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Find f when p=2 and c=4 if f varies jointly as p and the cube of c, and f=8 when p=4 and c=0.1.

User Gavy
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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.

User Orquesta
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