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) = (8 cos 2t, 8 sin 2t), for 0 ≤ t ≤ π
Step by Step Answer:
Note that x y 64 so the trajectory ...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
-
Using monthly data for Meta since its IPO date of 31/12/2019, estimate equity beta for Meta. Compare your estimate of Metas equity beta with Facebooks beta provided by Yahoo Finance and comment on...
-
As clearly as possible, define plane stress and plane strain.
-
On January 2, 2022, Grando Company sells production equipment to Fargo Inc. for $50,000. Grando includes a 2-year assurance warranty with the sale of all its equipment. The customer receives and pays...
-
In February 2014, defendant Ibrahim M. Shihadeh, d/b/a Creative Designs Kitchen and Baths, agreed to purchase 25% of his anticipated natural gas needs at a fixed price for the 201415 and 201516...
-
Nordic Company, a merchandising company, prepares its master budget on a quarterly basis. The following data have been assembled to assist in preparation of the master budget for the second quarter....
-
Calculate the dividends paid per share of common stock. ( Note: Number of shares shown on balance sheet is not shown in thousands. The number of shares " in thousands" is 2 , 0 0 0 . ) Round...
-
what are the dimensions indicated on the scale in figure 3-5? O 20 0" Os'0" 2-8 1/2 2. What pre the dimensions indicated on the drawing below? I
-
Consider the following position functions r and R for two objects. a. Find the interval [c, d] over which the R trajectory is the same as the r trajectory over [a, b]. b. Find the velocity for both...
-
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...
-
The following data relate to R.M. Williams' operations for the month of July. Actual number of activity drivers: Machine hours ......................................................... 200 Number of...
-
Assume that we have an input signal x consisting of the sum of sine waves of 1.75 kHz and 2 kHz. We are sampling x at a rate of 3 kHz. Will we be able to reconstruct the original signal after...
-
Plant AG is considering making an offer to purchase Palmer AG. Plants vice president of finance has collected the following information: Plant also knows that securities analysts expect the earnings...
-
I have lived in four countries: South Africa, where I grew up, the US, where I was a teenage exchange student, Greece, where I learnt how to be a journalist, and the UK or, more specifically, London,...
-
Model your daily schedule with a timed automaton. Hours are reflected by a variable h, days by a variable d. d = 1 means Monday, d = 7 means Sunday. On a weekend (d = 6 or d = 7), you leave the...
-
Suppose Agile Corporation of the United States acquires Mobile Plc of the United Kingdom. The value of Agile stock on the Nasdaq in the United States is $3 billion. Mobile sells on the London Stock...
-
What is ethnocentrism, and how can it be reduced?
-
You are thinking of investing in one of two companies. In one annual report, the auditors opinion states that the financial statements were prepared in accordance with generally accepted accounting...
-
Test for the statistical significance of the regression line using the t test? Hematology The data in Table 11.17 are given for 9 patients with aplastic anemia [11]. Table 11.17: Hematologic data for...
-
What are the standard errors of the slope and intercept for the regression line in Problem 11.1? Hematology The data in Table 11.17 are given for 9 patients with aplastic anemia [11]. Table 11.17:...
-
What is the z transformation of .34? Hematology The data in Table 11.17 are given for 9 patients with aplastic anemia [11]. Table 11.17: Hematologic data for patients with aplastic anemia
-
Economy Law, 1. How to improve the employee's legal consciousness in a corporate. 2. The paper should at least discuss the rules which should be known by the employee in a corporate based on the...
-
you have a very small calf-raising business where you raise day-old calves until 3 months of age. You have several production possibilities as seen in the chart below. You could raise from 1-10...
-
Corporate Groups and Bell Case Should the law recognize the single economic enterprise theory of corporate groups or remain with the separate legal entity approach endorsed by Walker v Wimborne?...
Study smarter with the SolutionInn App