SOLUTION: Find two positive numbers that satisfy the given requirements: the sum of the first number squared and the second is 54 and the product is a maximum.
Algebra ->
Test
-> SOLUTION: Find two positive numbers that satisfy the given requirements: the sum of the first number squared and the second is 54 and the product is a maximum.
Log On
Question 366968: Find two positive numbers that satisfy the given requirements: the sum of the first number squared and the second is 54 and the product is a maximum. Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website! Find two positive numbers that satisfy the given requirements: the sum of the first number squared and the second is 54 and the product is a maximum.
------------
1st: x
2nd: y
----
Equation:
x^2+y = 54
y = 54-x^2
----
Product = x(54-x)^2 = 54x-x^3
----
dP/dx = 54-3x^2
Solve: 54-3x^2 = 0
3x^2=54
x^2 = 18
x = sqrt(18)
y = 54-(sqrt(18))^2 = 36
-----
Cheers,
Stan H.
--------
(