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CalculusCalculus10th Edition

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Chapter 10.5, Problem 20E
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Calculus

10th Edition
Ron Larson + 1 other
ISBN: 9781285057095

Solutions

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Problem 1E
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Problem 19E
Problem 20E
Problem 21E
Problem 22E
Problem 23E
Problem 24E
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Problem 28E
Problem 29E
Problem 30E
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Problem 38E
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Problem 44E
Problem 45E
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Problem 49E
Problem 50E
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Problem 73E
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Problem 80E
Problem 81E
Problem 82E
Problem 83E
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Calculus

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

Finding the Area of a Polar Region In Exercises 19-26, use a graphing utility to graph the polar equation. Find the area of the given region analytically.

Inner loop of   r = 4 − 6 sin θ

To determine

To calculate: The value of the area of the inner loop of polar equation r=4−6sinθ and to draw the equation with the graphing utility.

Explanation

Given:

The provided polar equation r=4−6sinθ.

Formula used:

The area of the polar equation is given by:

A=12∫αβ[f(θ)]2dθ

Where; α and β are limits of the integration.

Calculation:

Now, use the following steps in the TI-83 calculator to obtain the graph:

Step 1: Press ON button to open the calculator.

Step 2: Press MODE button and then scroll down to press pol and press ENTER button.

Step 3: Now, press the button Y= and enter the provided equation.

Step 4: Press WINDOW button and then set the window as follows:

Xmin=−8,Xmax=8,Ymin=−12 and Ymax=2

Step 5: Press ENTER to get the graph.

The graph obtained is:

From the graph, it can be seen that there is symmetry in the graph above the y-axis.

So, the shaded region is the twice the region formed from the curve r=−2 to r=0.

Now equate the polar equation equal to 0;

That is,

r=04−6sinθ=06sinθ=4sinθ=23

That gives;

θ=sin−1(23)

And, at r=−2, the value of θ is;

−2=4−6sinθ−2=−2sinθ1=sinθ

That gives;

θ=π2

The area of the inner loop is twice the area formed by integration of the polar equation from θ=π2 to θ=arcsin(23)

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Let P(x1, y1) be a point on the hyperbola x2/a2 y2/b2 = 1 with foci F1 and F2 and let and be the angles betw...

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In Exercises 1-22, evaluate the given expression. C(7,5)

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True or False: A population that follows a logistic model will never reach its carrying capacity.

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Suppose that for a particular computer salesperson, the probability distribution of x = the number of systems s...

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Under what circumstances would you use a multiple-baseline design instead of an ABAB (reversal) design?

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Write an equation for each of the following problems, solve for the unknown, and check. The flute length of the...

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Decompose each fraction into partial fractions. x3+4x2+3x+6x2+2x2+x+2

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Identify the three modalities of measurement and explain the strengths and weaknesses of each.

Research Methods for the Behavioral Sciences (MindTap Course List)

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