Question: Consider the helix represented by the vector-valued function r(t) = (2 cos t, 2 sin t, t). (a) Write the length of the arc s

Consider the helix represented by the vector-valued function r(t) = (2 cos t, 2 sin t, t).

(a) Write the length of the arc s on the helix as a function of t
by evaluating the integral

S= [ [x'(u)]+ [y'(u)]+ [z'(u)] du.

(b) Solve for t in the relationship derived in part (a), and substitute the result into the original set of parametric equations. This yields a parametrization of the curve in terms of the arc length parameter s.

(d) Verify that

S= [ [x'(u)]+ [y'(u)]+ [z'(u)] du.

Step by Step Solution

★★★★★

3.48 Rating (168 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a b c... 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 Calculus 10th Edition Questions!

Repeat Exercise 17 for the curve represented by the vector-valued function Data from in Exercise 17 Consider the helix represented by the vector-valued function r(t) = (2 cos t, 2 sin t, t). (a)...

Managing Scope Changes Case Study Scope changes on a project can occur regardless of how well the project is planned or executed. Scope changes can be the result of something that was omitted during...

KYC's stock price can go up by 15 percent every year, or down by 10 percent. Both outcomes are equally likely. The risk free rate is 5 percent, and the current stock price of KYC is 100. (a) Price a...

Consider the helix represented by the vector-valued function r(t) = (2 cos(), 2 sin(), c)- (a) Write the length of the arc s on the helix as a function of t by evaluating the integral below. V5t (b)...

Sketch the plane curve. r(t) = 36 - ti. [0. 3] 0 Find its length over the given interval. E Sketch the space curve. Interval Function [0, 1] r(t) = -ti + 4tj + 3tk Z Z 5 15 5 5 - 2 X - 2 2 X 2 O O Z...

Consider the helix represented by the vector - valued function r ( t ) = ( 2 c o s ( t ) , 2 s i n ( t ) , t ) . ( a ) Write the length of the arc s on the helix as a function of t by evaluating the...

1. [-/0.273 Points] DETAILS LARCALC11 12.2.004. Find r'(2), r(t,), and r\\to) for the given value of to- r(t) = (5 + gi + #j, to = 1 r(0) = r(t ) r '(t ) Sketch the curve represented by the...

entiation of Vector-Valued Functions In Exercises 3, 4, 5, 6, 7, 8, 9, and 10 find r'(t), r(to), and r' (to) for the given value of to. Then sketch the curve represented by the vector-valued function...

Consider the following helix with vector equation r (t) = 2 cos (t) i + 2 sin (t) j + t k 3. Consider the following helix with vector equation r (t) = 2 cos (t) i + 2 sin (t) j + t k (a) (5 points)...

11. [-/1 Points] DETAILS LARCALCET7 12.2.053.MI. MY NOTES ASK YOUR TEACHER PRACTICE ANOTHER Find r(t) for the given conditions. r'(t) = 4e2ti + 7elj, r(0) = 2i r(t) = Need Help? Read It Watch It...

(1) Your search of title has revealed that there hasnt been a conveyance of the property within the required search period. What would your Conveyancing professor recommend that a law clerk should do...

Using the following standard reduction potentials, Fe3+(aq) + e- Fe2+(aq) E = +0.77 V Ni2+(aq) + 2 e- Ni(s) E = -0.23 V calculate the standard cell potential for the galvanic cell reaction given...

Should i accdpt a project if the IRR is greater than the required return

An April 14, 2015, article by Kara Brandeisky on Money magazines website states that overall the chance of being audited by the IRS in 2014 was 0.86%. If a persons adjusted gross income was between...

In 1893, George Ferris engineered the Ferris Wheel. It was 250 feet in diameter. If the wheel makes 1 revolution every 40 seconds, then the function represents the height h, in feet, of a seat on the...

An airplane is asked to stay within a holding pattern near Chicagos OHare International Airport. The function d(x) = 70 sin(0.65x) + 150 represents the distance d, in miles, of the airplane from the...

A golfer hits a golf ball with an initial velocity of 100 miles per hour. The range R of the ball as a function of the angle 0 to the horizontal is given by R() = 672 sin(2), where R is measured in...

Hormel Co. follows the practice of recording prepaid expenses and unearned revenues in balance sheet accounts. Hormel's annual accounting period ends on December 31, 2009. The following information...

During 2020, Raines Umbrella Corp. had sales of $740,000. Cost of goods sold, administrative and selling expenses, and depreciation expenses were $550,000, $90,000, and $95,000, respectively. In...

Compute FIFO, LIFO and Average Cost - Periodic and Perpetual) Some of the information found on a detail inventory card for Slatkin Inc. for the first month of operations is as follows. RECEIVED...