Show that the following trajectory lies on a sphere centered at the origin, and find the...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
Show that the following trajectory lies on a sphere centered at the origin, and find the radius of the sphere. 5 sin 2t 5 cos 2t 5 sin 9t 2 √1+ sin29t √√1+ sin 29t √1+ sin²9t r(t) = The trajectory described by r(t) lies on a sphere centered at the origin if the magnitude of r(t) equals which implies that the magnitude squared also equals Start by setting up the expression for the magnitude squared of r(t). |1|0(0)1² = 0². [√ [r(t)/² \v₁² = √² + √² + √² 1+ sin ²9t (Type the terms of your expression in the same order as they appear in the original expression.) Next expand each of the squared terms and factor out a constant. = 5 cos 21 25 sin ²2t+25 cos ²2t+ 25 sin ²9t 2. 1+ sin 9t sin 22t+ cos22t+ sin ²9t 2 1+ sin 9t (Simplify your answer.) Simplify the numerator using a trigonometric identity. |r0|² = 0 0st≤2* 1r01² = 0 (Simplify your answer.) The radius is. (Simplify your answer.) 1+ sin 9t (Type your answer in factored form.) Now simplify the entire expression to demonstrate that all points on the trajectory lie on a sphere. Expand and combine fractions. Factor. for 0≤ts 2x, Show that the following trajectory lies on a sphere centered at the origin, and find the radius of the sphere. 5 sin 2t 5 cos 2t 5 sin 9t 2 √1+ sin29t √√1+ sin 29t √1+ sin²9t r(t) = The trajectory described by r(t) lies on a sphere centered at the origin if the magnitude of r(t) equals which implies that the magnitude squared also equals Start by setting up the expression for the magnitude squared of r(t). |1|0(0)1² = 0². [√ [r(t)/² \v₁² = √² + √² + √² 1+ sin ²9t (Type the terms of your expression in the same order as they appear in the original expression.) Next expand each of the squared terms and factor out a constant. = 5 cos 21 25 sin ²2t+25 cos ²2t+ 25 sin ²9t 2. 1+ sin 9t sin 22t+ cos22t+ sin ²9t 2 1+ sin 9t (Simplify your answer.) Simplify the numerator using a trigonometric identity. |r0|² = 0 0st≤2* 1r01² = 0 (Simplify your answer.) The radius is. (Simplify your answer.) 1+ sin 9t (Type your answer in factored form.) Now simplify the entire expression to demonstrate that all points on the trajectory lie on a sphere. Expand and combine fractions. Factor. for 0≤ts 2x,
Expert Answer:
Answer rating: 100% (QA)
ut Now 5 sint I sin2t x y 3 5 cost Sin2t 25 sint It sin2t x y z 5 ... View the full answer
Related Book For
Calculus Early Transcendentals
ISBN: 978-0321947345
2nd edition
Authors: William L. Briggs, Lyle Cochran, Bernard Gillett
Posted Date:
Students also viewed these mathematics questions
-
An N-type sample of silicon has uniform density (Na = 101%cm) of arsenic, and a P-type silicon sample has a uniform density (Na = 1015 /cm) of boron. For each sample, determine the following: (a) The...
-
In year 1, AMC will earn $2000 before interest and taxes. The market expects these earnings to grow at a rate of 3% per year. The firm will make no net investments (i.e., capital expenditures will...
-
The hydrogen atom is composed of one proton in the nucleus and one electron, which moves about the nucleus. In the quantum theory of atomic structure, it is assumed that the electron does not move in...
-
A ball is attached to one end of a wire, the other end being fastened to the ceiling. The wire is held horizontal, and the ball is released from rest (see the drawing). It swings downward and strikes...
-
Policy Issue: Who Should Pay for Neighborhood Improvements? Related Accounting Issues Facts: Pursuant to its capital improvement plan, the City of Kirkland decided to make certain improvements to Oak...
-
Use the graphs from questions 3336 to answer the following questions; (a) Which team has the best pass offense? (b) Which team has the best pass defense? (c) Which team has the best rush offense? (d)...
-
Fraud deterrence is centered on the fear of getting caught and the fear of getting punished. In your opinion, which is stronger and why?
-
Kenseth Corp. has the following beginning-of-the-year present values for its projected benefit obligation and market-related values for its pension plan assets. The average remaining service life per...
-
Use the below table to answer the following questions. Selling Price $43.00 = Sales Volume Variable 2,200 3,200 Fixed Cost Cost 4,200 Profitability 5,200 6,200 $47,200 15 $14,400 $42,400 $70,400...
-
Suppose that the two-dimensional vectors (X1, Y1), (X2, Y2), . . . , (Xn, Yn) form a random sample from a bivariate normal distribution for which the means of X and Y, the variances of X and Y , and...
-
Exam Corporation reports taxable income of $800,000 on its federal income tax return. Given the following information from the corporation's records, determine its M-1 book income: Deduction for...
-
How does the concept of moral entrepreneurship, as discussed within symbolic interactionist literature, illuminate the ways in which moral crusaders and social reformers shape public perceptions of...
-
ABC Corp is going to transfer a piece of equipment to XYC Corp using Section 85. The transfer occurs on April 1, 2020. ABC Corp has a year end of June 30, 2020. YXC Corp has a year end of November...
-
In 2014, Mr. P bought a residential lot for $8,000 and built a house on it at a cost of $52,000. He added an in-ground swimming pool costing $15,000 in 2016. The house was destroyed by fire in 2022...
-
What is absorption costing and how does it differ from variable costing? 2. How do you calculate the predetermined overhead rate in absorption costing? 3. What are the advantages of absorption...
-
How are UNCONSOLIDATED SUBSIDIARIES an example of "off-balance-sheet financing"?
-
Think of a situation in which you were faced with the negotiators dilemma. Did you resolve the issue successfully? If so, how did you and the other party manage to transcend your reluctance to reveal...
-
What mass of KBr (in grams) should you use to make 350.0 mL of a 1.30 M KBr solution?
-
a. Derive a formula for the second derivative, d 2 /dx 2 (f(g(x))). b. Use the formula in part (a) to calculate d 2 /dx 2 (sin (3x 4 + 5x 2 + 2)).
-
The expression where the process continues indefinitely, is called a continued fraction. a. Show that this expression can be built in steps using the recurrence relation a 0 = 1, a n + 1 = 1 + 1/a n...
-
Compute u v if u is a unit vector, |v| = 2, and the angle between them is 3/4.
-
The purchasing officer for The Majestic Emporium has prepared a purchases budget for the financial year ending 31 March 2020, based on the following data. The cost of sales is 65% of sales, and the...
-
Greyt Dog Beds Ltd manufactures dog beds specifically designed for greyhounds and whippets. The company purchases all the required materials from external suppliers and designs and assembles the...
-
Ketton Ltd is in the process of preparing direct labour and factory overhead budgets for the year ending 30 June 2020. Relevant data are set out below. Required (a) Prepare the direct labour budget...
Study smarter with the SolutionInn App