You are in charge of the evacuation and repair of a storage tank shaped like a horizontal circular cylinder and buried 4 meters underground. The length of the cylinder is 5 meters and the radius is 2 meters. The storage tank is full of benzene (density 876 kg/m3 ). A firm you contracted says it can empty the tank for 15 cents per Joule of work. Find the work required to empty the tank by pumping the benzene to an outlet 4 meters above the top of the tank. If you have $150, 000 budgeted for the job, can you afford to hire the firm? Calculate the total work as an integral.

ok

explanation:

russian is not my first language, so i'm afraid i can't write out an answer in russian, but hopefully you can find a way to do so. here's my best translation of the problem: you're given a plot of a particle's position in one-dimensional space over time, and you're asked to find either the total distance traveled by the particle after 6 seconds had elapsed, or the total displacement of the particle after 6 seconds.

if you want the total distance traveled, you would first need to determine the particle's velocity as a function of time, then integrate that over the 6-second interval. we know the position function is quadratic with roots at 0 and 6, so we have

where is unknown. because the position is parabolic, there is symmetry about the midpoint at , and we know that

so that the position function is

which means the velocity is

then the total distance traveled is

so the total distance traveled is 20 m.

on the other hand, if you want to find displacement: the particle starts at and ends at , so its displacement is 0.

conduct current i mean it makes sense