Answer:
Step-by-step explanation:
In the case of each of the answers listed above, the second derivative is equal to -4 times the function, as required by the differential equation.
For y = 2/3t^3, the second derivative is 4t, not -4y.
For y = e^(2t), the second derivative is 4y, not -4y.
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The graph shows the sum of the second derivative and 4y is zero for the answers indicated above, and not zero for the other two proposed answers.
I'm assuming the function is f(x) = (2x+8)/(x^2+5x+6). If so, make sure to use parenthesis to indicate that you're dividing all of "2x+8" over all of "x^2+5x+6" as one big fraction. Otherwise, things are ambiguous and it leads to confusion.
Side Note: x^2 means "x squared"
Factor the numerator: 2x+8 = 2(x+4)
Factor the denominator: x^2+5x+6 = (x+2)(x+3)
There are no common factors between the numerator and denominator. So there is nothing to cancel out.
Recall that you cannot divide by zero. Something like 1/0 is undefined.
We need to find the x values that cause the denominator to be zero.
Set the denominator equal to zero and solve for x
x^2+5x+6 = 0
(x+2)(x+3) = 0
x+2 = 0 or x+3 = 0
x = -2 or x = -3
The x values x = -2 or x = -3 will lead to the denominator being zero. This means that the vertical asymptotes are x = -2 or x = -3 as shown by the blue dashed vertical lines in the attached image.
Cot( \theta) = 1/tan( 1\theta)
Tan (36o) = 0.7265
1 / tan(36o) = 1.3765
D <<<< answer
