(a) Take the Laplace transform of both sides:
where the transform of 
comes from
![L[ty'(t)]=-(L[y'(t)])'=-(sY(s)-y(0))'=-Y(s)-sY'(s)](https://tex.z-dn.net/?f=L%5Bty%27%28t%29%5D%3D-%28L%5By%27%28t%29%5D%29%27%3D-%28sY%28s%29-y%280%29%29%27%3D-Y%28s%29-sY%27%28s%29)
This yields the linear ODE,
Divides both sides by 
:
Find the integrating factor:
Multiply both sides of the ODE by 
:
The left side condenses into the derivative of a product:
Integrate both sides and solve for 
:
(b) Taking the inverse transform of both sides gives
![y(t)=\dfrac{7t^2}2+C\,L^{-1}\left[\dfrac{e^{s^2}}{s^3}\right]](https://tex.z-dn.net/?f=y%28t%29%3D%5Cdfrac%7B7t%5E2%7D2%2BC%5C%2CL%5E%7B-1%7D%5Cleft%5B%5Cdfrac%7Be%5E%7Bs%5E2%7D%7D%7Bs%5E3%7D%5Cright%5D)
I don't know whether the remaining inverse transform can be resolved, but using the principle of superposition, we know that 
is one solution to the original ODE.
Substitute these into the ODE to see everything checks out:
$8.50 x 1.06 = $9.01
The 1.06 comes from the cost of the whole shirt (1) plus the amountof tax (.06) added together.
E all of these are hexahedra
In first calculation Miranda was first calculating tax of a 7% of 19$ tennis racket and than she added it to cost of tennis racket. In second calculation she automatically calculated 107% of a price of tennis racket that she will pay at register.
Answer:
Below because there is a lot to explain
Step-by-step explanation:
The Minimum of the data set is 20 and the maximum is 75, the median of the data set is 50, and the interquartile range is 30. The data is most likey asymetrical due to the average being median and not mean. Hope this helps :)
