Explanation Given Info: The circle is in the plane z = 9 with radius 4 and centre ( 1 , 4 , 9 ) . Formula Used: If r ( t ) represents parametric equation of any structure then its arc length is given by, s ( t ) = ∫ 0 t ‖ r ( u ) · ‖ d u Where, ‖ r ( t ) · ‖ = ( d x d t ) 2 + ( d y d t ) 2 + ( d z d t ) 2 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 ) = 〈 1 , 4 , 9 〉 + 4 〈 cos t , sin t , 0 〉 = 〈 1 + 4 cos t , 4 + 4 sin t , 9 〉 Therefore, r · ( t ) ...

4th Edition

ISBN: 9781319055844

Author: FRANZOSA

Publisher: VST

See similar textbooks

Question

Chapter 14.3, Problem 30E

To determine

An arc length parametrization of the circle in the plane $z = 9$ with radius $4$ and centre

$(1, 4, 9)$ .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 14.3, Problem 29E

Chapter 14.3, Problem 31E

Students have asked these similar questions

A small company of science writers found that its rate of profit (in thousands of dollars) after t years of operation is given by P'(t) = (5t + 15) (t² + 6t+9) ³. (a) Find the total profit in the first three years. (b) Find the profit in the sixth year of operation. (c) What is happening to the annual profit over the long run? (a) The total profit in the first three years is $ (Round to the nearest dollar as needed.)

Find the area between the curves. x= -2, x = 7, y=2x² +3, y=0 Set up the integral (or integrals) needed to compute this area. Use the smallest possible number of integrals. Select the correct choice below and fill in the answer boxes to complete your choice. A. 7 [[2x² +3] dx -2 B. [[ ] dx+ -2 7 S [ ] dx The area between the curves is (Simplify your answer.)

The rate at which a substance grows is given by R'(x) = 105e0.3x, where x is the time (in days). What is the total accumulated growth during the first 2.5 days? Set up the definite integral that determines the accumulated growth during the first 2.5 days. 2.5 Growth = (105e0.3x) dx 0 (Type exact answers in terms of e.) Evaluate the definite integral. Growth= (Do not round until the final answer. Then round to one decimal place as needed.)

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

An arc length parametrization of the circle in the plane z = 9 with radius 4 and centre ( 1 , 4 , 9 ) .

Solution Summary: The author explains the arc length parametrization of the circle in the plane z = 9 with radius 4 and centre.

An arc length parametrization of the circle in the plane $z = 9$ with radius $4$ and centre

$(1, 4, 9)$ .

Want to see the full answer?

Chapter 14 Solutions

An arc length parametrization of the circle in the plane z = 9 with radius 4 and centre ( 1 , 4 , 9 ) .

Solution Summary: The author explains the arc length parametrization of the circle in the plane z = 9 with radius 4 and centre.

An arc length parametrization of the circle in the plane z=9 with radius 4 and centre (1,4,9).

Want to see the full answer?

Chapter 14 Solutions

An arc length parametrization of the circle in the plane $z = 9$ with radius $4$ and centre

$(1, 4, 9)$ .