Final answer:
To find f for p=2 and c=4 when f varies jointly as p and the cube of c, first solve for the constant k using the given values f=8, p=4, and c=0.1. Then, use the constant to calculate f for the new values of p and c. In this case, f equals 256,000.
Step-by-step explanation:
To find the value of f when p=2 and c=4, given that f varies jointly as p and the cube of c, and f=8 when p=4 and c=0.1, we use the joint variation equation f = kp(c^3).
First, solve for the constant k using the provided values:
f=8, p=4, c=0.1
Thus,
8 = k*4*(0.1^3)
Which simplifies to:
k = 8 / (4*0.001)
So, k = 2000.
Now use the value of k to find f when p=2 and c=4:
f = 2000*2*(4^3)
This simplifies to:
f = 2000*2*64
And we find that:
f = 256000
Therefore, the value of f when p=2 and c=4 is 256000.