Question 4 Let w aXu(q) + bX.(@) € T,S such that |lw||= 1. Then the normal curvature to the surface S at p in the direction of w is given by: VIt c) VI (P

Q: QUESTION 17 Let a , b and c be the last three digits of your student ID and let d=max(a,b,c). 2 How…

A: Given - Let a, b, c be the last three digits of your student ID and let d = max(a, b, c) To find -…

Q: Find the curvature and the radius of curvature at the point t = 0. %3D x = e' cos(t), y = e' sin(t),…

A: r(t)=et cos(t) i+et sin(t) j+7et kr'(t)=[etcost-etsin(t)] i          +[etsint+etcos(t)] j +7et k…

Q: 4. Find the curvature * 5 K of the curve ř (1) = (e' cos(t), e' sin(t), 3) at t = 0.

A: Given data: The given expression for the curve is r→(t)=et cost, et sint,3. The given point is t=0.…

Q: * Find the curvature .12 (ähä 2) K of the curve ř (t) = (e' cos(t), e' sin(t), 3) at t = 0. %3D

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 11 cos(t)i+ 9 sin(t)j +…

A:

Q: Question 15 Find the curvature k and radius of curvature R for the curve at the given point. y = sin…

A: The given curve is y=sin2x we have to find curvature and radius of curvature for the curve at the…

Q: a aa Jll J l a Find the curvature of 7 (t) - ( cos (2t)- sin (2t),4t>. a Jall JA psl ING A FUJITSU

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 2 cos(t)i +11 sin(t)j+…

A: A detailed solution is given below

Q: Question 16 Find the curvature of the plane curve y = 5x² +8 at x = -1. Round your answer to three…

A:

Q: Question 30 Find the curvature k and radius of curvature R for the curve at the given point. y = cos…

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 9 cos(t)i + 7 sin(t)j +…

A:

Q: D O 1.909 Question 14 Find the length of the plane curve given below. r(t) = 5cos(t)i+5 sin(t)j, [0,…

A:

Q: 3) Find the radius of curvature for the parametric X = сurve e-t cos t , y = e=t sin t.

A: R=1+dydx232d2ydx2 Given equations of curve- xt=e-tcostyt=e-tsint

Q: Find the curvature and the radius of curvature at the stated poin r(t) = 11 cos(t)i + 10…

A: Here we have r→(t)=11cost i +10sint j +10t k  at=π2 The formula for curvature is…

Q: QUESTION 6 Find the curvature of r(t)= (cos t, sin t, t?) at t =n/2.

A: Since not a particular question asked as per guidelines solution to only first question(i.e Q 6) is…

Q: QUESTION 3 Consider the metric on the number line R: |x-y 1+|x-yl d: R xR+R d(a, b) D- Find the open…

A: Let X,d be the metric space. The open sphere, Sd(a,r) is represented as x∈X|d(a,x)<r , where…

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 4 cos(t)i + 5 sin(t)j +…

A:

Q: Find the curvature and the radius of curvature at the stated point. ㅠ r(t) = 11 cos(t)i + 10 sin(t)j…

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 5 cos(t)i + 11 sin(t)j +…

A:

Q: a The curvature of the helix r(t) = (a cos t) i + (a sin t) j+ bt k (a.b2 0) is K= What is the…

A: • Since, b is fixed here, curvature is now a function of 'a' only. To find its maximum, we have to…

Q: 3) Find the radius of curvature for the parametric сurve e-t cos t y = e-t sin t.

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) 2 cos(t)i+ 3 sin(t)j+ 10tk;…

A: To find the curvature and the radius of curvature of  r(t)=2cost i+3sint j+10t k at t=π2

Q: Question 15 What is the radius of curvature at point (1, 2) of the curve 4x - y2 = 0. O A. 5.66…

A: given curve 4x-y2=0

Q: Question 3 (4+4pts) Let r(t) = a) Find parametric equations of the line tangent to the graph of r(t)…

A: Here I am attaching image so that you understand each and every step.

