SOLUTION: Show that the area of the Norman window is a maximum when both r and x are equal to P(pie+4)
*assume that the perimeter of the window is P
So I figured that the r is the radius a
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*assume that the perimeter of the window is P
So I figured that the r is the radius a
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Question 927974: Show that the area of the Norman window is a maximum when both r and x are equal to P(pie+4)
*assume that the perimeter of the window is P
So I figured that the r is the radius and the x is the length
So I made this equation x+r = P(pie+4)
You can put this solution on YOUR website! I think you have a typo. Both and are parts of a sum of lengths that is the perimeter, , so they cannot be .
Here is your Norman window: ---> and
If we have a fixed perimeter, the maximum area will be obtained when , and here is my proof: <---><--->
Substituting into , we get is a quadratic function of
A quadratic function like has a maximum if the leading coefficient (the in the term with the square) is negative.
The maximum happens when the variable has the value
In this case, the maximum happens when
Substituting into , we get --->
