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____ [38]
3 years ago
15

Can you help me with my geometry homework, I will give a brainlist.​

Mathematics
1 answer:
AleksAgata [21]3 years ago
8 0

Answer:

i can explain it to you.

Step-by-step explanation:

SO first you're going to label the graph with the munbers. If you don't know how they go just search one up because they all look the same.

Then you're going to place them on the coordinates that they correspond to. (x,y)

Then for the rotation you're going to move it 90* clockwise which would be right but in the shape of a circle. But you have to connect the dots.

Basically you're just laying it down on its side to the right.

<em>Hope this helps. :)</em>

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Find the solution of the differential equation that satisfies the given initial condition. y' tan x = 3a + y, y(π/3) = 3a, 0 &lt
Paladinen [302]

Answer:

y(x)=4a\sqrt{3}* sin(x)-3a

Step-by-step explanation:

We have a separable equation, first let's rewrite the equation as:

\frac{dy(x)}{dx} =\frac{3a+y}{tan(x)}

But:

\frac{1}{tan(x)} =cot(x)

So:

\frac{dy(x)}{dx} =cot(x)*(3a+y)

Multiplying both sides by dx and dividing both sides by 3a+y:

\frac{dy}{3a+y} =cot(x)dx

Integrating both sides:

\int\ \frac{dy}{3a+y} =\int\cot(x) \, dx

Evaluating the integrals:

log(3a+y)=log(sin(x))+C_1

Where C1 is an arbitrary constant.

Solving for y:

y(x)=-3a+e^{C_1} sin(x)

e^{C_1} =constant

So:

y(x)=C_1*sin(x)-3a

Finally, let's evaluate the initial condition in order to find C1:

y(\frac{\pi}{3} )=3a=C_1*sin(\frac{\pi}{3})-3a\\ 3a=C_1*\frac{\sqrt{3} }{2} -3a

Solving for C1:

C_1=4a\sqrt{3}

Therefore:

y(x)=4a\sqrt{3}* sin(x)-3a

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