Question: Show that the circular helix r(t) = (a cos t, a sin t, bt), where a and b are positive constants, has constant curvature and

Show that the circular helix r(t) = (a cos t, a sin t, bt), where a and b are positive constants, has constant curvature and constant torsion. [Use the result of Exercise 63(d).]

Step by Step Solution

★★★★★

3.34 Rating (181 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

First we find the quantities required to compute r t a sint a cost b rt a cost a sin t 0 r t a s... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Precalculus Questions!

Show that the spiral r = i cos t i + t sin t j + t k lies on the circular cone x2 + y2 - z2 = 0. On what surface does spiral r = 3t cos t i + t sin t j + t k lie?

The rate at which a drug is absorbed into the bloodstream is modeled by the first-order differential equation dC/dt = a - bC(t) Where a and b are positive constants and C(t) denotes the concentration...

Show that there is a composite integer in every arithmetic progression ak + b, k = 1, 2, . . . where a and b are positive integers.

Fraction of hosts infected Case Study 2 Hosts, Parasites, and Time-Travel 0.8 0.6 0.4 0.2 0 Past Contemporary Future Time Figure \u00031 Horizontal axis is the time from which the parasite was taken,...

776 CHAPTER 14 CALCULUS OF VECTOR-VALUED FUNCTIONS 46. Method for Computing N Let v(t) = Ir'(t)II. Show that v(t) r" (t) - v'(t) r (t) N (1 ) = 12 Iv(t)1" (t) - v'(t)r(t)ll Hint: N is the unit vector...

In Exercises 1 - 16, plot the point given in polar coordinates and then give three different expressions for the point such that (a) r 0 and 0 (c) r > 0 and 2 9. (20, 3) In...

MATLAB ASSIGN 1- Follow Directions and Complete. Will Thumbs Up! Directions: Unless otherwise specified, your write-up should contain the MATLAB input commands, the corresponding output, and the...

806 Chapter Fifteen OPTIMIZATION: LOCAL AND GLOBAL EXTREMA If f is not continuous or the region R is not closed and bounded, there is no guarantee that f achieves a global maximum or global minimum...

Which type of bond investment would you choose, and why, if you wanted a steady, predictable income?

Why is a derivative often an executory contract? Give another example of an executor contract.

17.60 Calculating capability indexes for the DRG 209 hospital losses. Table 17.7 (page 17-36) gives data on a hospitals losses for 120 DRG 209 patients, collected as 15 monthly samples of 8 patients...

Objective 3 List and define the steps in the business buying decision process. pg98 pg98 E-procurement and online purchasing (pp. 179180) pg98

Find the limit. Use lHospitals Rule where appropriate. If there is a more elementary method, consider using it. If lHospitals Rule doesnt apply, explain why. lim (csc x x-0 cot x)

(a) Find the intervals of increase or decrease. (b) Find the local maximum and minimum values. (c) Find the intervals of concavity and the inflection points. (d) Use the information from parts (a) ...

Use the guidelines of this section to sketch the curve. y = ln(1 + x 3 )

Carter Corporation's sales are expected to increase from $5 million in 2012 to $6 million in 2015, or by 20%. Its assets totaled $2 million at the end of 2014. Carter is at full capacity, so its...

A Japanese exporter has a 61,000,000 receivable due in one year. Detail a strategy using a money market hedge that will eliminate any exchange rate risk. 1-year rates of interest Spot exchange rates...

Investment A pays 8% simple interest for 10 years Investment B pays 7.75% compound interest for 10 years. Both require an initial $10,000 investment. The future value of A minus the future value of B...