Answer:
- 12 ft parallel to the river
- 6 ft perpendicular to the river
Step-by-step explanation:
The least fence is used when half the total fence is parallel to the river. That is, the shape of the rectangle is twice as long as it is wide.
72 = W(2W)
36 = W²
6 = W . . . . . . the width perpendicular to the river
12 = 2W . . . . the length parallel to the river
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<em>Development of this relation</em>
Let T represent the total length of the fence for some area A. Then if x is the length along the river, the width is y=(T-x)/2, and the area is ...
A = xy = x(T -x)/2
Note that the equation for area is that of a parabola with zeros at x=0 and at x=T. That is, for some fence length T, the area will be a maximum at the vertex of this parabola. That vertex is located halfway between the zeros, at ...
x = (0 +T)/2 = T/2
The corresponding area width (y) is ...
y = (T -T/2)/2 = T/4
Equivalently, the fence length T will be a minimum for some area A when x=T/2 and y=T/4. This is the result we used above.
Answer:
7.321852048×10³⁰
Step-by-step explanation:
4 quarts is equal to 1 gallon
Just multiply 26 by 4 and get 104
Step-by-step explanation:
1) the required equation in common form is:
(x-x₀)²+(y-y₀)²=r², where (x₀;y₀) - coordinates, where Michael is standing; r - the social distance;
According to the common form and given coordinates (x₀=-5; y₀=2; r=6) it is possible to make up the required equation:
<u>(x+5)²+(y-2)²=6².</u>
2) if the distance between two friends is:
this distance is longer than social (6 ft). For more info see the attachment.
