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3 years ago

Multiply. 132.71 × 10²

Mathematics

2 answers:

Darya [45]3 years ago

5 0

10*10=100
100*132.71=13271

katovenus [111]3 years ago

4 0

The answer is 13271 because you multiply 132.71 x 100 because 10 to the power if 2 is 100! hope this helps ^-^! :D

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2 years ago

Find the inverse laplace<br><br> F(s)=11s/ s^2-12s+52

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$11e^{6t}\cos 4t+\frac{33}{2}e^{6t}\sin 4t$

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We can write $\frac{11s}{s^2-12s+52}$ as follows:

$\frac{11s}{s^2-12s+52}\\=11\left [ \frac{s}{s^2-12s+52} \right ]\\=11\left [ \frac{s}{(s-6)^2+16} \right ]\\=11\left [ \frac{s-6+6}{(s-6)^2+16} \right ]\\=11\left [ \frac{s-6}{(s-6)^2+16} \right ]+\frac{66}{(s-6)^2+16}$

To find:

$L^{-1}\left [ \frac{11s}{s^2-12s+52 \right ]}\\=L^{-1}\left [ 11\left [ \frac{s-6}{(s-6)^2+16} \right ]+\frac{66}{(s-6)^2+16} \right ]$

We will use formulae:

$L^{-1}\left \{ \frac{s-a}{(s-a)^2+b^2} \right \}=e^{at}\cos bt\\L^{-1}\left \{ \frac{b}{(s-a)^2+b^2} \right \}=e^{at}\sin bt$

we get solution as :

$L^{-1}\left [ 11\left [ \frac{s-6}{(s-6)^2+16} \right ]+\frac{66}{(s-6)^2+16} \right ]\\=L^{-1}\left [ 11\left [ \frac{s-6}{(s-6)^2+4^2} \right ]+\frac{66}{4}\left [ \frac{4}{(s-6)^2+4^2} \right ] \right ]\\=11e^{6t}\cos 4t+\frac{33}{2}e^{6t}\sin 4t$

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