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Dennis_Churaev [7]
3 years ago
6

Dy/dx = (cos x) e^(y+sinx) and y = 0 when x = 0. find the original equation

Mathematics
1 answer:
Korvikt [17]3 years ago
3 0
Find the general solution by separating the variables then integrating: 
dy / dx = cosx℮^(y + sinx) 
dy / dx = cosx℮ʸ℮^(sinx) 
℮^(-y) dy = cosx℮^(sinx) dx 
∫ ℮^(-y) dy = ∫ cosx℮^(sinx) dx 
-℮^(-y) = ℮^(sinx) + C 
℮^(-y) = C - ℮^(sinx) 
-y = ln[C - ℮^(sinx)] 
y = -ln[C - ℮^(sinx)] 

Find the particular solution by solving for the constant: 
When x = 0, y = 0 
-ln(C - 1) = 0 
ln(C - 1) = 0 
C - 1 = 1 
C = 2 
<span>y = -ln[2 - ℮^(sinx)]


I hope my answer has come to your help. Thank you for posting your question here in Brainly. We hope to answer more of your questions and inquiries soon. Have a nice day ahead!</span>
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A circle is increased to have a circumference that is 4 times larger than the original. Which of the following options best desc
kogti [31]
Area of a circle is directly proportional to the square of radius of the circle while the circumference is proportional to the radius of the circle. This means that if the radius of a circle is increased x times, then its area will be increased to x^2 times the original area, and the circumference will increase to x times the original circumference.

Thus when the radius is doubled, or in other words if radius mad 2 time the original radius, the area of circle will become 2^2 = 4 time the original area. The circumference will become 2 times the original circumference.

We can calculate exact area and circumference of a circle from its radius using the following equations:

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I know this is a lot, sorry.
3 0
3 years ago
What are the solutions to<br> (m +11)2 = 64?
mel-nik [20]

Answer:

(21 + 11)2 = 64

So, I don't think teachers do this, but this is my way of doing it

Okay, so first, I divided 64 by 2 :

64 ÷ 2 = 32

Then, I subtracted 11 from 32:

21

Now, to check, just do the problem :

(21 + 11)2 = 64

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6 0
3 years ago
Read 2 more answers
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3 years ago
A ship leaves port and travels due west for 30 knots, then changes course to S 30° W and travels 50 more knots. Find the bearing
leva [86]

Answer:

  232°

Step-by-step explanation:

There are a couple of ways to find the desired direction. Perhaps the most straightforward is to add up the coordinates of the travel vectors.

  30∠270° +50∠210° = 30(cos(270°), sin(270°)) +50(cos(210°), sin(210°))

  = (0, -30) +(-43.301, -25) = (-43.301, -55)

Then the angle from port is ...

  arctan(-55/-43.301) ≈ 231.79° . . . . . . . 3rd quadrant angle

The bearing of the ship from port is about 232°.

_____

<em>Comment on the problem statement</em>

The term "knot" is conventionally used to indicate a measure of speed (nautical mile per hour), not distance. It is derived from the use of a knotted rope to estimate speed. Knots on the rope were typically 47 ft 3 inches apart. As a measure of distance 30 knots is about 1417.5 feet.

5 0
3 years ago
Fill in the missing values in the formula. What is the variance? 0 3.217 3.522 12.405 148.86
Lerok [7]

Answer: This’s the answer for your question 12.405

6 0
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