Explanation Given info. Radius of helix = 10 A 0 Height of helix = 34 A 0 Concept used: The parametric equation of a helix is x = a cos t y = a sin t z = b t Here: a radius of the helix, 2 π b : height of full turn of the helix. Calculation: Substitute a = 10 A 0 x = 10 cos t y = 10 sin t Substitute height of helix To determine (b) The arc length of one full turn of helix.

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

Chapter 14.3, Problem 22E

To determine

(a)

Show that the helix can be parameterized by

$r (t) = 〈 10 \cos t, 10 \sin t, \frac{34 t}{2 π} 〉$

To determine

(b)

The arc length of one full turn of helix.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.3, Problem 21E

Chapter 14.3, Problem 23E

Students have asked these similar questions

Good Day, Please assist with the following. Regards,

For each given function f(x) find f'(x) using the rules learned in section 9.5. 1. f(x)=x32 32x 2. f(x)=7x+13 3. f(x) = x4 4. f(x) = √√x³ 5. f(x) = 3x²+ 3 x2

Find: lim x →-6 f (x) limx-4 f (x) lim x-1 f (x) lim x →4 f (x) (-6,3) • (-1,5) -8 -7 (-6,-2) 4+ (4,5) (4,2) • (-1,1) -6

Chapter 14 Solutions

CALCULUS (CLOTH)

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

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

(a) Show that the helix can be parameterized by r ( t ) = 〈 10 cos t , 10 sin t , 34 t 2 π 〉

Solution Summary: The author explains that the helix can be parameterized by r (t) = 10 cos t, 10 sin

Concept explainers

Videos

(a)

Show that the helix can be parameterized by

$r (t) = 〈 10 \cos t, 10 \sin t, \frac{34 t}{2 π} 〉$

(b)

The arc length of one full turn of helix.

Want to see the full answer?

Chapter 14 Solutions

(a) Show that the helix can be parameterized by r ( t ) = 〈 10 cos t , 10 sin t , 34 t 2 π 〉

Solution Summary: The author explains that the helix can be parameterized by r (t) = 10 cos t, 10 sin

Concept explainers

Videos

(a) Show that the helix can be parameterized by r(t)=〈10cost,10sint,34t2π〉

(b) The arc length of one full turn of helix.

Want to see the full answer?

Chapter 14 Solutions

(a)

Show that the helix can be parameterized by

$r (t) = 〈 10 \cos t, 10 \sin t, \frac{34 t}{2 π} 〉$

(b)

The arc length of one full turn of helix.