Prove that ||r(t)|| is constant if and only if r(t) r'(t) = 0.

Question:

Prove that ||r(t)|| is constant if and only if r(t) ∙ r'(t) = 0.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Calculus

ISBN: 978-0131429246

9th edition

Authors: Dale Varberg, Edwin J. Purcell, Steven E. Rigdon

See More Books

Question Posted: Jun 21, 2016 10:58 AM

See More Questions

A differentiable function f on a convex set S is constant if and only if Df[x] = 0 for every x S.
The elasticity of a function f: is defined to be In general, the elasticity varies with x. Show that the elasticity of a function is constant if and only if it is a power function, that is, f (x) =...
Prove that f : R R is continuous if and only if for each closed set F in R, the inverse image f-1(F) is closed.
PROJECT SCENARIO You are recently appointed as the IT Consultant and Software Architect in BMS a Software Architect firm. As your first project, you are assigned by the Project Manager to propose and...
A stock recently increased in price from $48 to $63. Using (, what are the primary and secondary support areas for the stock?
Liz rushes down onto a subway platform to find her train already departing. She stops and watches the cars go by. Each car is 8.60m long. The first moves past her in 1.50 s and the second in 1.10 s....
What audit procedures are performed to determine (a) rights and obligations and (b) valuation or allocation of plant assets?
Jamal has a utility function U = W1/2, where W is his wealth in millions of dollars (which determines how much he gets to buy and consume over his lifetime) and U is the utility he obtains. a. Graph...
Given functions f(x) = =g(x)= X x+2 Solve for the following new functions and determine their respective domains. (a) f+g, (b) fg, (c) f/g (d) fog (e) go f (f) fof
At Webster Chemical Company, lumps in the caulking compound could cause difficulties in dispensing a smooth bead from the tube. Even when the process is in control, an average of four lumps per tube...
Show that if the speed of a moving particle is constant its acceleration vector is always perpendicular to its velocity vector.
In Problems a to b, find the length of the curve with the given vector equation. a. r(t) = t i + sin t j + cos t k; 0 t 2 b. r(t) = t cos t i + t sin t j + 2t k; 0 t 2
Air traffic control stations often have insufficient numbers of air traffic controllers, sometimes just one person on duty. In a recent study, a lone air traffic controller is managing an airstrip in...
An ambulance generally transports between one and eight patients a day. If the ambulance crew reports no particular pattern within that range, what is the expected value of the daily number of...
There is a 60% chance of a loss of $100, a 30% chance of sales of $100, and a 10% chance of sales of $200. What is the expected value of sales?
A processer has a 10% probability of freezing, at which point an identical backup processor is activated. What is the probability they both freeze?
In general, how is the equivalent stiffness of a combination of springs calculated?
A component has a reliability of 98% and is backed up by a redundant component with the same probability. What is their combined reliability?
Ramirez Wholesalers operates at capacity and sells furniture items to four department-store chains (customers). Mr. Ramirez commented, We apply ABC to determine product-line profitability. The same...
Find the area of the surface generated by revolving the para- metric curve x = cos 1, y = sin? 1 (0 < I sa/2) about the y-axis.
Population 3 starting from 500 individuals. The following table gives the per capita production for four populations over a period of 10 years. Find the population over the 10 years starting from the...
Population 4 starting from 200 individuals. The following table gives the per capita production for four populations over a period of 10 years. Find the population over the 10 years starting from the...
Population 1 starting from 10 individuals. The following table gives the immigration (positive values) or emigration (negative values) for four populations over a period of 10 years. Find the...
This is a slip and fall case. Plaintiff was injured when she slipped and fell in the defendant's fast food restaurant. Plaintiff claims the floor was wet and slippery when she fell. Defendant denies...
1. Explain what the "Deinstitutionalization Mandate" is. This should be done in at least two paragraphs. 2. In another two paragraphs, discuss how status offenses are connected to the...
You are the owner of a very small business that sells gourmet coffee. You sell only one product, a 12-ounce bag of whole-bean French roast coffee. You sell each bag of coffee for $14 each, but due to...

Prove that ||r(t)|| is constant if and only if r(t) r'(t) = 0.

Question:

Step by Step Answer:

If rt C similar to Problem 31 rt r...View the full answer

Calculus

Students also viewed these Calculus questions