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Volgvan
3 years ago
11

What are the gradients (slopes) and y-intercepts of these lines, please?​

Mathematics
1 answer:
masya89 [10]3 years ago
6 0

Answer:

a. gradient 4

b. gradient 3

c. gradient 1

d. gradient 1

e. gradient -2

f. gradient 3

Step-by-step explanation:

to find y intercept substitute x to be 0

i.e y=3x

y=0

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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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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

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

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

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L⁻¹[F(s)] = 1/2 L⁻¹[2/(s² + 2²)] = 1/2 sin(2t)

Then we find

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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2 years ago
Pythagorean Theorem &amp; irrational Numbers Question
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