Determine whether the following trajectories lie on a circle in R 2 or sphere in R 3
Question:
Determine whether the following trajectories lie on a circle in R2 or sphere in R3 centered at the origin. If so, find the radius of the circle or sphere and show that the position vector and the velocity vector are everywhere orthogonal.
r(t) = (sin t, cos t, cos t), for 0 ≤ t ≤ 2π
Step by Step Answer:
x y x sin t cos t cos t 1 ...View the full answer
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
Related Video
The area of a circle is given by the formula: A = ?r^2 Where A is the area, ? is a mathematical constant (approximately 3.14), and r is the radius of the circle. The radius is the distance from the center of the circle to the edge. So for example, if the radius of a circle is 5 units, the area would be: A = ?(5^2) = ?(25) = 78.5 square units Here three friends went out to a restaurant and decided to have pizza for lunch. While they were waiting for their order, one of them stepped out to take a call but promised to return in two minutes. The waiter came and presented them with the menu, and they decided to order two 10-inch pepperoni pizzas. The waiter took their order and left. Just then, the third friend returned and asked what they had ordered. They explained that they had ordered two small pepperoni pizzas as they were only three of them and it would be enough for them. However, the third friend suggested that for the same price, they could get a large pizza that would be much bigger than the two small ones. He asked the waiter for a pen and paper and proceeded to calculate the area of the two small pizzas and compared it to the area of one large pizza. The friends were amazed at how the circle measurements worked and decided to change their order from two small pizzas to one large pizza.
Students also viewed these Mathematics questions
-
Determine whether the following production functions exhibit constant, increasing, or decreasing returns to scale. A. Q = 0.5X + 2Y + 40Z B. Q = 3L + 10K + 500 C. Q = 4A + 6B + 8AB D. Q = 7L^2 + 5LK...
-
Determine whether the following sentences use parallel structure. Revise sentences as needed to make the structure parallel. a. The executive at Ernst & Young writes reports quickly, accurately, and...
-
Determine whether the following polynomials span P2. p1 = 1 - x + 2x2, p2 = 3 + x, p3 = 5 - x + 4x2, p4 = -2 - 2x + 2x2
-
A client of Park Street's expected a delivery of samples for an event on Friday evening. The order was setup correctly by Park Street, however the vendor that was hired to pick up and deliver the...
-
A penny-shaped piece of soft metal is brazed to the ends of two flat, round steel rods of the same diameter as the piece. The assembly is then subjected to uniaxial tension. What is the state of...
-
Lanier SA has pretax financial income (or loss) equal to taxable income (or loss) from 20172023 as follows. Pretax financial income (loss) and taxable income (loss) have been the same for all years...
-
Texas Inpatient Consultants, LLLP, is a partnership that employs physicians to deliver medical care to hospitalized patients of other physicians. Texas Inpatient recruited Julius Tabe, M.D., to work...
-
Hillsborough Co. has an available-for-sale investment in the bonds of Schuyler Corp. with a carrying (and fair) value of $70,000. Hillsborough determined that due to poor economic prospects for...
-
A customer enters a doctors office to acquire information about swine flu and the potential impact of the influenza. She speaks Creole and is lost in the building. Finally, she is able to locate a...
-
Nancy Tercek started a delivery service, Tercek Deliveries, on June 1, 2022. The following transactions occurred during the month of June. June 1 Stockholders invested $10,000 cash in the business in...
-
Determine whether the following trajectories lie on a circle in R 2 or sphere in R 3 centered at the origin. If so, find the radius of the circle or sphere and show that the position vector and the...
-
Determine whether the following trajectories lie on a circle in R 2 or sphere in R 3 centered at the origin. If so, find the radius of the circle or sphere and show that the position vector and the...
-
Helena leaves her car with OK Auto Sales & Service for repairs. OK sells the car to Pete, who does not know that OK has no right to sell the car. Helena can recover from a. OK only. b. Pete only. c....
-
Cooper Investments reported an unusual gain from the sale of certain assets in its 2015 income statement. How does intraperiod tax allocation affect the reporting of this unusual gain?
-
In the third quarter of 2016, David Beckham, the controller for Swiss Precision Company, discovers an error in ending inventory counts for the December 31, 2015, cutoff. After Beckham reports the...
-
Prepare the entries under U.S. GAAP for Diaz for (a) date of issue, (b) first interest payment date, and (c) January 1, 2016, when Diaz calls and extinguishes the bonds at 101.
-
Kwon Cellular provides cell phones and 1 year of cell service to students for an upfront, non-refundable fee of HK$300 and a usage fee of HK$5 per month. Students may renew the service for each year...
-
In 2015, Ghostbusters Corp. spent 420,000 for goodwill visits by sales personnel to key customers. The purpose of these visits was to build a solid, friendly relationship for the future and to gain...
-
List seven trends in the workplace that affect business communicators. Be prepared to discuss how they might affect you in your future career?
-
The sales department of P. Gillen Manufacturing Company has forecast sales in March to be 20,000 units. Additional information follows: Finished goods inventory, March 1 . . . . . . . . . . . . . . ....
-
Do you think the linear regression provides a good fit to the data? Why or why not? Use residual analysis to justify your answer. Table 11.18: 90th percentile of SBP in boys ages 117 of average height
-
Compute the correlation between 5-year lungcancer mortality and annual cigarette consumption when each is expressed in the log 10 scale? Cancer The following statistics are taken from an article by...
-
Test this correlation for statistical significance, and report a p-value? Cancer The following statistics are taken from an article by Burch relating cigarette smoking to lung cancer [13]. The...
-
Write a complete Java program that reads an odd number from the user. Your program should then use this odd number and nested for loops to print a cross made of stars. Some samples of how your...
-
How does diversity encompass many areas including underserved populations, socioeconomic status, language, acculturation level, traditions, belief systems, etc?
-
In this exercise, write a complete Java program that reads integer numbers from the user until a negative value is entered. It should then output the average of the numbers, not including the...
Study smarter with the SolutionInn App