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).]
• Plane II is spanned by the vectors:
P12
P2 = 1
• Subspace W is spanned by the vectors:
W₁ =
-- () ·
2
1
W2 =
0
Three streams - Stream A, Stream B, and Stream C - flow into a lake. The flow rates of these streams are
not yet known and thus to be found. The combined water inflow from the streams is 300 m³/h. The rate of
Stream A is three times the combined rates of Stream B and Stream C. The rate of Stream B is 50 m³/h less
than half of the difference between the rates of Stream A and Stream C.
Find the flow rates of the three streams by setting up an equation system Ax = b and solving it for x.
Provide the values of A and b. Assuming that you get to an upper-triangular matrix U using an elimination
matrix E such that U = E A, provide also the components of E.
dent Application X GA spinner is divided into five cox | +
9/26583471/4081d162951bfdf39e254aa2151384b7
A spinner is divided into five colored sections that are not of equal size: red, blue, green, yellow,
and purple. The spinner is spun several times, and the results are recorded below:
Spinner Results
Color Frequency
Red
5
Blue
11
Green
18
Yellow
5
Purple
7
Based on these results, express the probability that the next spin will land on purple as a
fraction in simplest form.
Answer Attempt 1 out of 2
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0
Feb 12
10:11 O
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