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Zinaida [17]
3 years ago
5

Prove the following with Euler's formula to write e^itheta and e^-itheta in terms of sine and cosine. Then subtract them.

Mathematics
1 answer:
kirill115 [55]3 years ago
8 0
Euler's formula tells us that

e^{i\theta}=\cos\theta+i\sin\theta
e^{-i\theta}=\cos\theta-i\sin\theta

Suppose we subtract the two. This eliminates the cosine terms.

e^{i\theta}-e^{-i\theta}=i\sin\theta-(-i\sin\theta)=2i\sin\theta

Divide both sides by 2i and you're done.
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Celeste hiked 1.8 miles in 0.75 hours.What is her average rate of speed?​
Ilya [14]

Answer:

average speed of hiker is 2.4 mph

Step-by-step explanation:

here is the solution : -

=》

speed =  \frac{distance}{time}

=》

speed =  \frac{1.8}{0.75}

=》

speed = 2.4

average speed of hiker is 2.4 miles per hour

5 0
3 years ago
There's a one time fee of $27 to join the gym the monthly cost of using the gym is $18 write an equation for the relationship th
Sonbull [250]

y = 18x + 27
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5 0
3 years ago
I need help on questions 48 49 and 50 and u need to find the surface area of the 3 polyhedras please and thank you!
White raven [17]

48. The surface area of a cylinder is given by

... A = 2πr² + 2πrh = 2πr(r+h)

For r = 13 mi and h = 7 mi, this becomes

... A = 2π(13 mi)(13 mi + 7 mi) = 520π mi²

The surface area of the cylinder is 520π mi² ≈ 1634 mi².

49. The surface area of a rectangular prism is

... A = 2(LW + H(L+W))

For L = 20 m, W = 10 m, H = 7 m, this becomes

... A = 2((20 m)(10 m) + (7 m)(20 m + 10 m)) = 2(200 m² + 210 m²) = 820 m²

The surface area of the prism is 820 m².

50. The formula is the same as for problem 48.

For r = 10 m and h = 13 m, this becomes

... A = 2π(10 m)(10 m + 13 m) = 460π m² ≈ 1445 m²

The surface area of the cylinder is 460π m² ≈ 1445 m².

_____

When calculations are repetitive, it is convenient to let a calculator or spreadsheet do them.

7 0
3 years ago
Your price on a particular model is $125 however to get a service contract you offer to sell it for $115 how much discount are y
Arisa [49]
It would be an 8 percent discount because 115 is 92 percent of 125.
6 0
3 years ago
Pls help i’ll mark brainliest!!
Luba_88 [7]
Answer: Aiden runs 187.5 meters per minute.
Explanation: Literally divide the two numbers
4 0
2 years ago
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