The sum of the two positive numbers is 120. What is the maximum value of the product of these two numbers?
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If one number is x, the other is (96 - x)...since if you add those two together, you will get 96..and the product is x(96 - x) = 96x - x^2

Since this is a quadratic function (x to the power of 2), it is a parabola. More specifically, it is a parabola opening downwards, because there is a negative in front of the x squared. Because it downward facing the maximum value of x is going to be where the vertex is. The x value of the vertex can be found by taking the negative of b (which is the number in front of teh x) over a squared (which is the number in front of the x squared which in this case is 1)

So x = -96 / 2(-1) = -96/-2 = 48

Since as we first stated one number is x, the first number is 48

The second number will be 48, because we stated the second number to be 96-x

Therefore 48 times 48 will give you the maximum product 2304.  

Hope This Helps

3,600

Step-by-step explanation:

x + y = 120

y = 120 - x

Product "P"

P = x × y = x(120-x) = 120x - x²

P = -(x² - 20x)

= -(x² - 2(x)(60) + 60² - 60²)

= -(x - 60)² + 3600

Max value is 3,600

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step-by-step explanation:

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