I don’t see the 2 part anywhere?
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:
n = 12 nickels
d = 11 dimes
q = 7 quarters
Step-by-step explanation:
.05n + .1d + .25q = 3.45
n + d + q = 30
n = q + 5
n = 12
d = 11
q = 7
｡☆✼★ ━━━━━━━━━━━━━━ ☾ ━━━━━━━━━━━━━━ ★✼☆｡
- The equation :
Area = length x width
- Substitute the values in :
Area = (x - 5)(x - 5 + 22)
(Note : the 'x' is for the algebraic expression x in the example above)
- Now you have to simplify the second parenthesis:
Area = (x - 5)(x + 17)
- Now expand :
Area = x^2 + 17x - 5x - 85
- Simplify by collecting like terms :
Area = x^2 + 12x - 85
(Note : x^2 means x squared)
Now you have your answer as:
x^2 + 12x - 85 feet^2
Have A Nice Day ❤
Stay Brainly! ヅ
- Ally ✧
｡☆✼★ ━━━━━━━━━━━━━━ ☾ ━━━━━━━━━━━━━━ ★✼☆｡
Answer:
Solve the equation for x by finding a, b, and c of the quadratic then applying the quadratic formula.
Exact Form:
x = − 70 ± √4210/30
Decimal Form:
x = −0.03
Step-by-step explanation:
5x(6x+28)=−23
Step 1: Simplify both sides of the equation.
30x2+140x=−23
Step 2: Subtract -23 from both sides.
30x2+140x−(−23)=−23−(−23)
30x2+140x+23=0
Step 3: Use quadratic formula with a=30, b=140, c=23.
x=−b±√b2−4ac/2a
x=−(140)±√(140)2−4(30)(23)/2(30)
x=−140±√16840/60
x=−7/3+1/30√4210 or x=−7/3+−1/30√4210
