1. ## Accumulators

A long lake is used as a reservoir to supply a hydro dam. The lake is approximately the shape of a rectangular prism with a length of 80 km, a width of 2km and a depth of 500m. On January 1st, the amound of water in the reservoir is 80 billion m^3.

The flow of water into the lake is E(t) = 90/ 2 + cos((2pi/365) t)
measured in m^3/day
The flow of water out of the lake is L(t) = 146/ 3 + cos((2pi/365) t)
measured in m^3/day

What is the rate of depth increase on the 182nd day of the year? (in cm/hour)

The answer in my text book says it's 0.4427 cm/hour

Could you please give a step by step guide, Thanks a ton

~G

2. ## Unless I misread it

which i often do...this is jsut a derivative at a point problem...ok $f(t)=\frac{90}{2}+cos\bigg(\frac{2\pi{t}}{365}\big g)$...so the derivative is $f'(t)=-sin\bigg(\frac{2\pi{t}}{35}\bigg)\cdot\frac{2\pi}{ 365}$...now evaluate it at $182$ and you get $f'(182)=-sin\bigg(\frac{2\pi}{182}{236}\bigg)\cdot\frac{2\p i}{365}$=-.000142....o I messed up... you have to add the two functions together and differntiate then plug in 182...use same concept as above...the answer should be -3.6666