Answer:
Step-by-step explanation:
Given is a differential equation
![y''-3y'+2y=3e^{2t}](https://tex.z-dn.net/?f=y%27%27-3y%27%2B2y%3D3e%5E%7B2t%7D)
Take Laplace on both the sides
![L(y")-3L(y')+2L(y) = L(e^{2t}](https://tex.z-dn.net/?f=L%28y%22%29-3L%28y%27%29%2B2L%28y%29%20%3D%20L%28e%5E%7B2t%7D)
![s^2 Y(s)-sy(0) -y'(0) -3sY(s)+3y(0)+2Y(s)= L(3e^{2t} )\\Y(s)(s^2-3s+2)-1=\frac{3}{s-3}](https://tex.z-dn.net/?f=s%5E2%20Y%28s%29-sy%280%29%20-y%27%280%29%20-3sY%28s%29%2B3y%280%29%2B2Y%28s%29%3D%20L%283e%5E%7B2t%7D%20%29%5C%5CY%28s%29%28s%5E2-3s%2B2%29-1%3D%5Cfrac%7B3%7D%7Bs-3%7D)
![Y(s)(s^2-3s+2)=\frac{3}{s-3}+1\\Y(s) = \frac{s}{(s-3)(s-1)(s-2)}](https://tex.z-dn.net/?f=Y%28s%29%28s%5E2-3s%2B2%29%3D%5Cfrac%7B3%7D%7Bs-3%7D%2B1%5C%5CY%28s%29%20%3D%20%5Cfrac%7Bs%7D%7B%28s-3%29%28s-1%29%28s-2%29%7D)
Resolve into partial fractions
![Y(s) = \frac{-2}{(s-2)} +\frac{1}{2(s-1)} +\frac{3}{2(2-3)}](https://tex.z-dn.net/?f=Y%28s%29%20%3D%20%5Cfrac%7B-2%7D%7B%28s-2%29%7D%20%2B%5Cfrac%7B1%7D%7B2%28s-1%29%7D%20%2B%5Cfrac%7B3%7D%7B2%282-3%29%7D)
Taking inverse
y(t) = ![-2e^{2t} +0.5e^t+1.5e^{3t}](https://tex.z-dn.net/?f=-2e%5E%7B2t%7D%20%2B0.5e%5Et%2B1.5e%5E%7B3t%7D)
To solve this problem you must apply the proccedure shown below:
1. You must apply the Pythagorean Theorem, which is:
a²=b²+c²
a is the hypotenuse and b and c the legs of the triangle.
2. You have that:
b=c=x
3. Therefore:
a²=2x²
(2√6)=2x²
4. Now, you must clear the x, as below:
x²/2=24
x²=24/2
x²=12
x=√12
x=2√3
5. Therefore, as you can see, the answer is 2√3
Answer:
2*(n-1) represent the product of 2 and the difference of number and 1.
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Answer:
B. The count of drawing a red ball is a binomial distribution.
Step-by-step explanation:
The count of drawing a red ball can be gotten by binomial distribution because:
the chance of success; p = 26/50 and chance of no failure; q = 24/50
For example, If we want to find probability of getting 5 red balls out of 20 selections, we will use the binomial probability distribution formula;
P(X = 5) = C(20, 5) × p^(5) × q^(20 - 5)
This same procedure also applies if we want to get the probability of getting a number of yellow balls out of a number of selections from the bag.
Looking at the options, the best option that explains how it's binomial probability that works is option B
Answer:
18 is .20
19 is c+5 over 3
Step-by-step explanation:
18.
p= 4C 1 /4C1 * 5C1 = 4 / 4*5 = .20
19.
(3a - 5) / c = 1
3a - 5 = c
3a = c + 5
a = (c + 5) / 3