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Chapter 1: Problem 59

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(F\) is jointly proportional to \(r\) and the third power of \(s\) \((F=4158 \text { when } r=11 \text { and } s=3 .)\)

Short Answer

Expert verified
The constant of proportionality \(k\) is 14.

Step by step solution

01

Write down the equation

First, write down the general form of the equation with the unknown constant \(k\). The equation is as follows: \(F=krs^3\)
02

Substitute the Known Values into the Equation

Next, substitute the known values \(F=4158\), \(r=11\) and \(s=3\) into the equation from Step 1. This gives the equation \(4158=k*11*3^3\)
03

Solve for the constant of proportionality \(k\)

Finally, solve the equation from Step 2 for \(k\), by dividing both sides of the equation by \(11*3^3\). So, \(k = 4158 / (11*3^3) = 14\)

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