Let C be the curve given by r(t) (t cos t, t sin t, t) (a) Show that C lies on the cone x 2 y 2 z 2 (b) Sketch the cone and make a rough sketch of C on the cone

Question: Let C be the curve given by r(t) = (t cos t, t sin t, t). (a) Show that C lies on the cone x

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

Step by Step Solution

★★★★★

3.31 Rating (151 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a x t cost y t sint and z t hence for any point x y z on the curve we ge... 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 4th Questions!

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.

Use a computer algebra system to plot the projections onto the xy- and xz-planes of the curve r(t) = (t cos t, t sin t, t) in Exercise 25. Data From Exercise 25 Let C be the curve given by r(t) = (t...

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...

I need help solving this question, please show all steps Problem #8: Let C be a curve given by r(:') = (2 cos 1', 2 sin 1'), r E [0, Jr]. [5 marks] (a) _ Find I xafy - yak C (b) Let C be the opposite...

Given F(x, y) = (sin yte,xcosy) and let C be the curve given by r (t ) = (t, t(3-t) ); Ost53 Find the following (On part (a), set up only, do not evaluate) (a) Evaluate J F . dr directly. (b) Show...

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...

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...

1. The paraboloid z = 4.2 + 4y2 and the cone z = V3.2 + 3y2 intersect at a point P and a closed curve C that does not contain P. Determine the point P and find a smooth vector-valued function r(t)...

". Let F(x, y, z) = (sin y, z cos y + cos z, -y sin 2). Let C be the curve given by r(t) 0 t 2. (a) Is F conservative? (b) Evaluate JF. dr. = (sint, t, 2t) for

Please help with this question: 1. (8 points) Justify all your steps for full marks. (a) Let C be the curve given by parametrization r(t) = ((2+cos(t)) cos(t), (2+cos(t) ) sin(t)) and let F = (cos x...

1:You will invest $94 per month. If the rate is 7.29%, how much will you have in 8 years? 2:You would like to buy a house in in 11 years and estimate that you will need a deposit of $97025. You plan...

Consider the volleyball net shown. Determine the angle formed by guy wires AC and AD.

Marfy companles record both purchase orders and purchases; when would such a company recognize in the financial stasements the purchase? Multiple Cholce When the purchase order is insued. When the...

P1027 Integrative: Conflicting Rankings The High-Flying Growth Company (HFGC) has been growing very rapidly in recent years, making its shareholders rich in the process. The average annual rate of...

Sketch the region enclosed by the given curves and find its area. x = 2y 2 , x = 4 + y 2

Sketch the region enclosed by the given curves and find its area. y = x - 1, x - y = 1

Sketch the region enclosed by the given curves and find its area. y = cos x, y = 4x 2 - 1

In cell b 1 0 , add the total amounts for bedtime set

Please I need someone to solve C programming ASAP int egg =25; while(egg > 5) egg--; printf("\%d ", egg)

Problem 4 - 6 A 3 0 - year fully amortizing mortgage loan was made 1 0 years ago for $ 8 5 , 0 0 0 at 6 percent interest. The borrower would like to prepay the mortgage balance by $ 1 2 , 0 0 0 ....