Answer:
-24/5
Step-by-step explanation:
The solution to the problem is as follows:
cscx < 0 means 1/sinx < 0, or sinx < 0.
sinx = -3/5 because you're dealing with a 3-4-5 triangle, and we established
sinx is negative.
sin2x = 2sinxcosx = 2*-3/5*4/5 = -24/25
cos(2x) = cos^2(x) - sin^2(x) = 16/25 - 9/25 = 5/25 = 1/5
tan2x = sin2x / cos2x = -24/5
Answer:
The answer to the problem is -15.52
Answer:
C = 5.
Step-by-step explanation:
First, you need to remember that:
For the function:
h(x) = Sinh(k*x)
We have:
h'(x) = k*Cosh(k*x)
and for the Cosh function:
g(x) = Cosh(k*x)
g'(x) = k*Cosh(k*x).
Now let's go to our problem:
We have f(x) = A*cosh(C*x) + B*Sinh(C*x)
We want to find the value of C such that:
f''(x) = 25*f(x)
So let's derive f(x):
f'(x) = A*C*Sinh(C*x) + B*C*Cosh(C*x)
and again:
f''(x) = A*C*C*Cosh(C*x) + B*C*C*Sinh(C*x)
f''(x) = C^2*(A*cosh(C*x) + B*Sinh(C*x)) = C^2*f(x)
And we wanted to get:
f''(x) = 25*f(x) = C^2*f(x)
then:
25 = C^2
√25 = C
And because we know that C > 0, we take the positive solution of the square root, then:
C = 5
