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20.03.2020 •
Mathematics
A piece of wire 40 cm long is to be cut into two pieces. One piece will be bent to form a circle and; the other will be bent to form a square. Find the lengths of the two pieces that cause the sum of the area of the circle and the area of the square to be a minimum. The perimeter of the square is cm The circumference of the circle is cm
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Ответ:
Step-by-step explanation:
The total length of the wire = 40 cm
Let us assume the circumference of the circle = k cm
So, the circumference of the square = ( 40 - k) cm
Now,as circumference of circle = 2πR
⇒2πR = k cm or, R =![(\frac{k}{2\pi})](/tpl/images/0555/6375/fb30c.png)
Area of the circle = πR²
or, A =
Similarly , perimeter of square = 4 x Side
⇒ 4 x Side = ( 40 - k) cm ⇒ S =![(\frac{40 - k}{4} )](/tpl/images/0555/6375/e9f58.png)
Area of the square = (Side)² =![(\frac{40 - k}{4} ) ^2](/tpl/images/0555/6375/b5bd9.png)
Solving, we get:
....... (1)
So, combining (1) and (2), total area A is
or, we get: A = 0.07962 k² + 0.0625 k² + 100 - 5 k
A = 0.1422 k² - 5 k + 100
For axis of symmetry :![k = (\frac{-b}{2a} ) = (-\frac{-5}{2(0.1420}) = 17.6](/tpl/images/0555/6375/f01e3.png)
⇒ k = 17.6 inches
So, the perimeter of circle = 17.6 cm
Perimeter of square = (40 - 17.6 ) = 22.4 cm
Ответ:
Cantorville used more kilowatt-hours than Jacobia
Step-by-step explanation: