Please draw out the rectangular prism parts PLEASE HELP
1 answer:
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Answer:
The solution for this system is:
Step-by-step explanation:
The problem states that we have to solve this system by the elimination method
In the elimination method, we transform the system in such a way that one variable can cancel each other. With this, we find the result of the other variable. Then, we can replace the variable we found in any of the equations, and we have the value of the variable that we had initially canceled.
In this problem, we have the following system:
If we add equations 1) and 2), the variable x is going to be eliminated
Now, we can replace the value of y in any of the equations, to find x:
I will replace in equation 2)
The solution for this system is:
Answer:
a) y₁(t) = (2.5e⁰•⁸ᵗ - 2.5e⁰•⁴ᵗ)
b) y₂(t) = (2e⁰•⁴ᵗ - e⁰•⁸ᵗ)
c) W(y₁,y₂) = -e¹•²ᵗ
Step-by-step explanation:
To solve, 25y" - 30y' + 8y = 0
With conditions, y₁'(0) = 1 and y₁(0) = 0 for y₁
And y₂'(0) = 0 and y₂(0) = 1 for y₂
Solving for y₁ first, using Laplace transforms.
Note:
L(y") = s² Y(s) - sy(0) - y'(0)
L(y') = s Y(s) - y(0)
L(y₁") = s² Y(s) - sy₁(0) - y'₁(0) = s² Y(s) - 0 - 1 = s² Y(s) - 1
L(y₁') = s Y(s) - y₁(0) = s Y(s)
L [25y" - 30y' + 8y] = L (0)
25(s²Y(s) - 1) - 30(sY(s)) + 8Y(s) = 0
25s²Y(s) - 25 - 30sY(s) + 8Y(s) = 0
Y(s) [25s² - 30s + 8] - 25 = 0
Y(s) [25s² - 30s + 8] = 25
Y(s) = (25)/[25s² - 30s + 8]
Y(s) = (25)/[(5s-4)(5s-2)]
To continue, we need to resolve 1/[(5s-4)(5s-2)] into partial fractions.
The calculation is continued on the attached images.
