Question 4. You may use a calculator on both parts of this question. Part A. Imagine an elliptical oil slick that at some moment in time is 3 meters long and 2 meters wide. At this instant, it's length is increasing at a rate of 2 centimeters per minute, and its width at a rate of 1 centimeter per minute. How fast is the oil slick's area increasing? Helpful information: The area of an ellipse is given by the equation A πα5, where A is area, and a and b are the lengths of the semi-major and semi-minor axes respectively. What does that mean? The long axis of an ellipse is called its major axis; the short axis is called the minor axis. Half of these axes, i.e., the lines from the center of the ellipse to its edge in the longest and shortest dimensions, are the semi-major and semi-minor axes. Part B. If the oil slick is a constant 1 millimeter thick, how fast (in units of volume per minute, e.g., cubic centimeters per minute) is oil entering the slick at the moment described in Part A? More helpful information: The volume of such an oil slick is simply its thickness times its area.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter11: Topics From Analytic Geometry
Section11.2: Ellipses
Problem 17E
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Question 4. You may use a calculator on both parts of this question.
Part A. Imagine an elliptical oil slick that at some moment in time is 3 meters long and 2 meters wide.
At this instant, it's length is increasing at a rate of 2 centimeters per minute, and its width at
a rate of 1 centimeter per minute. How fast is the oil slick's area increasing?
Helpful information: The area of an ellipse is given by the equation A πα5, where A is area,
and a and b are the lengths of the semi-major and semi-minor axes respectively. What does
that mean? The long axis of an ellipse is called its major axis; the short axis is called the
minor axis. Half of these axes, i.e., the lines from the center of the ellipse to its edge in the
longest and shortest dimensions, are the semi-major and semi-minor axes.
Part B. If the oil slick is a constant 1 millimeter thick, how fast (in units of volume per minute, e.g.,
cubic centimeters per minute) is oil entering the slick at the moment described in Part A?
More helpful information: The volume of such an oil slick is simply its thickness times its area.
Transcribed Image Text:Question 4. You may use a calculator on both parts of this question. Part A. Imagine an elliptical oil slick that at some moment in time is 3 meters long and 2 meters wide. At this instant, it's length is increasing at a rate of 2 centimeters per minute, and its width at a rate of 1 centimeter per minute. How fast is the oil slick's area increasing? Helpful information: The area of an ellipse is given by the equation A πα5, where A is area, and a and b are the lengths of the semi-major and semi-minor axes respectively. What does that mean? The long axis of an ellipse is called its major axis; the short axis is called the minor axis. Half of these axes, i.e., the lines from the center of the ellipse to its edge in the longest and shortest dimensions, are the semi-major and semi-minor axes. Part B. If the oil slick is a constant 1 millimeter thick, how fast (in units of volume per minute, e.g., cubic centimeters per minute) is oil entering the slick at the moment described in Part A? More helpful information: The volume of such an oil slick is simply its thickness times its area.
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