Answer:
Step-by-step explanation:
Given that the solution of a certain differential equation is of the form
![y(t) = ae^{7t} +be^{11t}](https://tex.z-dn.net/?f=y%28t%29%20%3D%20ae%5E%7B7t%7D%20%2Bbe%5E%7B11t%7D)
Use the initial conditions
i) y(0) =1
... I
ii) y'(0) = 4
Find derivative of y first and then substitute
![y'(t) = 7ae^{7t} +11be^{11t}\\y'(0) =7a+11b \\7a+11b =4 ...II](https://tex.z-dn.net/?f=y%27%28t%29%20%3D%207ae%5E%7B7t%7D%20%2B11be%5E%7B11t%7D%5C%5Cy%27%280%29%20%3D7a%2B11b%20%5C%5C7a%2B11b%20%3D4%20...II)
Now using I and II we solve for a and b
Substitute b = 1-a in II
![7a+11(1-a) = 4\\-4a+11 =4\\-4a =-7\\a = 1.75 \\b = -0.75](https://tex.z-dn.net/?f=7a%2B11%281-a%29%20%3D%204%5C%5C-4a%2B11%20%3D4%5C%5C-4a%20%3D-7%5C%5Ca%20%3D%201.75%20%5C%5Cb%20%3D%20-0.75)
Hence solution is
![y(t) = 1.75e^{7t} -0.75e^{11t}](https://tex.z-dn.net/?f=y%28t%29%20%3D%201.75e%5E%7B7t%7D%20-0.75e%5E%7B11t%7D)
Each friend should get 1/3 if there is only 2/3 left
They would be parallel lines
Answer:
10999
Step-by-step explanation:
9560 + 1439 = 10999
Thenks and mark me brainliest :)