the flow of water into a small dam over the course of a year varies with time and is approximated by dW / dt = 1.2 - cos^2 pi/12t, where W is the volume of the water in the dam, measured in thousands of cubic metres, and t is the time measured in months from the beginning of jannuary.
What is the max flow rate into the dam and when does this happen?
i tried (failed) :
dW / dt = 1.2 - cos^2 pi/12t
dW / dt for possible st.p
1.2 = cos^2 pi/12t
1.2 = (cos pi/6 t +1)/2
1.4 = cos pi/6 t
~ got raped here
I did (correct):
cos^2 pi/12t = (cos pi/6 t +1)/2
|cos pi/6 t| <= 1, min at t = 6
1200m^3 per month at the beginning of July
now my question is how come my first part got stuffed when trying to do a diff method, and do you have to double diff in that case to prove its a max always? WAITT i think i got it, correct me if im wrong. for method 1 i was suppose to make dW^2 / d^2t = 0 riight, not dW / dt? I'm too lazy to double diff now, sleepy xDD
its amazing what happens whilst you post
What is the max flow rate into the dam and when does this happen?
i tried (failed) :
dW / dt = 1.2 - cos^2 pi/12t
dW / dt for possible st.p
1.2 = cos^2 pi/12t
1.2 = (cos pi/6 t +1)/2
1.4 = cos pi/6 t
~ got raped here
I did (correct):
cos^2 pi/12t = (cos pi/6 t +1)/2
|cos pi/6 t| <= 1, min at t = 6
1200m^3 per month at the beginning of July
now my question is how come my first part got stuffed when trying to do a diff method, and do you have to double diff in that case to prove its a max always? WAITT i think i got it, correct me if im wrong. for method 1 i was suppose to make dW^2 / d^2t = 0 riight, not dW / dt? I'm too lazy to double diff now, sleepy xDD
its amazing what happens whilst you post