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)
The statement <S and <H are equal in measure is False
<h3>How to determine the true statement?</h3>
The similarity statement is given as:
ΔRST is similar to ΔHGF
This means that:
- Angles R and H are congruent
- Angles S and G are congruent
- Angles T and F are congruent
Hence, the statement <S and <H are equal in measure is False
Because S equals G and R equals H
Read more about similar triangles at:
brainly.com/question/14285697
#SPJ1
It would be a 12.5% increase. First you find her monthly wages: $10.50 x 160 hours= $1680 a month. Her insurance is $210/month. So you need to find what percentage 210 is of 1680. So
. Solve for x by dividing 1680 on both sides and you get 0.125. Multiply by 100 to get the percentage and you get 12.5%. Check your answer by multiplying 1680 x 0.125 and you get 210.
Step-by-step explanation:
The answer is 8
Because you have to put each value of x given in the equation 3x = 24
So when you put the value 8
3(8) = 24
24 = 24
Answer:
x + 4 < 8
- 4 -4
x < 4
Step-by-step explanation:
So, Basically anything less than 4 is a solution for this equation.
