Answer:
y(t)= 11/3 e^(-t) - 5/2 e^(-2t) -1/6 e^(-4t)
Step-by-step explanation:
We know that 
, so we have
By using the method of partial fraction we have:
Now we have:
](https://tex.z-dn.net/?f=%20y%28t%29%3DL%5E%7B-1%7D%5BY%28s%29%5D%28t%29%20)
Using linearity of inverse transform we get:
 -L^{-1}[\frac{5}{2(s+2)}](t) -L^{-1}[\frac{1}{6(s+4)}](t)](https://tex.z-dn.net/?f=%20y%28t%29%3DL%5E%7B-1%7D%5B%5Cfrac%7B11%7D%7B3%28s%2B1%29%7D%5D%28t%29%20-L%5E%7B-1%7D%5B%5Cfrac%7B5%7D%7B2%28s%2B2%29%7D%5D%28t%29%20-L%5E%7B-1%7D%5B%5Cfrac%7B1%7D%7B6%28s%2B4%29%7D%5D%28t%29%20)
Using the inverse transforms
![L^{-1}[c\frac{1}{s-a}]=ce^{at}](https://tex.z-dn.net/?f=%20L%5E%7B-1%7D%5Bc%5Cfrac%7B1%7D%7Bs-a%7D%5D%3Dce%5E%7Bat%7D%20)
we have:
Answer:
C. 2
Step-by-step explanation:
If the discriminant is >0 we have 2 real solutions
If the discriminant is =0 we have 1 real solutions
If the discriminant is <0 we have 2 complex solutions (no real solutions)
since 10>0 we have 2 real solutions
Which of the following best represents the average rate at which infants grow in height during the first four years after birth? <span>B: 3inches per year</span>
Answer:
60 cm & 60 mL
Hope this helps! Let me know if this is right or not.
Answer:
t = 204
Step-by-step explanation:
Let t = initial number of trees
"remove 5 trees at the start of the season" means
(t - 5) remain
"each remaining tree made 210 oranges for a total of 41,790 oranges" means
( t - 5) * 210 = 41790
Now, you can solve for t:
(t-5)(210) = 41790 [just re-writing]
210t - 1050 = 41790 [distribute]
210t = 42840 [add 1050 to each side]
t = 204 [divide each side by 210]
There were initially 204 trees. After 5 were removed, the remaining 199 produced 210 oranges each for a total of 199*210 = 41790 oranges.
