Let x and y be the dimensions of the rectangle. If the perimeter is 40, we have
We can expression one variable in terms of the others as
Since the area is the product of the dimensions, we have
This is a parabola facing down, so it's vertex is the maximum:
So, the maximum is
And since we know that , we have
as well.
This is actually a well known theorem: out of all the rectangles with given perimeter, the one with the greatest area is the square.
Answer:
The angle of rotation is 2.11 °
Step-by-step explanation:
Given as :
The radius of the round path = r = 18 feet
The length of the distance cover by wheel = l = 38 feet
Let The angle of rotation = Ф
Now, According to question
∵ length of the arc of a circle subtending an angle at center = Ф
So,
length of the distance cover by wheel = π × radius ×
Since 180° = π radian
And π = 3.14
So, length of the distance cover by wheel = 180 °× radius ×
i.e l = r × Ф
Or, Ф =
Or, Ф =
Or, Ф = 2.11 °
So, The angle of rotation = Ф = 2.11 °
Hence, The angle of rotation is 2.11 ° Answer