30 percent of 120 is the same as 80 percent of what number?
2 answers:
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Let r = the radius of the circle.
Let x = the length of a side of the square.
The sum of the circumference of the circle and the perimeter of the square is 16.
Therefore
2πr + 4x = 16
That is
(1)
The combined area of the circle and the square is
(2)
From (1), obtain
In order for A to be minimum, A' = 0.
That is,
The second derivative should be positive in order for A to be minimum.
A'' = 8/π + 2 > 0 , so the condition is satisfied.
The graph shown below confirms this.
From (1), obtain
r = (2/π)*(4 - 2.2404) = 1.1202
Answer:
r = 1.12 and x = 2.24
Let x = the length of a side of the square.
The sum of the circumference of the circle and the perimeter of the square is 16.
Therefore
2πr + 4x = 16
That is
The combined area of the circle and the square is
From (1), obtain
In order for A to be minimum, A' = 0.
That is,
The second derivative should be positive in order for A to be minimum.
A'' = 8/π + 2 > 0 , so the condition is satisfied.
The graph shown below confirms this.
From (1), obtain
r = (2/π)*(4 - 2.2404) = 1.1202
Answer:
r = 1.12 and x = 2.24