The answers are -4 and 3 :)
Answer:
a) x=(t^2)/2+cos(t), b) x=2+3e^(-2t), c) x=(1/2)sin(2t)
Step-by-step explanation:
Let's solve by separating variables:

a) x’=t–sin(t), x(0)=1

Apply integral both sides:

where k is a constant due to integration. With x(0)=1, substitute:

Finally:

b) x’+2x=4; x(0)=5

Completing the integral:

Solving the operator:

Using algebra, it becomes explicit:

With x(0)=5, substitute:

Finally:

c) x’’+4x=0; x(0)=0; x’(0)=1
Let
be the solution for the equation, then:

Substituting these equations in <em>c)</em>

This becomes the solution <em>m=α±βi</em> where <em>α=0</em> and <em>β=2</em>
![x=e^{\alpha t}[Asin\beta t+Bcos\beta t]\\\\x=e^{0}[Asin((2)t)+Bcos((2)t)]\\\\x=Asin((2)t)+Bcos((2)t)](https://tex.z-dn.net/?f=x%3De%5E%7B%5Calpha%20t%7D%5BAsin%5Cbeta%20t%2BBcos%5Cbeta%20t%5D%5C%5C%5C%5Cx%3De%5E%7B0%7D%5BAsin%28%282%29t%29%2BBcos%28%282%29t%29%5D%5C%5C%5C%5Cx%3DAsin%28%282%29t%29%2BBcos%28%282%29t%29)
Where <em>A</em> and <em>B</em> are constants. With x(0)=0; x’(0)=1:

Finally:

Answer:
−8/3
Step-by-step explanation:
Step 1: Add 12 to both sides.
−3y−12+12=−4+12
−3y=8
Step 2: Divide both sides by -3.
−3y−3=8−3
y=−8/3
Using the formula
L=rx (x=angle)
x=L/r
x=8/3
x=2.6 radians
Answer:
A building is 38 feet tall. Answer) 38
The scuba diver was 38 feet below sea level. Answer) -38
The basement is 8.3 feet below ground. Answer) -8.3
Oliver owes his sister $27. Answer) -27
Erica jumped 2.7 feet above ground. Answer) 2.7
I took the test so hope this helps you :)