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
the new radius be to meet the client's need is 4.9 cm .
<u>Step-by-step explanation:</u>
Here we have , can company makes a cylindrical can that has a radius of 6 cm and a height of 10 cm. One of the company's clients needs a cylindrical can that has the same volume but is 15 cm tall. We need to find What must the new radius be to meet the client's need . Let's find out:
Let we have two cylinders of volume with parameters as follows :
We know that volume of cylinder is , According to question volume of both cylinder is equal i.e
⇒
⇒
⇒
⇒
⇒ Putting all values
⇒
⇒
⇒
⇒
⇒
Therefore , the new radius be to meet the client's need is 4.9 cm .
The 105 per hour mechanic worked for 10 hours and the other worked for 15. here's the math.
If the model is 196 inches, then the real heart is 196/32 inches long (6.125 and i guess just round to 6 if you need to)
Answer:
The independent variable is s
The dependent variable is c
Step-by-step explanation:
Identify the independent and dependent variables:
The equation c = 0.09s gives the amount c (in dollars) of commission a salesperson receives for making a sale of s dollars.
c = 0.09s
Where
c = commission the salesperson makes
s = amount of sales
The variables in the equation are c and s
The independent variable is s
The dependent variable is c because it's value is determined by the amount of sales of the salesperson