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Chapter 1: Problem 58

Find a mathematical model that represents the statement. (Determine the constant of proportionality.) \(z\) varies jointly as \(x\) and \(y .(z=64 \text { when } x=4\) and \(y=8 .)\)

Short Answer

Expert verified
The mathematical model representing the statement 'z varies jointly as x and y' and the constant of proportionality is z = 2xy.

Step by step solution

01

Understanding the Problem

Identify the type of variation and the constants given in the problem. The question states that 'z' varies jointly as 'x' and 'y' and provides the values z=64, x=4, y=8 to help find the constant of proportionality. So our equation will follow the form of z=kxy.
02

Solve for Constant of Proportionality

We are going to use the values provided to determine 'k'. Substitute the values of 'z', 'x', and 'y' into the equation of z=kxy: 64=k(4)(8) or 64=k*32. Solving for 'k', we now divide both sides by 32 to get k=64/32=2.
03

Create Mathematical Model

Now that we have k=2, we can write out the mathematical model using k and ensuring the model represents 'z' vary jointly as 'x' and 'y'. Our model is z = 2xy.

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