(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:
1/2, because 9/16 is closer to 8/16 which reduces to 1/2. It is not as close to 0/16 (0) or 16/16 (1)
Original:
<span>The width and length of a rectangle are consecutive odd integers
</span>so W = x and L = x + 2
<span>If the length is increased by 5 feet, then new L = x + 2 + 5 = x + 7
</span>
A = L x W
60 = (x + 7) x
60 = x^2 + 7x
x^2 + 7x - 60 = 0
(x - 5)(x + 12) = 0
x = 5 and x = -12
From here you have x = W = 5 ft and L = x + 2 = 5 + 2 = 7 feet
Area of original = 5 x 7 = 35
answer
<span>the area of the original rectangle: </span>35 ft^2
22.5 i think but i have no idea good luck
Rewrite the decimal number as a fraction with 1 in the denominator
0.225=0.22510.225=0.2251
Multiplying by 1 to eliminate 3 decimal places, we multiply top and bottom by 103 = 1000
0.2251×10001000=2251000
