SOLUTION: A RECTANGLE IS PLACED UNDER THE PARABOLIC ARCH GIVEN BY f(x)=27-3x2 BY USING A POINT (x,y) ON A PARABOLA. WRITE A FORMULA FOR THE FUNCTION A(x) THAT GIVES THE AREA OF THE RECTANGL

Algebra ->  Linear-equations -> SOLUTION: A RECTANGLE IS PLACED UNDER THE PARABOLIC ARCH GIVEN BY f(x)=27-3x2 BY USING A POINT (x,y) ON A PARABOLA. WRITE A FORMULA FOR THE FUNCTION A(x) THAT GIVES THE AREA OF THE RECTANGL      Log On


   

Question 63162: A RECTANGLE IS PLACED UNDER THE PARABOLIC ARCH GIVEN BY f(x)=27-3x2 BY USING A POINT (x,y) ON A PARABOLA. WRITE A FORMULA FOR THE FUNCTION A(x) THAT GIVES THE AREA OF THE RECTANGLE AS A FUNCTION OF THE x-COORDINATE OF THE POINT CHOSEN.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
A RECTANGLE IS PLACED UNDER THE PARABOLIC ARCH GIVEN BY f(x)=27-3x2 BY USING A POINT (x,y) ON A PARABOLA. WRITE A FORMULA FOR THE FUNCTION A(x) THAT GIVES THE AREA OF THE RECTANGLE AS A FUNCTION OF THE x-COORDINATE OF THE POINT CHOSEN
:
The axis of symmetry will be at 0
:
The height of the square will be y which is 27- 3x^2
:
Length of the square will be 2x
:
A(x) = 2x(27-3x^2)
:
An example when x = 2, Length = 4, y = 15 (height), Area = 15*4 = 60
:
A(2) = 2(2)(27 - 3(2^2)
A(2) = 4(27 - 12)
A(2) = 4(15)
A(2) = 60



Looks kind of like this:
+graph%28+300%2C+200%2C+-6%2C+6%2C+-10%2C+30%2C+-3x%5E2+%2B+27%2C+15%29+
:
A graph of the area of the rectangle equation:
+graph%28+300%2C+200%2C+-2%2C+6%2C+-10%2C+80%2C+-6x%5E3+%2B+54x+%29+
:
As you can probably see I have not done this particular problem before but got
to thinking about it and this is what I came up, hope it's helpful