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 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?
\[
\text{maximum area} = \text{ }
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc9b69680-5ad4-41fa-bd27-ae6a7c1e734f%2F54ad820f-a247-4074-8f02-0209016a2399%2Fkcbijps_processed.png&w=3840&q=75)
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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