a) To show that r ( t ) parametrizes a helix of radius R and height h making N complete turns.

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Answer 1

Question

Chapter 14.3, Problem 23E

To determine

a)

To show that $r (t)$ parametrizes a helix of radius $R$ and height $h$ making $N$ complete turns.

To determine

b)

To guess which of the two springs in the given figure uses more wire.

To determine

c)

To compute and compare the lengths of two springs.

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3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 + 2 sin (t) } + tk (a) Determine the arclength function of the helix. (b) in the direction of increasing t. Reparametrize the helix with respect to arclength measured from (2,0, 0)

The position vector for a particle moving on a helix is c(t) = (5 cos(t), 5 sin(t), t² ) . Find the speed s(to) of the particle at time to 11r. (Express numbers in exact form. Use symbolic notation and fractions where needed.) s(to) Find parametrization for the tangent line at time to 11r. Use the equation of the tangent line such that the point of tangency occurs when t = to. (Write your solution using the form (*,*,*). Use t for the parameter that takes all real values. Simplify all trigonometric expressions by evaluating them. Express numbers in exact form. Use symbolic notation and fractions as needed.) 1(t) = Where will this line intersect the xy-plane? (Write your solution using the form (*,*,*). Express numbers in exact form. Use symbolic notation and fractions where needed.) point of intersection:

1. Let R and b be positive constants. The vector function r(t) = (R cost, R sint, bt) traces out a helix that goes up and down the z-axis. a) Find the arclength function s(t) that gives the length of the helix from t = 0 to any other t. b) Reparametrize the helix so that it has a derivative whose magnitude is always equal to 1. c) Set R = b = 1. Compute T, Ñ, and B for the helix at the point (√2/2,√2/2, π/4).

Answer 2

Question

Chapter 14.3, Problem 23E

To determine

a)

To show that $r (t)$ parametrizes a helix of radius $R$ and height $h$ making $N$ complete turns.

To determine

b)

To guess which of the two springs in the given figure uses more wire.

To determine

c)

To compute and compare the lengths of two springs.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 14.3, Problem 23E

To determine

a)

To show that $r (t)$ parametrizes a helix of radius $R$ and height $h$ making $N$ complete turns.

To determine

b)

To guess which of the two springs in the given figure uses more wire.

To determine

c)

To compute and compare the lengths of two springs.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 14.3, Problem 23E

To determine

a)

To show that $r (t)$ parametrizes a helix of radius $R$ and height $h$ making $N$ complete turns.

To determine

b)

To guess which of the two springs in the given figure uses more wire.

To determine

c)

To compute and compare the lengths of two springs.

Expert Solution & Answer

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Check out a sample textbook solution

See solution

Answer 5

Chapter 14.3, Problem 23E

To determine

a)

To show that $r (t)$ parametrizes a helix of radius $R$ and height $h$ making $N$ complete turns.

To determine

b)

To guess which of the two springs in the given figure uses more wire.

To determine

c)

To compute and compare the lengths of two springs.

Answer 6

Chapter 14.3, Problem 23E

To determine

a)

To show that $r (t)$ parametrizes a helix of radius $R$ and height $h$ making $N$ complete turns.

Answer 7

Chapter 14.3, Problem 23E

To determine

a)

To show that $r (t)$ parametrizes a helix of radius $R$ and height $h$ making $N$ complete turns.

Answer 8

To determine

b)

To guess which of the two springs in the given figure uses more wire.

Answer 9

To determine

b)

To guess which of the two springs in the given figure uses more wire.

Answer 10

To determine

c)

To compute and compare the lengths of two springs.

Answer 11

To determine

c)

To compute and compare the lengths of two springs.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

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Answer 15

Ch. 14.1 - Prob. 1PQ Ch. 14.1 - Prob. 2PQ Ch. 14.1 - Prob. 3PQ Ch. 14.1 - Prob. 4PQ Ch. 14.1 - Prob. 5PQ Ch. 14.1 - Prob. 6PQ Ch. 14.1 - Prob. 1E Ch. 14.1 - Prob. 2E Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E

a) To show that r ( t ) parametrizes a helix of radius R and height h making N complete turns.

Concept explainers

Videos

a)

To show that $r (t)$ parametrizes a helix of radius $R$ and height $h$ making $N$ complete turns.

b)

To guess which of the two springs in the given figure uses more wire.

c)

To compute and compare the lengths of two springs.

Want to see the full answer?

Chapter 14 Solutions

a) To show that r ( t ) parametrizes a helix of radius R and height h making N complete turns.

Concept explainers

Videos

a) To show that r(t) parametrizes a helix of radius R and height h making N complete turns.

b) To guess which of the two springs in the given figure uses more wire.

c) To compute and compare the lengths of two springs.

Want to see the full answer?

Chapter 14 Solutions

a)

To show that $r (t)$ parametrizes a helix of radius $R$ and height $h$ making $N$ complete turns.

b)

To guess which of the two springs in the given figure uses more wire.

c)

To compute and compare the lengths of two springs.