(a) To find: The parametric equations for the curve, using θ as the parameter.

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Answer 1

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 8.4, Problem 53E

To determine

(a)

To find:

The parametric equations for the curve, using θ as the parameter.

To determine

(b)

To graph:

The curve using a graphing device with a=3 and b=2.

To determine

(c)

To identify:

The curve by eliminating the parameter.

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An air traffic controller spots two planes at the same altitude flying toward each other (see figure). Their flight paths are 20° and 315°. One plane is 150 miles from point P with a speed of 375 miles per hour. The other is 190 miles from point P with a speed of 450 miles per hour. (a) Find parametric equations for the path of each plane where t is the time in hours, with t = 0 corresponding to the time at which the air traffic controller spots the planes. (b) Use the result of part (a) to write the distance between the planes as a function of t. (c) Use a graphing utility to graph the function in part (b). When will the distance between the planes be minimum? If the planes must keep a separation of at least 3 miles, is the requirement met?

Answer 2

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 8.4, Problem 53E

To determine

(a)

To find:

The parametric equations for the curve, using θ as the parameter.

To determine

(b)

To graph:

The curve using a graphing device with a=3 and b=2.

To determine

(c)

To identify:

The curve by eliminating the parameter.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 8.4, Problem 53E

To determine

(a)

To find:

The parametric equations for the curve, using θ as the parameter.

To determine

(b)

To graph:

The curve using a graphing device with a=3 and b=2.

To determine

(c)

To identify:

The curve by eliminating the parameter.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Polygon with three sides, three angles, and three vertices. Based on the properties of each side, the types of triangles are scalene (triangle with three three different lengths and three different angles), isosceles (angle with two equal sides and two equal angles), and equilateral (three equal sides and three angles of 60°). The types of angles are acute (less than 90°); obtuse (greater than 90°); and right (90°).

Chapter 8.4, Problem 53E

To determine

(a)

To find:

The parametric equations for the curve, using θ as the parameter.

To determine

(b)

To graph:

The curve using a graphing device with a=3 and b=2.

To determine

(c)

To identify:

The curve by eliminating the parameter.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 8.4, Problem 53E

To determine

(a)

To find:

The parametric equations for the curve, using θ as the parameter.

To determine

(b)

To graph:

The curve using a graphing device with a=3 and b=2.

To determine

(c)

To identify:

The curve by eliminating the parameter.

Answer 6

Chapter 8.4, Problem 53E

To determine

(a)

To find:

The parametric equations for the curve, using θ as the parameter.

Answer 7

Chapter 8.4, Problem 53E

To determine

(a)

To find:

The parametric equations for the curve, using θ as the parameter.

Answer 8

To determine

(b)

To graph:

The curve using a graphing device with a=3 and b=2.

Answer 9

To determine

(b)

To graph:

The curve using a graphing device with a=3 and b=2.

Answer 10

To determine

(c)

To identify:

The curve by eliminating the parameter.

Answer 11

To determine

(c)

To identify:

The curve by eliminating the parameter.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 8.1 - CONCEPTS We can describe the location of a point...Ch. 8.1 - Prob. 2E Ch. 8.1 - Prob. 3E Ch. 8.1 - Prob. 4E Ch. 8.1 - Prob. 5E Ch. 8.1 - Prob. 6E Ch. 8.1 - SKILLS 5-10 Plotting Points in Polar Coordinates...Ch. 8.1 - Prob. 8E Ch. 8.1 - Prob. 9E Ch. 8.1 - Prob. 10E

(a) To find: The parametric equations for the curve, using θ as the parameter.

Solution Summary: The following figure shows the sketch of the concentric circles curve with all the triangles and length using simple trigonometry.

Concept explainers

(a)

To find:

The parametric equations for the curve, using θ as the parameter.

(b)

To graph:

The curve using a graphing device with a=3 and b=2.

(c)

To identify:

The curve by eliminating the parameter.

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Chapter 8 Solutions

(a) To find: The parametric equations for the curve, using θ as the parameter.

Solution Summary: The following figure shows the sketch of the concentric circles curve with all the triangles and length using simple trigonometry.

Concept explainers

(a) To find: The parametric equations for the curve, using θ as the parameter.

(b) To graph: The curve using a graphing device with a=3 and b=2.

(c) To identify: The curve by eliminating the parameter.

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Chapter 8 Solutions

(a)

To find:

The parametric equations for the curve, using θ as the parameter.

(b)

To graph:

The curve using a graphing device with a=3 and b=2.

(c)

To identify:

The curve by eliminating the parameter.