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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
Answer:
D. is the answer
Step-by-step explanation:
Well,
If the slope of the lines are the same, then the lines are parralel.
We need to manipulate 2y - 10x = 4 into y = mx + b form.
Add 10x to both sides
2y = 10x + 4
Divide both sides by 2
y = 5x + 2
Do the same thing with the other equation.
Add 2 to both sides
y = 5x + 2
y = 5x + 2
It appears that, not only are they parallel, but they lie on exactly the same line! If this was a System of Simultaneous Linear Equations, then there would be an infinite number of solutions!<span />
