Can someone help me? I attached the question on here, I could really use some help.
1 answer:
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Step-by-step explanation:
Let x be the length and y be the width of the rectangular plot.
The plot is bounded on one side by a river and on the other three sides by a single-strand electric fence. It means,
x+2y = 1500
x = 1500 - 2y ....(1)
We know that the area of a rectangular plot is given by :
A = xy ....(2)
Put the value of x from equation (1) in (2)
.....(3)
For largest area, differentiate above area equation wrt y.
Put the value of y in equation (1).
x = 1500-2(375)
= 750 m
Put the value of y in equation (3).
Hence, the largest area is 281250 m² and its dimensions are 750 m and 375 m.
Answers:
- Part a)
- Part b) 3
- Part c) 2.24
- Part d) 1.58
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Work Shown:
Part (a)
The origin is the point (0,0) which we'll make the first point, so let (x1,y1) = (0,0)
The other point is of the form (x,y) where y = x^2-3. So the point can be stated as (x2,y2) = (x,y). We'll replace y with x^2-3
We apply the distance formula to say...
We could expand things out and combine like terms, but that's just extra unneeded work in my opinion.
Saying is the same as writing d = sqrt(x^2-(x^2-3)^2)
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Part (b)
Plug in x = 0 and you should find the following
This says that the point (x,y) = (0,3) is 3 units away from the origin (0,0).
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Part (c)
Repeat for x = 1
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Part (d)
Graph the d(x) function found back in part (a)
Use the minimum function on your graphing calculator to find the lowest point such that x > 0.
See the diagram below. I used GeoGebra to make the graph. Desmos probably has a similar feature (but I'm not entirely sure). If you have a TI83 or TI84, then your calculator has the minimum function feature.
The red point of this diagram is what we're after. That point is approximately (1.58, 1.66)
This means the smallest d can get is d = 1.66 and it happens when x = 1.58 approximately.
