4 * -1 * 3 + 2 = -10
Sorry if I didn't do this right!
Answer:
Step-by-step explanation:
DE given is
y''+8y'+15y=0, y(0)=0, y'(0)=1
Take Laplace on the DE
We get
![s^2 Y(s) -sY(0) -y'(0)+8(sY(s)-y(0))+15Y(s) =0\\s^2 Y(s) -s(0) -1+8(sY(s)-0)+15Y(s) =0\\Y(s)(s^2+8s+15)-1=0\\Y(s) = \frac{1}{s^2+8s+15}](https://tex.z-dn.net/?f=s%5E2%20Y%28s%29%20-sY%280%29%20-y%27%280%29%2B8%28sY%28s%29-y%280%29%29%2B15Y%28s%29%20%3D0%5C%5Cs%5E2%20Y%28s%29%20-s%280%29%20-1%2B8%28sY%28s%29-0%29%2B15Y%28s%29%20%3D0%5C%5CY%28s%29%28s%5E2%2B8s%2B15%29-1%3D0%5C%5CY%28s%29%20%3D%20%5Cfrac%7B1%7D%7Bs%5E2%2B8s%2B15%7D)
Simplify to get
Y(s) = ![\frac{1}{2}[ {\frac{1}{s+3} -\frac{1}{s+5} }]](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B2%7D%5B%20%7B%5Cfrac%7B1%7D%7Bs%2B3%7D%20-%5Cfrac%7B1%7D%7Bs%2B5%7D%20%7D%5D)
Take inverse
![y(t) = \frac{e^{-3t} -e^{-5t}}{2}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20%5Cfrac%7Be%5E%7B-3t%7D%20-e%5E%7B-5t%7D%7D%7B2%7D)
Answer:
6) 48/52
7)48/73
Step-by-step explanation:
SohCahToa
- Sine of an angle = Opposite side/Hypotenuse
- Cosine of an angle = Adjacent side/Hypotenuse
- Tangent of an angle = Opposite side/Adjacent side
These three operators can be thought of as ratios of certain sides of a triangle. A ratio is just a comparison of two quantities; or lengths of the sides in this case.
Answer:
$7.54 is the right answer