8 0
3 years ago
Alma wants to prove to her parents that listening to music while she studies for her tests will help her get better grades. She
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She asked her friends, which does not represent a random sample.

She tried to show cause and effect without doing an experiment (which includes simple random sample, control group, treatment, etc).

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