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Genrish500 [490]
2 years ago
11

The function f(x)=Acosh(Cx)+Bsinh(Cx). I need help determining the value of constant C>0 when the second derivative f''(x)=25

(f(x)).
Mathematics
1 answer:
Rus_ich [418]2 years ago
6 0

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

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pochemuha

     •   f(x) = 3x + 4

     •   g(x) = 8x + 1


Sum both functions above:

     (f + g)(x) = f(x) + g(x)

     (f + g)(x) = (3x + 4) + (8x + 1)

     (f + g)(x) = 3x + 8x + 4 + 1

     (f + g)(x) = 11x + 5


Therefore,

     (f + g)(0) = 11 · 0 + 5

     (f + g)(0) = 0 + 5

     (f + g)(0) = 5   <———   this is the answer.


I hope this helps! =)

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The <em>speed</em> intervals such that the mileage of the vehicle described is 20 miles per gallon or less are: v ∈ [10 mi/h, 20 mi/h] ∪ [50 mi/h, 75 mi/h]

<h3>How to determine the range of speed associate to desired gas mileages</h3>

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To learn more on quadratic functions: brainly.com/question/5975436

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