Explanation Given Info: The circle in the plane y = 10 with radius 4 and centre ( 2 , 10 , − 3 ) with constant speed. Formula Used: Arc length parametrization, r 1 ( s ) = r ( g ( s ) ) Where g ( s ) is the inverse of arc length function s ( t ) Calculation: The parametrization of the circle can be written as, r ( t ) = 〈 2 , 10 , − 3 〉 + 4 〈 cos t , 0 , sin t 〉 = 〈 2 + 4 cos t , 10 , − 3 + 4 sin t 〉 Therefore, r · ( t ) = 〈 − 4 sin t , 0 , 4 cos t 〉 The arc length parametrization of the circle is given by, r 1 ( s ) = r ( g ( s ) ) The new parametrization should satisfy ‖ r 1 · ( s ) ‖ = 8 r 1 · ( s ) = d d s ( r ( g ( s ) ) ) = r · ( g ( s ) ) g · ( s ) r · ( g ( s ) ) = 〈 − 4 sin g ( s ) , 0 , 4 cos g ( s ) 〉 Therefore, r 1 · ( s )

4th Edition

ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

See similar textbooks

Concept explainers

Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made p…

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.

Videos

Question

Chapter 14.3, Problem 31E

To determine

A path that traces the circle in the plane $y = 10$ with radius $4$ and centre $(2, 10, - 3)$ with constant speed $8$ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.3, Problem 30E

Chapter 14.3, Problem 32E

Students have asked these similar questions

Find the tangent line approximation 7 to the graph of f at the given point. T(x) = f(x) = csc(x), (8, csc(8)) Complete the table. (Round your answers to four decimal places.) x f(x) T(x) 7.9 7.99 8 8.01 8.1

Can you solve it numerical method

Use the information to find and compare Ay and dy. (Round your answers to four decimal places.) Function x-Value Differential of x Ду = dy = y = x² + 2 x = -4 Ax = dx = 0.01

Chapter 14 Solutions

EBK CALCULUS

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 path that traces the circle in the plane y = 10 with radius 4 and centre ( 2 , 10 , − 3 ) with constant speed 8 .

Concept explainers

Videos

A path that traces the circle in the plane y=10 with radius 4 and centre (2,10,−3) with constant speed 8.

Want to see the full answer?

Chapter 14 Solutions

A path that traces the circle in the plane $y = 10$ with radius $4$ and centre $(2, 10, - 3)$ with constant speed $8$ .