Answer:
x = 59.4 ft
y = 84.18ft
Step-by-step explanation:
The cost of exterior walls is $150 per linear foot.
The cost of interior walls is $100 per linear foot.
xy = 5000
y = 5000/x
For the exterior walls, we have 2(x+y)(120)
For the interior wall, we have 100x
The cost function = C
C = 2(x+y)(120) + 100x
C= 240(x+y) + 100x
= 240x + 240y + 100x
= 340x + 240y
Recall that y = 5000/x
C = 340x + 240(5000/x)
C = 340x + 1200000/x
Differentiate C with respect to x
C'(x) = 340 - 1200000/x^2
= (340x^2 -1200000) / x^2
To minimize cost C'(x) = 0
(340x^2 -1200000) / x^2 = 0
340x^2 -1200000 = 0
340x^2 = 1200000
x^2 = 1200000/340
x = √1200000/340
x = 59.4 ft
Recall that y = 5000/x
y = 5000/59.4
y = 84.18 ft
Answer:
x = -1/3
Step-by-step explanation:
4(3x-1)+8=2(3x+5)-8
Distribute
12x -4 +8 = 6x +10 -8
Combine like terms
12x +4 = 6x +2
Subtract 6x from each side
12x-6x +4 = 6x-6x +2
6x+4 =2
Subtract 4 from each side
6x+4-4=2-4
6x =-2
Divide each side by 6
6x/6 = -2/6
x = -1/3
Solidify the W then do the rest of the problem
the answer should be the W
Answer:
4 meters
Step-by-step explanation:
Assuming that the garden is a rectangular garden, its area would be length ×width.
Let the length be L meters and the width be W meters.
Area= L ×W
48= LW -----(1)
Given that the length is 3 times the width,
L= 3W -----(2)
Substitute (2) into (1):
48= 3W(W)
3W²= 48
Divide both sides by 3:
W²= 48 ÷3
W²= 16
Square root both sides:
W= 4 (reject negative as width cannot be a negative number)
Thus, the width of the garden is 4 meters.
