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Chapter 44: Problem 1246

If y varies inversely as the cube of \(\mathrm{x}\), and \(\mathrm{y}=7\) when \(\mathrm{x}=2\), express \(\mathrm{y}\) as a function of \(\mathrm{x}\).

Short Answer

Expert verified
The function expressing y as a function of x is \(y(x) = \frac{56}{x^3}\).

Step by step solution

01

Write the Inverse Variation Formula

For y varying inversely as the cube of x, the formula is given by: \[y = \frac{k}{x^3}\] where k is the constant of variation.
02

Substitute the given values

We are given that when x = 2, y = 7. Substitute these values into the above formula: \[7 = \frac{k}{2^3}\]
03

Solve for the constant k

Now, simplify and solve for the constant k: \[7 = \frac{k}{8}\] \[k = 7\times8\] \[k = 56\]
04

Write the function involving x and y

Now that we have found the constant k = 56, we can express y as a function of x using the inverse variation formula: \[y = \frac{56}{x^3}\] So, the function expressing y as a function of x is: \[y(x) = \frac{56}{x^3}\]

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Most popular questions from this chapter

The resistance \(\mathrm{R}\) of a given size of wire at constant temperature varies directly as the length \(\ell\). It is found that the resistance of 100 feet of number 14 copper is \(0.253\) ohm. Construct a table of values for the given lengths of number 14 copper wire assuming the temperature is constant.

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