Answer:
The objective function in terms of one number, x is
S(x) = 4x + (12/x)
The values of x and y that minimum the sum are √3 and 4√3 respectively.
Step-by-step explanation:
Two positive numbers, x and y
x × y = 12
xy = 12
S(x,y) = 4x + y
We plan to minimize the sum subject to the constraint (xy = 12)
We can make y the subject of formula in the constraint equation
y = (12/x)
Substituting into the objective function,
S(x,y) = 4x + y
S(x) = 4x + (12/x)
We can then find the minimum.
At minimum point, (dS/dx) = 0 and (d²S/dx²) > 0
(dS/dx) = 4 - (12/x²) = 0
4 - (12/x²) = 0
(12/x²) = 4
4x² = 12
x = √3
y = 12/√3 = 4√3
To just check if this point is truly a minimum
(d²S/dx²) = (24/x³) = (8/√3) > 0 (minimum point)
You have to add up all the numbers then divide by the amount of numbers there are
24+38+19=81
81/3=27
The average is 27
Should be simple:
Let's take this one at a time.
2x(x-3y)
You'd get:
for the first one.
2nd one:
5y(x-3y)
you'd get:
Put them both together:
Combine like terms.
Your Answer:
Answer:
<h3>
(base)² + (altitude)² = (hypotenuse) ²</h3>
Therefore,
2²+5² = c² will be matched.
This would be 10-2 which would equal 8
