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CalculusCalculus10th Edition

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Chapter 10.6, Problem 21E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095
Textbook Problem

Identifying and Sketching a Conic In Exercises 13-22, find the eccentricity and the distance from the pole to the directrix of the conic. Then identify the conic and sketch its graph. Use a graphing utility to confirm your results.

r = 300 − 12 + 6 sin θ

To determine

To Calculate:

The eccentricity and distance from the pole to the directrix of the conic for the equation r=300−12+6sinθ and identify the conic. Also, sketch its graph and confirm the results with that of the graphing utility.

Explanation

Given: The polar equation is given as r=300−12+6sinθ

Formula Used:

For the equation of the type r=ed1+esinθ, e is the eccentricity and d is the distance between focus at pole and corresponding directrix.

Calculation:

The given equation is: r=300−12+6sinθ

And the equation can be re-written as,

r=300−12(1−12sinθ)

r=−12×50(1−12sinθ)

Compare this equation with the standard equation r=ed1−esinθ to get the eccentricity as e=12 and the distance as |d|=50

Here e=12<1, hence the curve is ellipse

And the distance of directrix from the pole is |d|=50

Graph:

Use Desmos graphing calculator and write the equation, plot the following graph:

To draw the graph of an Ellipse, plot some points by taking different values for θ as in the table

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Construct a stem-and-leaf display for the following data. Use a leaf unit of 10. 1161 1206 1478 1300 1604 1725 ...

STATISTICS F/BUSINESS+ECONOMICS-TEXT

The accompanying data are a subset of data from the report Great Jobs, Great Lives (Gallup-Purdue Index 2015 Re...

Introduction To Statistics And Data Analysis

Practice Solve each inequality, graph the solution set, and write the answer in interval notation. Do not worry...

College Algebra (MindTap Course List)

Describe the process of conducting a literature search, including using an online database such as PsycINFO, an...

Research Methods for the Behavioral Sciences (MindTap Course List)

Make a list of some of the factors in your life that change from one day to the next. Possible examples include...

Research Methods for the Behavioral Sciences (MindTap Course List)

In exercise 10, data showing the values of several pitching statistics for a random sample of 20 pitchers from ...

Statistics for Business & Economics, Revised (MindTap Course List)

Solve the following exercises based on Principles 18 through 21, although an exercise may require the applicati...

Mathematics For Machine Technology

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