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Q: The sum of two positive numbers is 89 Find a function that models their product P in terms of x one of the numbers?

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Let one number be x, the other is 83-xTheir product is x(83-x)so the function isf(x)=x(83-x)or f(x)=83x-x2

If x is one of the numbers and y the other, then their sum is x+y = 53. So y = 53-x where x>0 and y>0 implying that x<53. Then, their product, P = x*y = x*(53-x) = 53*x - x2 for 0<x<53 [P is not defined for other values of x]

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