A rectangle is inscribed in an ellipse given by the equation x^2/49+y^2/196=1. If (x,y) is a vertex of the rectangle in the first quadrant, what is y in terms of x?   y = square root of ?-4x^2   What is the area of the rectangle in terms of x? A(x) = ? square root of ? -4x^2   What value for x maximizes the area? x= ?/ square root of 2   What is the maximum area? maximum area =?

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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A rectangle is inscribed in an ellipse given by the equation x^2/49+y^2/196=1.
If (x,y) is a vertex of the rectangle in the first quadrant, what is y in terms of x?
 
y = square root of ?-4x^2
 
What is the area of the rectangle in terms of x?
A(x) = ? square root of ? -4x^2
 
What value for x maximizes the area?
x= ?/ square root of 2
 
What is the maximum area?
maximum area =? 
 
 
A rectangle is inscribed in an ellipse given by the equation 

\[
\frac{x^2}{49} + \frac{y^2}{196} = 1.
\]

If \((x, y)\) is a vertex of the rectangle in the first quadrant, what is \(y\) in terms of \(x\)?

\[ 
y = \sqrt{\text{Ex: } -4x^2} 
\]

What is the area of the rectangle in terms of \(x\)?

\[ 
A(x) = \text{Ex: } 2x \sqrt{\text{ }-4x^2} 
\]

What value for \(x\) maximizes the area?

\[ 
x = \frac{\text{ }}{\sqrt{2}} 
\]

What is the maximum area?

\[ 
\text{maximum area} = \text{ } 
\]
Transcribed Image Text:A rectangle is inscribed in an ellipse given by the equation \[ \frac{x^2}{49} + \frac{y^2}{196} = 1. \] If \((x, y)\) is a vertex of the rectangle in the first quadrant, what is \(y\) in terms of \(x\)? \[ y = \sqrt{\text{Ex: } -4x^2} \] What is the area of the rectangle in terms of \(x\)? \[ A(x) = \text{Ex: } 2x \sqrt{\text{ }-4x^2} \] What value for \(x\) maximizes the area? \[ x = \frac{\text{ }}{\sqrt{2}} \] What is the maximum area? \[ \text{maximum area} = \text{ } \]
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