Answer:
y = (11x + 13)e^(-4x-4)
Step-by-step explanation:
Given y'' + 8y' + 16 = 0
The auxiliary equation to the differential equation is:
m² + 8m + 16 = 0
Factorizing this, we have
(m + 4)² = 0
m = -4 twice
The complimentary solution is
y_c = (C1 + C2x)e^(-4x)
Using the initial conditions
y(-1) = 2
2 = (C1 -C2) e^4
C1 - C2 = 2e^(-4).................................(1)
y'(-1) = 3
y'_c = -4(C1 + C2x)e^(-4x) + C2e^(-4x)
3 = -4(C1 - C2)e^4 + C2e^4
-4C1 + 5C2 = 3e^(-4)..............................(2)
Solving (1) and (2) simultaneously, we have
From (1)
C1 = 2e^(-4) + C2
Using this in (2)
-4[2e^(-4) + C2] + 5C2 = 3e^(-4)
C2 = 11e^(-4)
C1 = 2e^(-4) + 11e^(-4)
= 13e^(-4)
The general solution is now
y = [13e^(-4) + 11xe^(-4)]e^(-4x)
= (11x + 13)e^(-4x-4)
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According to the given diagram, the diameter of the circle is 9 feet.
Remember that the radius is half the diameter, so the radius is 4.5 feet.
<h2>Hence, the answer is 4.5 feet.</h2>
Answer:
Step-by-step explanation:
<u>Simplify</u>
- 4^10 divided by 4^10 . 7^0
- 4^10/(4^10*7^0) =
- 4^10/4^10 =
- 1
The equation given in the question is
13 + (w/7) = - 18
(91 + w) / 7 = - 18
91 + w = - 126
w = - 126 - 91
= - 217
I hope that the procedure is clear enough for you to understand. I also hope that this is the answer that you were looking for and the answer has actually come to your desired help.
