Question

Leave K in fraction form or round to at least 3 decimal places. Round off your final answer to the nearest hundredth.

Answer 1

By definition, an equation of a Combined Variation has the following form:

`z=k((x)/(y))`

Where "k" is the Constant of Variation.

In this case, you know that the resistance "R" of a wire varies directly as its length and inversely as the square of its diameter.

Then, let be "R" the resistance of the wire (in ohms), "l" its length of the wire (in feet), and "d" its diameter (in inches).

Therefore, you can set up that the equation has this form:

`R=k((l)/(d^2))`

According to the information given in the exercise, when:

`\begin{gathered} l=3300 \\ d=0.16 \end{gathered}`

The resistance is:

`R=10357`

Then, you can substitute values into the equation and solve for "k":

`\begin{gathered} 10357=k((3300)/((0.16)^2)) \\ \\ (10357)(((0.16)^2)/(3300))=k \end{gathered}`
`k\approx0.080`

Therefore, you can set up the following equation that represents this situation (using the value of "k"):

`R=0.080\cdot(l)/(d^2)`

Hence, if:

`\begin{gathered} l=2900 \\ d=0.15 \end{gathered}`

You can substitute these values into the equation and then evaluate, in order to find the corresponding resistance. This is:

`\begin{gathered} R=0.080\cdot((2900))/((0.15)^2) \\ \\ R\approx10311.11 \end{gathered}`

Therefore, the answer is:

`10311.11\text{ }ohms`