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brilliants [131]
2 years ago
7

What is the value of 6i/1+i? 2 – 6i 2 + 6i 3 – 3i 3 + 3i

Mathematics
2 answers:
mihalych1998 [28]2 years ago
6 0

6i/ (1+i)  

multiply by the complex conjugate (1-i)/(1-i)

6i/(1+i) *  (1-i)/(1-i)

6i* (1-i) = 6i - 6i^2 = 6i - 6(-1) = 6i +6

(1+i)*(1-i)= 1-i +i -i^2 = 1 -i+i -(-1) = 1+1=2

(6+6i)/2

3+3i

Answer: 3+3i

alekssr [168]2 years ago
3 0

Answer:

D. 3+3i

Step-by-step explanation:

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If t represent the number of tickets purchased for a baseball game, which scenario is modeled by the equation, 32.50t + 5 = 28.7
tino4ka555 [31]

Answer:

Replacing t with 4, 32.5*4 + 5 is 135 and 28.75 * 4 + 20 is also 135. Since these two are equal, the equation is verified.

or

If you substitute 4 for t in the equation, you get a true statement. That means it would cost the Burns family $135 for 4 tickets and parking for either lower-level or middle-level seats.

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Which part of the proof does the fourth statement and reason represent?
denis-greek [22]

Answer:

Option B is correct.

Reason:It is an argument

Step-by-step explanation:

Given: AB \cong BC  and BC \cong EF

By transitive property:  a = b  and b = c then, a =c

⇒AB \cong EF

AB = EF                                [def of \cong segment]

By Segment Addition Postulate states that given  two points A and C, and a third point B lies on the line segment AC if and only if the distances between the  points satisfy the equation

AB + BC = AC.

Since, the line segment EG , F lies on the line segment;

then, by segment addition postulates we have;

EG = EF + FG

By substitution AB=EF

⇒ EG = AB + FG                     hence proved!

Since, in the fourth statement reason is:  It is an argument

3 0
2 years ago
The harmonic motion of a particle is given by f(t) = 2 cos(3t) + 3 sin(2t), 0 ≤ t ≤ 8. (a) When is the position function decreas
iren [92.7K]

For the last part, you have to find where f'(t) attains its maximum over 0\le t\le8. We have

f'(t)=-6\sin3t+6\cos2t

so that

f''(t)=-18\cos3t-12\sin2t

with critical points at t such that

-18\cos3t-12\sin2t=0

3\cos3t+2\sin2t=0

3(\cos^3t-3\cos t\sin^2t)+4\sin t\cos t=0

\cos t(3\cos^2t-9\sin^2t+4\sin t)=0

\cos t(12\sin^2t-4\sin t-3)=0

So either

\cos t=0\implies t=\dfrac{(2n+1)\pi}2

or

12\sin^2t-4\sin t-3=0\implies\sin t=\dfrac{1\pm\sqrt{10}}6\implies t=\sin^{-1}\dfrac{1\pm\sqrt{10}}6+2n\pi

where n is any integer. We get 8 solutions over the given interval with n=0,1,2 from the first set of solutions, n=0,1 from the set of solutions where \sin t=\dfrac{1+\sqrt{10}}6, and n=1 from the set of solutions where \sin t=\dfrac{1-\sqrt{10}}6. They are approximately

\dfrac\pi2\approx2

\dfrac{3\pi}2\approx5

\dfrac{5\pi}2\approx8

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2\pi+\sin^{-1}\dfrac{1+\sqrt{10}}6\approx7

2\pi+\sin^{-1}\dfrac{1-\sqrt{10}}6\approx6

4 0
2 years ago
Däne has a stamp collection. in one boo he has 6 pages with 15 stamps on each page. in another book,he has 9 pages with 20 stamp
galben [10]
6x15= 90

9x20= 180


180+90= 270


270 - 25 = 245        dane has 245 stamps left
8 0
2 years ago
A plane left Atlanta at 4:50 and arrived at Boston in 3 hours and 15 minutes. When did it arrive in Boston?
sashaice [31]

Answer: 8:05 pm

Step-by-step explanation: 4 hours + 3 hours = 7 hours

50 min + 15 min = 1 hour, 5 min

add those together

watch out for time zones when crossing

4 0
2 years ago
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