Answer:
[tex]work \ done= 45937.5[/tex]
Step-by-step explanation:
Work done is given by
[tex]work \ done=\int_a^b w(d-x) \ dx[/tex] , where d = length of cable and w = weight of cable.
Here, d = 175 ft and w = 3 lb/ft
Now, [tex]work \ done=\int_0^{175} 3(175-x) \ dx[/tex]
[tex]work \ done= 3\left [175x-\frac{x^2}{2} \right ]_0^{175}[/tex]
[tex]work \ done= 3\left [175^2-\frac{175^2}{2} \right ][/tex]
[tex]work \ done= 3\cdot \frac{175^2}{2}[/tex]
[tex]work \ done= 45937.5[/tex]
