Use the laplace transform to solve the initial value problem"3y +2y=0, y(0)=1, y(0)=0.

Y(s) = 2/(s+2) - 1/(s+1)

y(t) = 2e^(-2t) - e^(-t)

Step-by-step explanation:

Let's solve y'' + 3y' + 2y = 0, by the Laplace transform.

So, the first step is to find the Laplace transform of each component of the differential equation

L{y''(t)} = s^2Y(s) - sy(0) - y'(0) = (s^2)Y(s) - s

L{3y'(t)} = 3L{y'(t)} = 3(sY(s) - y(0)) = 3sY(s)

L{2y(t)} = 2L{y(t)} = 2Y(s)

So now we have to solve the following equation:

(s^2)Y(s) - s + 3sY(s) + 2Y(s) = 0

Y(s)(s^2 + 3s + 2) = s

Y(s)(s+2)(s+1) = s

Y(s) = (s/(s+2)(s+1))

Now to find y(t) and solve the initial value problem, we need to do the inverse Laplace transform of Y(s), that we can do the following way:

Y(s) = (s/(s+2)(s+1)) = (A/(s+2)) + (B/(s+1))

where A = s/(s+1) when s = -2, so A = 2

B = s/(s+2) when s = -1, so B = -1

So

Y(s) = 2/(s+2) - 1/(s+1)

Doing the inverse Laplace transform

y(t) = 2e^(-2t) - e^(-t)

2. angles qrt and qst both measures 156 degrees.

step-by-step explanation:  

we have been given a diagram of a circle and we are told that measure of arc qvt is 156 degrees.  

we can see from our given diagram that angle qrt and angle qst subtends to arc qvt.

since we know that angles subtended by the same arc at the circumference are always equal.

by angle subtended by same arc theorem, measure of angle qrt and angle qst will be equal to the measure of arc qvt.

therefore, angles qrt and qst both measures 156 degrees and 2nd statement is the correct choice.

22.83 repeating

step-by-step explanation:

137 ÷ 6 is 22.8333333 therefore we understand that 3 is repeating.

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