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Find f(t) for each of the following functions a) b) c) d)

Chapter 12, Problem 12.41

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QUESTION:

Find f(t) for each of the following functions a) b) c) d) F(s) = 8(s + 1)2 (s2 + 10s + 34)(s2 + 8s + 20). F(s) = 14s2 + 56s + 152 (s + 6)(s2 + 4s + 20). F(s) = -s2 + 52s + 445 s(s2 + 10s + 89) . F(s) = 280 s2 + 14s + 2

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QUESTION:

Find f(t) for each of the following functions a) b) c) d) F(s) = 8(s + 1)2 (s2 + 10s + 34)(s2 + 8s + 20). F(s) = 14s2 + 56s + 152 (s + 6)(s2 + 4s + 20). F(s) = -s2 + 52s + 445 s(s2 + 10s + 89) . F(s) = 280 s2 + 14s + 2

ANSWER:

Step 1 of 5

(a)

Consider the given expression.

                                                                  

The denominator of the given expression has two distinct roots of the quadratic function.

Find the roots as follows.

                                                                      

The  can be written as follows.

                                                          

Solve for  at  as follows.

                                                                        

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