Neishab932
04.07.2020 •
Mathematics
A piece of wire of length 7070 is cut, and the resulting two pieces are formed to make a circle and a square. Where should the wire be cut to (a) minimize and (b) maximize the combined area of the circle and the square?
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Ответ:
a.x=39.2
b.Use whole wire as a circle
Step-by-step explanation:
We are given that
Length of piece of wire=70 units
Let length of wire used to make a square =x units
Length of wire used in circle=70- x
Side of square=
Circumference of circle=
Combined area of circle and square,A=
Using the formula
Area of circle=
Area of square=
a.
Differentiate w.r.t x
x=39.2
Again differentiate w.r.t x
>0
Hence, the combined area of circle and the square is minimum at x=39.2
b.When the wire is not cut and whole wire used as a circle . Then, combined area is maximum.
Ответ:
the answer is 16a2-4a+4a-1
it can be simplified to 16a2-1, which can be factored to
(4a+1)(4a-1)