Answer:

Step-by-step explanation:
Hello,
let's follow the advise and proceed with the substitution
first estimate y'(x) and y''(x) in function of y'(t), y''(t) and t

Now we can substitute in the equation
![x^2y''(x)+9xy'(x)-20y(x)=0\\ e^{2t}[ \ e^{-2t}(\dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}) \ ] + 9e^t [ \ e^{-t}\dfrac{dy}{dt} \ ] -20y=0\\ \dfrac{d^2y}{dt^2}-\dfrac{dy}{dt}+ 9\dfrac{dy}{dt}-20y=0\\ \dfrac{d^2y}{dt^2}+ 8\dfrac{dy}{dt}-20y=0\\](https://tex.z-dn.net/?f=x%5E2y%27%27%28x%29%2B9xy%27%28x%29-20y%28x%29%3D0%5C%5C%3C%3D%3E%20e%5E%7B2t%7D%5B%20%5C%20e%5E%7B-2t%7D%28%5Cdfrac%7Bd%5E2y%7D%7Bdt%5E2%7D-%5Cdfrac%7Bdy%7D%7Bdt%7D%29%20%5C%20%5D%20%2B%209e%5Et%20%5B%20%5C%20e%5E%7B-t%7D%5Cdfrac%7Bdy%7D%7Bdt%7D%20%5C%20%5D%20-20y%3D0%5C%5C%3C%3D%3E%20%5Cdfrac%7Bd%5E2y%7D%7Bdt%5E2%7D-%5Cdfrac%7Bdy%7D%7Bdt%7D%2B%209%5Cdfrac%7Bdy%7D%7Bdt%7D-20y%3D0%5C%5C%3C%3D%3E%20%5Cdfrac%7Bd%5E2y%7D%7Bdt%5E2%7D%2B%208%5Cdfrac%7Bdy%7D%7Bdt%7D-20y%3D0%5C%5C)
so the new equation is

the auxiliary equation is

so the solutions of the new equation are

with a and b real
as


hope this helps
do not hesitate if you have any questions
Answer:
1. 4x ≤ 25
⇒ x ≤ 6.25
2. x + 4 < 25
⇒ x < 21
3. x + 4 ≥ 25
⇒ x ≥ 21
4. 4 + x ≤ 25
⇒ x ≤ 21
Step-by-step explanation:
1. 4x ≤ 25
⇒ x ≤ 6.25
2. x + 4 < 25
⇒ x < 21
3. x + 4 ≥ 25
⇒ x ≥ 21
4. 4 + x ≤ 25
⇒ x ≤ 21
Answer:
(a)

(b)
-1
(c)
30
Step-by-step explanation:
(a)
Your random variable will have two possible values, 30 and 0, one of them with a probability of 0.45 and the other one with a probability of 0.55. Therefore it looks like this.

(b)
The expected value of this PMF would be
therefore on average you will have a dollar less.
(c)
For this one, if you play 20 times and your initial amount is 50$ then you have to compute the following expectation.
![E[50+20*X] = 50+20*E[X] = 50-20 = 30](https://tex.z-dn.net/?f=E%5B50%2B20%2AX%5D%20%3D%2050%2B20%2AE%5BX%5D%20%3D%2050-20%20%3D%2030)
Answer:
Step-by-step explanation:
1(8)^2-1
its the first variable then the the third one and u raise it by what the number is and u subtract by one