What Are the Coordinates of the Rectangle with Maximum Area?

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Discussion Overview

The discussion revolves around finding the coordinates of a rectangle with maximum area, positioned in the first quadrant with one leg on the Y-axis and the other on the X-axis, while its vertex lies on the curve defined by the equation y=1-0.61x^2. Participants explore the mathematical formulation of the area and the differentiation process to determine the coordinates.

Discussion Character

  • Mathematical reasoning, Homework-related, Technical explanation

Main Points Raised

  • One participant describes the setup of the rectangle and the need to find its coordinates based on the curve.
  • Another participant requests clarification on the initial attempts and current challenges faced in solving the problem.
  • A participant presents their calculations for the area of the rectangle, deriving the area function A=x(1-0.61x^2) and its derivative to find critical points.
  • There is a confirmation from another participant that the calculations appear correct, while also suggesting a quicker method to find y.
  • One participant expresses relief at the correctness of their approach but admits to sometimes struggling with shortcuts in calculations.

Areas of Agreement / Disagreement

Participants generally agree on the mathematical approach to finding the coordinates, but there is no explicit consensus on the best method or any alternative approaches to solving the problem.

Contextual Notes

Some assumptions about the curve and the rectangle's positioning may not be fully articulated, and the discussion does not resolve the potential for different methods to arrive at the solution.

jtesttubes
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Draw a rectangle , start quadrant having one leg on the Axis -Y and other on the Axix -X and vertex on the curve
y=1-0.61x^2

You need to find the co-ordinates of the rectangle and find out which form of rectangle has got more area.
 
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Hi jtesttubes! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:
 
jtesttubes said:
Draw a rectangle , start quadrant having one leg on the Axis -Y and other on the Axix -X and vertex on the curve
y=1-0.61x^2

You need to find the co-ordinates of the rectangle and find out which form of rectangle has got more area.

Yes, I can answer that. Thank you for asking.
 
tiny-tim said:
Hi jtesttubes! :wink:

Show us what you've tried, and where you're stuck, and then we'll know how to help! :smile:

I have worked out a calculation, but i just want to confirm with you whether this is the way to work out this question, i got the co-ordinates of the rectangle. Is it correct

Area = x*y - basic formula for area.
A=x(1-0.61x^2)
A=x-0.61x^3
dA/dx = 1-1.83x^2
0=1-1.83x^2
x=sqrt(1/1.83)
x=0.739
y=1-0.61(0.739)^2
y=0.66667
coordinates are (0.739,0.6667)
 
Hi jtesttubes! :smile:

(try using the X2 tag just above the Reply box :wink:)
jtesttubes said:
I have worked out a calculation, but i just want to confirm with you whether this is the way to work out this question, i got the co-ordinates of the rectangle. Is it correct

Area = x*y - basic formula for area.
A=x(1-0.61x^2)
A=x-0.61x^3
dA/dx = 1-1.83x^2
0=1-1.83x^2
x=sqrt(1/1.83)
x=0.739
y=1-0.61(0.739)^2
y=0.66667
coordinates are (0.739,0.6667)

yes, that looks fine. :smile:

(except you could have got y more quickly by noting that 0.61x2 is 1/3 of 1.83x2, and you know exactly what that is :wink:)
 
Oh thanks i have some doubts on my workings now I am happy that it is the right way to work out, yes sometimes i do not follow shortcuts on working out this kind of equations.
 

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