A farmer wants to build a pen for his sheep. One side of the pen will be a river. The sheep need 2000 m2 of area to graze. The farmer wants to use the least amount of fencing as possible. Which equation should the farmer use to find the minimum amount of fencing?
Answers
x as the length of the pen
y as the width of the pen
The area is
xy = 2000
The perimeter is
P = 2(x+y)
From the area
y = 2000/x
Substituting
P = 2(x + 2000/x)
which is the equation used to find the least amount of fencing possible.
Final answer:
To get the minimum amount of fencing, the farmer should use the equation P = x + 2*(2000/x), representing the total fence length, where x is the length of the fence parallel to the river, and solve this to find the minimum.
Explanation:
The problem involves resolving a mathematical problem using functions in optimization. The farmer's goal is to minimize the fencing used which means minimizing the perimeter of the pen. Considering that one side of the pen will be a river, we are essentially looking for the dimensions of a rectangle (with one side along the river) which uses the least amount of fencing. Let's say the length of the fence parallel to the river is x, and the length of the fence perpendicular to the river is y.
Since area (A) is given by A = x*y, which must be 2,000 m2, we can rewrite y equation in terms of x as y = 2,000/x. The total fence length (perimeter, P) is calculated as P = x + 2y and substituting the new equation for y, we get P = x + 2*(2000/x), which is the function that the farmer needs to optimize in order to use the least amount of fencing.
Learn more about Optimization here:
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Thank you btw!
Answers
Answer:
D.
Step-by-step explanation:
To get from one point to the other, you have to go down 7 points and right 6 points, resulting in a negative slope. The y-intercept (where it crosses the y-axis, or the line in the middle going up and down) is at y=-7. Hope this helps!
Answer:
The answer is d
Step-by-step explanation:
The equation for slope is y=mx+b
First find the y-intercept (b) which is -7
Then you pick two points on the line to find the rise and run of the line (the slope which is m). The slope of this line in -7/6
Answers
hope it helped!
hit the brainiest button pleaseee!
Answers
20 x 20 = 400 x 18 = 7200 in.
40 x 12 = 480 x 12 = 5760 in.
So, the first aquarium is larger.
Subtract to find the difference.
7200 - 5760 = 1440 in.
the second A 40 x 12 x 12= 5670
the first is bigger by 1530
Answers
Answer: Proper order form least to greatest is given by
Step-by-step explanation:
Since we have given that
We need to write it in proper order from least to greatest.
For this we are required to take the L.C.M. of denominators:
1) L.C.M. of 2,6,7,2 = 42
2) Make the denominator 42:
From least to greatest :
B) $33
C) $37
D) $55
E) $70
Answers
Answers
40 = 3y
Divide both by 3
Answer= 13.3