(a) To prove: That the graphs of the two limacons are exactly the same for both b and − b .

Question

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Answer 1

Question

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

To determine

(e)

The points where tangent line is vertical.

Expert Solution & Answer

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4. A car travels in a straight line for one hour. Its velocity, v, in miles per hour at six minute intervals is shown in the table. For each problem, approximate the distance the car traveled (in miles) using the given method, on the provided interval, and with the given number of rectangles or trapezoids, n. Time (min) 0 6 12 18|24|30|36|42|48|54|60 Speed (mph) 0 10 20 40 60 50 40 30 40 40 65 a.) Left Rectangles, [0, 30] n=5 b.) Right Rectangles, [24, 42] n=3 c.) Midpoint Rectangles, [24, 60] n=3 d.) Trapezoids, [0, 24] n=4

Answer 2

Question

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

To determine

(e)

The points where tangent line is vertical.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

To determine

(e)

The points where tangent line is vertical.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

To determine

(e)

The points where tangent line is vertical.

Expert Solution & Answer

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See solution

Answer 5

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

To determine

(e)

The points where tangent line is vertical.

Answer 6

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

Answer 7

Chapter 12.3, Problem 64E

To determine

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

Answer 8

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

Answer 9

To determine

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

Answer 10

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

Answer 11

To determine

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

Answer 12

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

Answer 13

To determine

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

Answer 14

To determine

(e)

The points where tangent line is vertical.

Answer 15

To determine

(e)

The points where tangent line is vertical.

Answer 16

Expert Solution & Answer

Answer 17

Expert Solution & Answer

Answer 18

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Answer 19

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

(a) To prove: That the graphs of the two limacons are exactly the same for both b and − b .

Solution Summary: The author illustrates how the graph of r = b + cos is identical for both the polar equations, and explains how it changes the shape.

Videos

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

(e)

The points where tangent line is vertical.

Want to see the full answer?

Chapter 12 Solutions

(a) To prove: That the graphs of the two limacons are exactly the same for both b and − b .

Solution Summary: The author illustrates how the graph of r = b + cos is identical for both the polar equations, and explains how it changes the shape.

Videos

(a) To prove: That the graphs of the two limacons are exactly the same for both b and −b.

(b) To plot: The limacon for the given values of b and describe how it changes the shape.

(c) To plot: The limacon for the given values of b and describe how it changes the shape.

(d) To show: dydx=−(bcosθ+cos2θb+2cosθ)cscθ

(e) The points where tangent line is vertical.

Want to see the full answer?

Chapter 12 Solutions

(a)

To prove:

That the graphs of the two limacons are exactly the same for both $b and - b$ .

(b)

To plot:

The limacon for the given values of b and describe how it changes the shape.

(c)

To plot:

The limacon for the given values of b and describe how it changes the shape.

(d)

To show:

$\frac{d y}{d x} = - (\frac{b \cos θ + \cos 2 θ}{b + 2 \cos θ}) \csc θ$

(e)

The points where tangent line is vertical.