Q: Question 3. Find the work done by the force fie ld F = xyi+y 2j in moving a particle along the curve…

A:

Q: na on y =a sec 4 7. Find the radius of curvature at x =

A:

Q: Let B:(-1,1) R be a unit speed curve with curvature such that x(0) 1. Assume that the normal…

A: Answer is mentioned below

Q: 7.3.1 Let y be a regular, but not necessarily unit-speed, cur ve on a sur- face. Prove that (with…

A: Since γ is regular but not necessarily unit-speed curve . Let us consider βs to be a unit-speed…

Q: Find the curvature of r(t) = (2 sin 1, cos 31, t) at t = 4 and t = 5 (Figure ). 3. FIGURE The curve…

A: We will use concept of vector functions to solve it. A vector-valued function, also referred to as a…

Q: 3. Let a = a(s) a regular unit-speed curve and p(s, v) = a(s) + vT(s), where T(s) = a'(s) %3D Find K…

A:

Q: Question 7 2 pts Find the curvature k of the x2 curve C : :1 at 9 | 16 + the point (4, 0) 9. 3 3 16…

A:

Q: Find the curvature k(t) of the curve r(t) = (-1sint) i+(-1sint)j+(-4 cos t) k %3D

A: Given : rt=-sinti+-sintj+-4costk To find : curvature κt Curvature is given by  κt=r't×r"tr't3…

Q: Consider the curve ´9 F(t) := 27 cos(t), 27 cos sin(t) 10 t, 27sin 10 sin(t) + 162 cos 10 0<t<T. -…

A: Given that, r(t)=27cost,27cos9π10sint-162sin9π10t,27sin9π10sint+162cos9π10t Take the derivative for…

Q: 12.3 24 determine the curvature and the radius of curvature of the given curves at the specified…

A:

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 10 cos(t)i + 10 sin(t)j +…

A: The solution is given as

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 11 cos(t)i + 10 sin(t)j +…

A:

Q: Find the curvature and the radius of curvature at the stated point r(t) = 11 cos(t)i + 10 sin(t)j +…

A:

Q: Find and completely simplify the formula for the curvature of r(t)=sin(3t)i+cos(3t)j +4tk

A:

Q: Question Seven a) Show that: dx = sin" +c b) If x-a cost+ In an), y=a sint , show that = tan x. dx…

A: radius o curvature  is given by  R=y'2+132y''

Q: Question 10 Find the radius of curvature of y=x³ at x=1 7/ 10 A) 3 5/ 10 B 17/ 10 (C) 13 15/10 (D 13…

A:

Q: QUESTION 7 The tangent plane to the graph of the surface z=In(x2+y2) at the point (1,0,0) contains…

A: To find the value of t

Q: A curve C is given by the polar equation r = f(θ). Show that the curvature K at the point (r, θ) is

A: A curve C is given by the polar equation r=fθ. We have to show that the curvature K at the point r,θ…

Q: Question 8. [. t = 1. 'Let r(t) = 5i+ t²j-²k. Compute the curvature k(t) at the point where (1,0,0)…

A:

Q: Determine the curvature of the graph of 7(t) = (2 cos t) î + (3 sin t) ĵ at the COS point (0, 3)…

A: Follow the procedure given below.

Q: 2) The(Beltrami) pseudo sphere is given by the chart x(u,v) = (Coslu) Sin(vl. Sin(ul Sin(ul. Cos(v)…

A: Gaussian curvature (K) = eg-f^2 / EG - F^2

Q: 10. Find the curvature K of the given curve. r(1) = ti +2sin(t)j+2cos (1)k

A: Curvature κ of the given curve r→(t) is T→'(t)r→'(t) where T→(t) = r→'(t)r→'(t).

Q: Question 13 Find the center of curvature of the curve y=Inx at (1, 0). A (4, 3) B) (3, 4) (3, -2)…

A:

Q: Question 12 Find the center of curvature of the curve y=; e ¯*) at (0, 1). A) (0, 2) B) (1, 1) c)…

A:

Q: 2. Find the curvature of f(x)= x cos²x at x = π

A: The solution is given below