Question

Suppose the breaking strength s in tons of a steel cable of diameter din inches is given by s = 6(5.5). If an engineer wants a cable to have a breaking strength of 30 tons, what
diameter cable (in inches) is needed? Round to the nearest hundredth.

Answer 1

Solving the exponential equation, it is found that a diameter cable of 0.94 inches is needed.

The breaking strength s needed to break a cable with a diameter of d inches is given by:

$s = 6(5.5)^d$

In this problem, breaking strength of 30 tons, hence $s = 30$ and we have to solve for d.

$s = 6(5.5)^d$

$30 = 6(5.5)^d$

$(5.5)^d = \frac{30}{6}$

$(5.5)^d = 5$

$\log{(5.5)^d} = \log{5}$

$d\log{5.5} = \log{5}$

$d = \frac{\log{5}}{\log{5.5}}$

$d = 0.94$

A diameter cable of 0.94 inches is needed.

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