A farmer wants to fence a rectangular corral adjacent to the side of a barn; however, she has only 200 ft of fencing and wants to enclose the largest possible area. See the figure. a .If x represents the length of the corral and y represents the width, explain why the dimensions of the corral are subject to the constraint 2 x + y = 200 . b . The area of the corral is given by A = x y . Use the constraint equation from part ( a ) to express A as a function of x , where 0 < x < 100 . c .Use the function from part ( b ) to find the dimensions of the corral that will yield the maximum area. [ Hint : Find the vertex of the function from part ( b ).]
A farmer wants to fence a rectangular corral adjacent to the side of a barn; however, she has only 200 ft of fencing and wants to enclose the largest possible area. See the figure. a .If x represents the length of the corral and y represents the width, explain why the dimensions of the corral are subject to the constraint 2 x + y = 200 . b . The area of the corral is given by A = x y . Use the constraint equation from part ( a ) to express A as a function of x , where 0 < x < 100 . c .Use the function from part ( b ) to find the dimensions of the corral that will yield the maximum area. [ Hint : Find the vertex of the function from part ( b ).]
Solution Summary: The farmer wants to fence a rectangular corral and has 200ft of fencing to enclose the largest possible area.
A farmer wants to fence a rectangular corral adjacent to the side of a barn; however, she has only 200 ft of fencing and wants to enclose the largest possible area. See the figure.
a.If x represents the length of the corral and y represents the width, explain why the dimensions of the corral are subject to the constraint
2
x
+
y
=
200
.
b. The area of the corral is given by
A
=
x
y
. Use the constraint equation from part (a) to express A as a function of x, where
0
<
x
<
100
.
c.Use the function from part (b) to find the dimensions of the corral that will yield the maximum area.
[Hint: Find the vertex of the function from part (b).]
A research study in the year 2009 found that there were 2760 coyotes
in a given region. The coyote population declined at a rate of 5.8%
each year.
How many fewer coyotes were there in 2024 than in 2015?
Explain in at least one sentence how you solved the problem. Show
your work. Round your answer to the nearest whole number.
Answer the following questions related to the following matrix
A =
3
³).
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