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denisturcios18
05.05.2020 •
Mathematics
Fence is to be built to enclose a rectangular area of 250 square feet. The fence along three sides is to be made of material that costs 4 dollars per foot, and the material for the fourth side costs 13 dollars per foot. Find the dimensions of the enclosure that is most economical to construct
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Ответ:
23.05 x 10.85
Step-by-step explanation:
Area of Rectangular Fence = L * W = 250![ft^{2}](/tpl/images/0632/8465/8b0c7.png)
L * W = 250
W =
................................... (i)
Perimeter = 2L + 2W
Three sides cost 4 dollars per foot = 4(2L) + 4W
(The two lengths must be constructed with the 4 dollars materials)
Fourth side costs 13 dollars per foot = 13W
Cost = 4(2L) + 4W + 13W
C = 8L + 17W ...................................... (ii)
Substitute (i) into (ii)
C = 8L + 17 (
)
C = 8L +
Plotting this equation with L on the x-axis and cost on the y-axis
minimum cost will be when L ≈ 23.05 ft
W =
≈ 10.85 ft
minimum cost = 8(23.05) +![\frac{4250}{23.05}](/tpl/images/0632/8465/34cbe.png)
minimum cost = 184.4 + 184.382
minimum cost ≈ 368.78 dollars
Ответ:
m=(y2-y1)/(x2-x1)=(9-5)/(6-2)=4/4=1 so far we have:
GH=x+b, using point (2,5) we can solve for the y-intercept or "b"...
5=2+b
3=b so the line GH is:
y=x+3