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Mathematics

2 answers:

rewona [7]3 years ago

6 0

Answer:

1. Perpendicular

2. Complementary

3. A vertex

4. Midpoint

5. Vertical

6. Angle bisector

7. Supplementary

8. Coplanar

9. An acute angle

10. Congruent

Keith_Richards [23]3 years ago

3 0

Answer:

number one is 90°

Step-by-step explanation:

number 9 is an acute angle

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salantis [7]

Answer:

Step-by-step explanation:

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2 years ago

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Inveres laplace transform (3s-14)/s^2-4s+8

Olenka [21]

Complete the square in the denominator.

$s^2 - 4s + 8 = (s^2 - 4s + 4) + 4 = (s-2)^2 + 4$

Rewrite the given transform as

$\dfrac{3s-14}{s^2-4s+8} = \dfrac{3(s-2) - 8}{(s-2)^2+4} = 3\times\dfrac{s-2}{(s-2)^2+2^2} - 4\times\dfrac{2}{(s-2)^2+2^2}$

Now take the inverse transform:

$L^{-1}_t\left\{3\times\dfrac{s-2}{(s-2)^2+2^2} - 4\times\dfrac{2}{(s-2)^2+2^2}\right\} \\\\ 3L^{-1}_t\left\{\dfrac{s-2}{(s-2)^2+2^2}\right\} - 4L^{-1}_t\left\{\dfrac{2}{(s-2)^2+2^2}\right\} \\\\ 3e^{2t} L^{-1}_t\left\{\dfrac s{s^2+2^2}\right\} - 4e^{2t} L^{-1}_t\left\{\dfrac{2}{s^2+2^2}\right\} \\\\ \boxed{3e^{2t} \cos(2t) - 4e^{2t} \sin(2t)}$