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

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) (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:

:
A graph of the area of the rectangle equation:

:
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
RELATED QUESTIONS
A rectangle is placed under the parabolic arch given by f(x)=27-3x squared by using a... (answered by scott8148)

Hi. I have a problem with a rectangle being placed under the parabolic arch given by (answered by venugopalramana)

A rectangle is placed under the parabolic arch given by f(x)=27-3x^2 by using a point... (answered by stanbon)

A rectangle is placed under the parabolic arch by f(x)=27-3x^2 by using a point (x,y) on... (answered by stanbon)

A rectangle is placed under the parabolic arch given by f(x)=27-3x^2 by using a point... (answered by rapaljer)

A parabolic arch supports a bridge. The arch is 200 m wide at its base and 4 m tall in... (answered by josgarithmetic)

Suppose you wanted to design a parabolic arch (a parabola opening downward) as a trellis... (answered by scott8148)

Stein Glass, Inc., makes parabolic headlights for a variety of automobiles. If one of... (answered by ikleyn,MathLover1)

Please help. Suppose you wanted to design a parabolic arch (a parabola opening... (answered by scott8148)