Use the graph of the polynomial function to find the factored form of the

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

Rus_ich [418]

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

6 0

3 years ago

A park is 4.6 miles long and 2.7 miles wide. A:what is the total distance around the park? B:if a racecar drove 50 times around

Vlada [557]

Answer:

A) Total distance around the park is 14.6 miles

B) The total distance drove by racer 730 miles

Step-by-step explanation:

Given as :

The length of park = 4.6 miles

The width of park = 2.7 miles

Let the total distance cover around park = Perimeter of park = P miles

So, Perimeter of rectangular park = 2 × Length + 2 × width

or, P = 2 × 4.6 + 2 × 2.7

I.e P = 9.2 + 5.4

Or, perimeter = 14.6 miles

A ) ∴ Total distance around the park = 14.6 miles

B ) The total distance drove by racer = 50 times around the park

So, The total distance drove by car = 50 × Total distance around the park

∴The total distance drove by car = 50 × 14.6 = 730 miles

Hence A) Total distance around the park is 14.6 miles

B) The total distance drove by racer 730 miles answer

6 0

3 years ago

Apply the distributive property to create an equivalent expression. 12(2a - 6b+ 8) = 2 1 (2a−6b+8)

liberstina [14]

Answer:

a+4=11b

Step-by-step explanation:

Distributive property in mathematics means to multiply the sum by a number of two or more add-ons will provide the same result that each add-on multiplies by a single number and then together add the products.

for example a( b+c) = ab+ac

Therefore, applying distributive property in asked eapression

12(2a - 6b+ 8) = 21(2a−6b+8)

24a+72b+96 = 42a-126b+168

198b=18a+72

9a +36=99b

3a+12=33b

a+4=11b

5 0

3 years ago

5x=4y+8 3y=3x-3 using elimination

suter [353]

Let's rewrite the equation with x and y on the left side of the equal sign.
5x-4y=8 --------(1)
3x-3y=3---------(2)
Divide equation (2) by 3,
x - y= 1
now we have,
5x-4y = 8 --------(1)
x - y = 1 ---------(2)
To eliminate x, multiply equation (2) by 5. This makes both the coefficients of x to be 5. Subtract the second equation from the first equation.
5x - 4y = 8
(2) * 5 5x - 5y = 5
(-) (+) (-)
----------------
0x +y =3
Therefore, y=3
Substitute the value of y, in any one of the two equations. Let's substitute y in the second equation.
x-3=1
x=4
x=4 and y=3

8 0

4 years ago

What is the remainder of 67 divided by 3?

hammer [34]

The remainder for 67 divided by 3 would be 1 because (this might be a bad explanation since i'm not good at explaining math without showing u my work) if u do divide 6 by 3, 3x2 is 6 and 6-6 is 0. Then if u divide 7 by 3, then 6 is the closest u can get to 7 without multiplying by a decimal. Then if u do 7-6, u get 1 and u cant divide 1 by 3 so the remainder would be 1.

8 0

3 years ago