A 150-foot-long cable of diameter 6 inches is submerged in seawater. Because of corrosion, the surface area of the cable decreases at the rate of 780 in2 per year. Express the diameter d of the cable as a function of time t (in years).

Damon Campos

Damon Campos

Answered question

2022-08-05

A 150-foot-long cable of diameter 6 inches is submerged in seawater. Because of corrosion, the surface area of the cable decreases at the rate of 780 in2 per year. Express the diameter d of the cable as a function of time t (in years).

Answer & Explanation

Madilyn Dunn

Madilyn Dunn

Beginner2022-08-06Added 16 answers

150 ft = 1800 inches
Surface area = circumference length = p d L = p 6 1800 = 10800 p   i n 2
The surface area decreases by 780 in² each year, so the surface area any given year is
S = 10800 p   i n ² 780   i n ² t
Back to our original surface area equation, S = pdL. L = 10800 & S = 10800p - 780t, so we get
d = S p L = 10800 p 780 t 1800 p = 6 i n ( 0.138 i n / y r ) t

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