The first thing we must do in this case is find the derivatives:
y = a sin (x) + b cos (x)
y '= a cos (x) - b sin (x)
y '' = -a sin (x) - b cos (x)
Substituting the values:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
We rewrite:
(-a sin (x) - b cos (x)) + (a cos (x) - b sin (x)) - 7 (a sin (x) + b cos (x)) = sin (x)
sin (x) * (- a-b-7a) + cos (x) * (- b + a-7b) = sin (x)
sin (x) * (- b-8a) + cos (x) * (a-8b) = sin (x)
From here we get the system:
-b-8a = 1
a-8b = 0
Whose solution is:
a = -8 / 65
b = -1 / 65
Answer:
constants a and b are:
a = -8 / 65
b = -1 / 65
I don't know all of them but I can tell you that B and E are answers that you should check.
Answer: 10.16 centimeters are in 4 inchs
Step-by-step explanation:
Differentiating once, we have
Differentiating again,
as needed.
First, it would help to simplify each side more:
Left side: 36 + 3(4x - 9) = 36 + 12x - 27 = 12x + 9
Right side: c(2x + 1) + 25 = 2cx + c + 25
Write the simplified equation:
12x + 9 = 2cx + c + 25
Usually when there is no solution, the coefficients of the variable on both sides are the same, so we can make the coefficient if x on the right side into 12:
2cx >>> 12x
Then, c must equal 6 to make this true.
The answer is choice (C).
