SOLUTION: i need to write a proportion that indicates that 50% of a number is 17.
I also need to find two integers whose sum is 12 and whose product is a maximum.
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-> SOLUTION: i need to write a proportion that indicates that 50% of a number is 17.
I also need to find two integers whose sum is 12 and whose product is a maximum.
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Question 82752: i need to write a proportion that indicates that 50% of a number is 17.
I also need to find two integers whose sum is 12 and whose product is a maximum.
You can put this solution on YOUR website! i need to write a proportion that indicates that 50% of a number is 17.
:
We know that 50% indicates a relationship of 1:2 or 1/2
Therefore: =
Cross multiply & find x
1x = 2*17
x = 34
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I also need to find two integers whose sum is 12 and whose product is a maximum.
:
Let the two integers be x and (12-x); their product:
x(12-x) = 12x - x^2
:
-x^2 + 12x = 0; a quadratic equation
:
Find the max by finding the axis of symmetry: x = -b/(2a)
In our equation a = -1; b = 12:
x = -12/(2(-1)
x = -12/-2
x = 6, obviously the two integers are 6 & 6
:
You can find the vertex using x = 6
-6^2 + 12(6) =
-36 + 72 = + 36 is the max
:
If you graph it, it's easy to see
;
One of the integers is on the horizontal axis, the max product on the vertical
