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:
17
Step-by-step explanation:
The total distance traveled by cycle = 50 * 12 = 600 inch
1 complete rotation measures = 2 * 3.14 * 24 = 150.72 inch
Total rotation = 600 / 150.72
= approx. 4
In short, Your Answer would be Option C
Hope this helps!
When an exponent is outside the parentheses, you "distribute" it to the other exponents inside the parentheses.
(4^p)^3 would become 4^3p
(4^1)^3 would become 4^3
When the bases are the same, you just simply add the exponents.
Let's just ignore the bases so it'll look less confusing.
3p + 3 = 15
Subtract 3 from both sides.
3p = 12
Divide both sides by 3.
<em>p = 4</em>
Answer:
ans done
please mark me as brainliest
