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Ghella [55]
3 years ago
5

(2.5 x 10^-8) (9 x 10^-10) Express your answer in scientific notation.

Mathematics
2 answers:
KATRIN_1 [288]3 years ago
8 0

2.25 x 10^-17

I hope this helps

Marrrta [24]3 years ago
4 0

\bf (2.5\times 10^{-8})(9\times 10^{-10})\implies (2.5\cdot 9)\times (10^{-8}\cdot  10^{-10}) \\\\\\ (22.5)\times (10^{-8-10})\implies (2.25\times 10^1)\times 10^{-18} \\\\\\ 2.25\times 10^{1-18}\implies 2.25\times 10^{-17}

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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 :

(s²Y - s y(0) - y'(0)) - 4 (sY - y(0)) + 8Y = exp(-s) L[δ(t)]

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Recall that

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

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

u(t) = \begin{cases}1 & \text{if }t \ge 0 \\ 0 & \text{if }t < 0\end{cases}

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

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Then we find

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and so we end up with

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

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