exam Maths Puzzle Numerical Ability

Given the ATC function
TC=5000Q-100Q^2+1.0Q^3
a. What is the level of output that maximizes profit
b. Show the value of Q as in a. where it minimizes the ATC

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exam Other Question

i am searching for help with length vs. numbers using connecting links problem set 5.1 #13 page 396

(2/3)^t =9/4

is this how you would do it or am I off?!
2-3^2/ 3-2^

not sure if i'm even on the right track please help