To illustrate that the length of a smooth space curve does not depend on the parametrization you
Question:
To illustrate that the length of a smooth space curve does not depend on the parametrization you use to compute it, calculate the length of one turn of the helix in Example 1 with the following parametrizations.
Transcribed Image Text:
a. r(t) = (cos 4t)i + (sin 4t)j + 4tk, 0≤t≤ π/2 b. r(t) = [cos (t/2)] + [sin (t/2)]j + (t/2)k, 0≤ t ≤ 4π c. r(t) = (cos t)i - (sin t)j - tk, -2π ≤ t ≤0
Fantastic news! We've Found the answer you've been seeking!
Step by Step Answer:
Answer rating: 83% (6 reviews)
To calculate the length of a smooth space curve we can use the arc length formula L dxdt dydt dzdt d...View the full answer
Answered By
Abdul Wahab Qaiser
Before working at Mariakani, I volunteered at a local community center, where I tutored students from diverse backgrounds. I helped them improve their academic performance and develop self-esteem and confidence. I used creative teaching methods, such as role-playing and group discussions, to make the learning experience more engaging and enjoyable.
In addition, I have conducted workshops and training sessions for educators and mental health professionals on various topics related to counseling and psychology. I have presented research papers at conferences and published articles in academic journals.
Overall, I am passionate about sharing my knowledge and helping others achieve their goals. I believe that tutoring is an excellent way to make a positive impact on people's lives, and I am committed to providing high-quality, personalized instruction to my students.
0.00
0 Reviews
10+ Question Solved
Related Book For
Thomas Calculus Early Transcendentals
ISBN: 9780321884077
13th Edition
Authors: Joel R Hass, Christopher E Heil, Maurice D Weir
Question Posted:
Students also viewed these Mathematics questions
-
How do you find the length of a smooth parametrized curve x = (t), y = g(t), a t b? What does smoothness have to do with length? What else do you need to know about the parametrization in order to...
-
The engineering and catering courses will require much greater use of expensive machinery and equipment, which in turn will need more room. In addition these courses will probably require much...
-
In Gamble 1 you have a 99% chance of winning a trip to Venice and a 1% chance of winning tickets to a movie about Venice; and in Gamble 2, you have a 99% of winning the same trip to Venice and a 1%...
-
How does the trade-off between decision management and decision control affect the form that an absorption cost system takes within a particular firm?
-
If you hold a valid contract that will pay you $8,000 cash 10 years from now and the going rate of interest is 10 percent, what is its present value?
-
Youre the supervisor of a group of employees whose task is to assemble disk drives that go into computers. You find that quality is not what it should be and that many of your groups devices have to...
-
Hemlock Semiconductor Operations, LLC, and SolarWorld Industries Sachsen GmbH, are both companies involved in the manufacture of components for solar power products. Prior to the lawsuit, the two...
-
WORK SHEET, ADJUSTING ENTRIES, AND FINANCIAL STATEMENTS Herrera Company had the following trial balance columns on its work sheet: Data for adjusting the accounts are as follows: (a) Factory overhead...
-
3. A region has the peak-period electricity demand in MWh given by D(r) = { 40,008 rif r 64 104,000 1,000r if r64 6 Exercises for Markets Module by Metin akanyldrm where r is the wholesale price in...
-
Oranges are grown, picked, and then stored in warehouses in Tampa, Miami, and Fresno. These warehouses supply oranges to markets in New York, Philadelphia, Chicago, and Boston. The following table...
-
The length 22 of the turn of the helix in Example 1 is also the length of the diagonal of a square 2 units on a side. Show how to obtain this square by cutting away and flattening a portion of the...
-
Find T, N, B, , and at the given value of t. r(t) = " (1 + 1)/ i + # (1 - rp/2j + 2rk.r=0 4 tk, t
-
Rectangles ABCD and DEFG are similar. The length of ABCD is 24 feet and the perimeter is 84 feet. The width of DEFG is 3 yards. Find the ratio of the area of ABCD to the area of DEFG.
-
Determine the wavelength and energy for light with a frequency of 5.823 1014 s-1. = E = nm kJ/mol
-
Spinning Gears has reported their beginning materials of $75,800 and ending material inventory of $79,200. In order to produce their 12" gear, they need $500,000 for production. How much in direct...
-
A typical level of sodium in blood is 3.24 mg/mL. What is the millimolar concentration of sodium in blood?
-
Using the link below, determine why you as an international student who has been in Canada for less than a year, has a part time job, and has a credit and debit card from Canada must file an income...
-
In 2013 collected $25,000 from customers for sales made in 2012 and $210,000 for sales made in 2013 . In 2014 it collected $23,000 from customers for sales made in 2013. At that point, all 2012 and...
-
Discuss the following statement: Its better for a manager to try to carry out a poor decision for the sake of worker confidence. You cant build worker confidence by continually admitting the poor...
-
Why do CPA firms sometimes use a combination of positive and negative confirmations on the same audit?
-
Write an expression for the nth term of the sequence and then determine whether the sequence you have chosen converges or diverges. (There is more than one correct answer.) 1 2 3 2.3'34'4.5'5.6'' 4
-
Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. 00 If 0
-
The figure shows the first 20 terms of the series c n using squares and the first 20 terms of the series d n using circles. If d n converges, can you determine anything about the convergence or...
-
Question 3 Nice life (NL) plc an entertainment business is considering acquisition of one of its competitors BC plc another firm listed on the Lusaka Securities Exchange (LuSE). The share capital of...
-
As employees health changes, they may miss work due to illness or injury increasing healthcare cost for employees and employers. Furthermore, employees may be less productive while at work due to...
-
West Area hospital leadership team is having their monthly meeting. At the meeting federal re-certification is addressed as well as a pending Joint Commission accreditation visit. What outcome is...
Study smarter with the SolutionInn App