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Tom [10]
3 years ago
13

A right cylinder has a radius of 2 units and a height of 5 units. What is the volume of the cylinder? Round to the nearest 10th.

Mathematics
2 answers:
disa [49]3 years ago
4 0

Answer: 62.8

Step-by-step explanation:

i took the test

NeTakaya3 years ago
3 0

Answer:

62.8 units

Step-by-step explanation:

The formula for a cylinder πr²h. R being the radius and h being the height.

Therefore, plug in the numbers and solve.

π(2)²(5) = 20π = 62.8 units

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Take the Laplace transform of both sides:

L[y'' - 4y' + 8y] = L[δ(t - 1)]

I'll denote the Laplace transform of y = y(t) by Y = Y(s). Solve for Y :

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s²Y - 4sY + 8Y = exp(-s)

(s² - 4s + 8) Y = exp(-s)

Y = exp(-s) / (s² - 4s + 8)

and complete the square in the denominator,

Y = exp(-s) / ((s - 2)^2 + 4)

Recall that

L⁻¹[F(s - c)] = exp(ct) f(t)

In order to apply this property, we multiply Y by exp(2)/exp(2), so that

Y = exp(-2) • exp(-s) exp(2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-s + 2) / ((s - 2)² + 4)

Y = exp(-2) • exp(-(s - 2)) / ((s - 2)² + 4)

Then taking the inverse transform, we have

L⁻¹[Y] = exp(-2) L⁻¹[exp(-(s - 2)) / ((s - 2)² + 4)]

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L⁻¹[exp(-cs) F(s)] = u(t - c) f(t - c)

where F is the Laplace transform of f, and u(t) is the unit step function

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To apply this property, we first identify c = 1 and F(s) = 1/(s² + 4), whose inverse transform is

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L⁻¹[Y] = exp(2t - 2) u(t - 1) • 1/2 sin(2 (t - 1))

and so we end up with

y = 1/2 exp(2t - 2) u(t - 1) sin(2t - 2)

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