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OK, we're going to find the anti derivative.
So we're going to get DSDT equaling negative KT plus C1.
We were given DSDT is 80 when T is 0, so our C1 is 80.
Now we're going to find the original S by taking the
integral again.
So s = -K / 2 T squared plus ADT plus C2.
Now we're given that S is 0 when T is 0, so our C2 is 0.
So s = -K / 2 T squared plus ADT.
Part 2 says figure out what happens when DSDT equals zero.
Well, DSDT equaled negative KT plus 80, so zero is going to
equal negative KT plus 80.
Take the KD to one side, solve for T so we get 80 / K Part
three says what happens when S is 200?
What is our K value?
Our K is a constant, so we're going to put 200 in for us and
we're going to put 80 / K in for our T and we're going to solve
for K and we get K = 16.