Use the laplace transform to solve the given initial-value problem. use the table of laplace transforms in appendix iii as needed. y'' + 4y = cos 2t, y(0) = 5, y'(0) = 3

Step-by-step explanation:

we are given

y(0)=5

y'(0)=3

we can take Laplace transform both sides

now, we can plug values

now, we can solve for Y(s)

now, we can take inverse Laplace transform both sides

we can use Laplace transform table

and we get

step-by-step explanation:

there is a formula i can give you:

it is r^2*n*sin(360/n) divided by 2 where r represents the "radius" and n is the number of sides.

plug them in:

(10sqrt(3))^2*6*sin(360/6) divided by 2

100*3*6*sin(60) divided by 2

900*sin(60)

900*sqrt(3)/2

450*sqrt(3)

approx is 779.4 cm^2