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Oduvanchick [21]
3 years ago
8

Emily gad a decorative box that is shaped like a cube with a height of 5 inches. What’s the surface area of the box?

Mathematics
1 answer:
lina2011 [118]3 years ago
4 0

times the length by width and you will get your answer use a calculator that will be the answer

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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
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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)

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

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

Evaluating the integrals:

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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

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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:

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