Answer:
Total cost F (w) = 160/w + 200* √(2w)
Step-by-step explanation:
Volume in cubic feet
V (box) = x*y*w and square base means x=y so V= 2 = x^(2)*w
hence x^(2) = 2/w (1)
Area of base and top in square feet, and cost in $
Area(t+b) = 2*x*y = 2x^(2) C(1) = Cost of ( base + top) C(1) = 40*2x^(2)
C(1) =80*x^(2) and from eq. 1
C(1) = 80*2/w = 160/w
Area of sides = 4 * x* w = 4*√((2/w))*w
C(2) = Cost of sides. is: C(2)= 50*4*√((2/w))*w C(2) = 200* √2w
Total Cost = F(c) = 160/w +200*√2w
9514 1404 393
Answer:
p = 3x+10
Step-by-step explanation:
The attached diagram pretty much explains it.
The unknown dimension at the top was the subject of a previous problem. It is the difference in length between the two marked horizontal segments:
(2x +15) -(x) = x +15 . . . . . length of unmarked solid horizontal line
Similarly, the length of the unmarked vertical line on the right is the difference between the marked vertical lines:
(2x -5) -(x -5) = x . . . . . length of unmarked solid vertical line
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The formula for the area of a rectangle is used to find the areas of the left-side and right-side rectangles. Respectively, those areas are ...
left-side area = x(2x -5)
right-side area = x(x +15)
Then the total area enclosed by the solid line is ...
x(2x -5) +x(x +15) = x(2x -5 +x +15) = x(3x +10)
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The area of the lot extension is the product of its dimensions:
extension area = x·p
We want this to be the same as the area in the solid line, so ...
x·p = x·(3x +10)
Dividing by the coefficient of p (which is x), we have ...
p = 3x +10