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My instructor doesn't have the most intelligible answer keys. Could you explain how to solve this? Math...

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Advance Math

My instructor doesn't have the most intelligible answer keys.Could you explain how to solve this?

Math 266, Quiz 15: Answers due today, April 22, by 1:00 PM viaemail.

1. Let g(t) be given by

?(?) = {

0, 0 < ? < 1

? − 1, 1 < ? < 2

3 − ?, 2 < ? < 3

1, ? > 3

Rewriting ?(?) using the unit step function gives:

a) ?(?) = (? − 1)?(? − 1) + (4 − 2?)?(? − 2) + (? − 2)?(? −3)

b) ?(?) = (? − 1)?(? − 1) − (? − 1)?(? − 2) + (? − 3)?(? − 2) −(? − 3)?(? − 3) + ?(? − 3)

c) ?(?) = (? − 1) − (? − 1)?(? − 2) + (3 − ?)?(? − 2) − (3 −?)?(? − 3) + ?(? − 3)

d) ?(?) = (? − 1)?(? − 1) + (1 − ?)?(? − 2) − (? − 3)?(? − 2) +(? − 3)?(? − 3)

e) None of the above.

2. Use Laplace transforms to solve ?′′ + ? = ?(? − 1) − ?(? − 2)with ?(0) = 0, ? ′ (0) = 1

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