Question: Let C be the curve r(t) = (t cos t, t sin t, t). Show that C lies on the cone x2 + y2 =

Let C be the curve r(t) = (t cos t, t sin t, t).
Show that C lies on the cone x2 + y2 = z2.
Sketch the cone and make a rough sketch of C on the cone.

Step by Step Solution

★★★★★

3.61 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

x t cos t y t sin t and z t hen... View full answer

blur-text-image
Question Has Been Solved by an Expert!

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

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

931-C-L-D (2093).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

Q:

Let C be the curve obtained by intersecting a cylinder of radius r and a plane. Insert two spheres of radius r into the cylinder above and below the plane, and let F1 and F2 be the points where the...

Q:

Let C be the curve with equations x = 2 - t 3 , y = 2t - 1, z = ln t. Find (a) the point where C intersects the xz-plane, (b) parametric equations of the tangent line at (1, 1, 0), and (c) an...

Q:

Let C be the piecewise smooth curve ɸ(I1 U I2), where I1 = (-, -1), I2 = (-1, ), and 3 312

Q:

Show that the vector-valued function r(t) = ti + 2t cos tj + 2t sin tk lies on the cone 4x = y2 + z. Sketch the curve.

Q:

14.1 SUMMARY . A vector-valued function is a function of the form A sample is shown fort cate with a diagram the position vectors r ( t ) = (x (1 ) . y (1), z(1) > = x(1)i + >(1)j+ z(1)k (10 - DZ + 1...

Q:

SPIRAT GOING IS A-NEHISI COATES. EGOING 748 CHAPTER 14 CALCULUS OF VECTOR-VALUED FUNCTIONS functions: 14. Match the space curves in Figure 7 with the following vector-valued 18. Describe the...

Q:

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?

Q:

Calculate C F(r) d r for the given data. If F is a force, this gives the work done by the force in the displacement along C. Show the details. F = [x 2 , y 2 , z 2 ], C: r = [cos t, sin t, e t ]...

Q:

Let C be the smooth curve r(t) = (2 cos t)i + (2 sin t)j + (3 - 2 cos 3 t)k, oriented to be traversed counterclockwise around the z-axis when viewed from above. Let S be the piecewise smooth...

Q:

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Q:

Correct Answer You Answered Question 1 A company gives each of its 75 employees (assume they were all employed continuously through 2017 and 2018) 12 days of vacation a year if they are employed at...

Q:

Book Value of Debt $2,500,000,000 Market Value of Debt $2,250,000,000 Book Value of Equity $3,500,000,000 Market Value of Equity $4,000,000,000 Beta for Behnke 1.15 Risk free rate 3% Expected return...

Q:

Which of the following learning goals is an example of "Design and code a computer software that fulfils client needs" cognitive strategies motor skills intellectual skills attitudes

Q:

More tips. The waiter in Exercise 49 usually waits on about 40 parties over a weekend of work. a) Estimate the probability that he will earn at least $500 in tips. b) How much does he earn on the...

Q:

An equilibrium that is stable when time goes forward should be unstable when time goes backward. Find the inverses of the updating functions associated with the following discrete-time dynamical...

Q:

Consider a population xt with per capita production of After writing the discrete-time dynamical system, compute the following for the given values of the parameter r. a. Find the equilibria. b....

Q:

Consider a population xt with per capita production of After writing the discrete-time dynamical system, compute the following for the given values of the parameter r. a. Find the equilibria. b....

Q:

Jason Kidwell is considering whether or not to acquire a local toy manufacturing company, Toys'n Things Inc. The company's annual income statements for the last three years are as follows: 2014 2013...

Q:

Cost of common stock equity Ross Textiles wishes to measure its cost of common stock equity. The firm's stock is currently selling for $65.74. The firm expects to pay a $3.28 dividend at the end of...

Q:

$ $ The Ferrell Transportation Company uses a responsibility reporting system to measure the performance of its three investment centers: Planes, Taxis, and Limos. Segment performance is measured...