(a) Use appropriate algebra and Theorem to find the given inverse Laplace transform. (Write your answer as a function of t.) L−1 {3s − 10/ s2 + 25}
(b) Use the Laplace transform to solve the given initial-value problem.
y' + 3y = e6t, y(0) = 2

(a) Expand the given expression as

You should recognize the Laplace transform of sine and cosine:

So we have

(b) Take the Laplace transform of both sides:

Solve for :

Decompose the right side into partial fractions:

So we have

and taking the inverse transforms of both sides gives

answer: 25.4 units

step-by-step explanation: radius = 12.7 units

diameter = twice the radius

diameter = 12.7 x 2

= 25.4