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)
30,000
the way you can solve this is by removing all numbers in front of the selected number(in this case, 2 should be removed) then change all numbers behind to 0.
<span>The first quartile (Q1) is defined as the middle number between the smallest number and the median of the data set.</span>
180 °- 121°
= 59°
the answer is 59°
Answer:
2 
Step-by-step explanation:
Change the mixed numbers to improper fractions
(
- 
) + 
← the LCM of 2 and 3 is 6
= 
- 
+ 
= 
- 
+ 
= 
+
= 
= 
= 2
