Step-by-step explanation:
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Answer:
20 ft by 60 ft
Step-by-step explanation:
"What should the dimensions of the garden be to maximize this area?"
If y is the length of the garden, parallel to the stream, and x is the width of the garden, then the amount of fencing is:
120 = 3x + y
And the area is:
A = xy
Use substitution:
A = x (120 − 3x)
A = -3x² + 120x
This is a downward facing parabola. The maximum is at the vertex, which we can find using x = -b/(2a).
x = -120 / (2 · -3)
x = 20
When x = 20, y = 60. So the garden should be 20 ft by 60 ft.
Answer:
Yes
Step-by-step explanation:
Triangle inequality theorem states that a triangle can exist if
a + b > c; a + c > b; b + c > a
a = 2; b = 10; c = 11
2 + 10 = 12; 12 > 11.
2 + 11 = 13; 13 > 10.
10 + 11 = 21; 21 > 2.