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tayjohnson0042
23.10.2019 •
Mathematics
You have a wire that is 44 cm long. you wish to cut it into two pieces. one piece will be bent into the shape of a square. the other piece will be bent into the shape of a circle. let a represent the total area of the square and the circle. what is the circumference of the circle when a is a minimum?
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Ответ:
The circumference of the circle is 29.36 cm
Step-by-step explanation:
Let
x -----> the length of first piece (shape of square)
y ------> the length of the other piece (shape of a circle)
we know that
step 1
Find out the area of square
The perimeter of square is equal to the length of the first piece
where
b is the length side of square
Find the total area A
The area of square is
step 2
Find out the area of the circle
The circumference of the circle is equal to the length of the other piece
The circumference is equal to
so
Find the radius of the circle
Find the area of the circle
substitute the value of r
step 3
Find out the total area
substitute
This is a vertical parabola open upward
The vertex is a minimum
using a graphing tool
The vertex is the point (14.64, 67.77)
see the attached figure
For x=14.64 cm -----> the area is a minimum
The lengths of the wire are
therefore
The circumference of the circle is 29.36 cm
Ответ:
collect like terms
3e-7e=-4e
-19+10=-9
so it would be -4e-9