Suppose the length of the triangle is x, if the perimeter of the rectangle is 100 ft, the width of the rectangle will be (50-x) ft.
Area of rectangle will be:
A=length*width
A=x(50-x)
A=50x-x^2
at maximum area, dA/dx=0
thus
dA/dx=50-2x=0
solving for x we get
2x=50
x=25
thus for maximum area length=25 ft
the size of the width will be
50-x=50-25=25 ft
thus the maximum area will be:
25*25=625 sq. feet
The equation that can be used to find the number of wolves in the state on January 1 is w - 23 = 84
<h3>How to represent a situation with an equation?</h3>
A zoologist is recording the loss of wolves in her state. She notes the number of wolves, w, in the state on January 1. One year later, there were 84 wolves in the state, which is 23 fewer wolves than were in the state a year earlier.
The equation that can be used to find the number of wolves in the state on January 1 can be calculated as follows:
where
- w = number of wolves in the state January 1.
Therefore, the equation to represent the situation is as follows:
w - 23 = 84
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A. (x+8)^ 2 + 1
B. (x-3)^ 2 - 8
C. ( x - 3/2) ^ 2 - 1/4
