1.3 so closer to 1 !! Best of luck
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)
Answer:
8.25 is the answer.
Step-by-step explanation:
Hope this helps!
Answer: 54
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Explanation:
The first ratio is 1:6. The jump from 1 to 6 has us multiplying the 1 by 6 to get 6.
1*6 = 6
So we follow the same rule of "multiply by 6" to go from 9 to 54 (9*6 = 54)
Or you can use a proportion to get
1/6 = 9/x
1*x = 6*9 ... cross multiply
x = 54
and we get the same answer
