3. Givea parametrie description fora sphere with radis, ineluding the intervats for the peremeter

Q: 1+ 1 А 3. Based on the trapezoid shown in the standard (x, y) coordinate plane above, what is the…

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

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Q: 29. The shaded band shown here is cut from a sphere of radius R by parallel planes A units apart.…

A: To show: That the surface area of the band is 2πRh. Given: The shaded band is cut from a surface pf…

Q: If a bug walks on the sphere x + y? + z² + 2x – 4y – 2z – 30 = 0 how close and how far can it get…

A: Sphere

Q: Consider the unit sphere x² + y² + z² = 1. Find the average distance from its north pole to a point…

A: Given: x2+y2+z2=1 It is equation of sphere of radius r=1 unit. We have to find the average distance…

Q: on? 26. Use spherical coordinates to evaluate: on height Vx? + y² + z² dz 1+[x² + y² + z²1} Jo psing…

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Q: 2. Give illustrations for the thrce - line and four - line geometries.

A: 2.   Axioms for the Three line Geometry:  •There exist exactly 3 lines in this geometry.  •Two…

Q: A beam whose centre of gravity divides it into two portions, a and b. is placed inside a smooth…

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Q: Chapter 12, Section 12.5, Question 013 Find the curvature and the radius of curvature at the stated…

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Q: Chapter 12, Section 12.5, Question 013 Find the curvature and the radius of curvature at the stated…

A: The given vector-valued function is rt=6cost i+6sint j+7t k at t=π2 to find the curvature and the…

Q: 4.10 Repeat Prob. 4.9 but for a copper sphere with radius = 0.15 ± 0.01 m, e = 0.90 ± 0.05, and T =…

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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

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Q: Eliminate the parameteu, wite your answer in standand for m: A hy pe bola : x = h+ a sec t, y=R+b…

A: To eliminate the parameter and to write the answer in standard form:A hyperbola: x=h+a sec t, y=k+b…

Q: Give for the line through the point a vectur parametri? eauatiun Cl-2) that is -4,41345pendicular'to…

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Q: and the plane - 3 X + Z Intersect along a line. Find Parametnic desenetion of this la

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Q: A beam whose centre of gravity divides it into two portions, a and b. is placed inside a smooth…

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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: Find the total length of the astroid defined by the parametric equations x(t) = acos't and y(t) =…

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Q: 2) The (Beltrami) pseudo sphere is given by the chart xlu,v) = (cosculsinlv), sincu) sincv) , cos(vl…

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Q: For a sphere parameterized using the spherical coordinates and , describe in words the part of the…

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Q: Find the curvature and the radius of curvature at the stated point. ㅠ r(t)=10cos(t)i+11sin(t)j+9tk;…

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Q: . A beam whose centre of gravity divides it into two portions, a and b. is placed inside a smooth…

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Q: A beam whose centre of gravity divides it into two portions, a and b, is placed insıde a smooth…

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Q: dø What is the curvature of the circle, x2 + y2 = 36 ? hint: k = ds change in angle of circle change…

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Q: Consider a unit sphere centred at the origin. Find an arc length parametrised geodesic connecting…

A: The objective is to compute the arc length parametrised geodesic connecting the points 0,0,1 and…

Q: I. Give one other possible application that are not stated in the material of the following…

A: Solution :-

Q: (a) exactly one point P in R³. Do NOT put one sphere inside the other one. Draw a picture of two…

A: a) The objective is to draw two spheres of different sizes tangent to each other at exactly one…

Q: consider surtace S with paramtrization. Gcu,v) = cu,V,uv) , tuts of s also compute the surface areu

A: Given that  G(u,v) = <u,v,uv> , u2+v2≤1 Surface area is given by, S=∫∫D|Gu×Gv|du dv To find Gu…

Q: A curve has a vector equation r = ti+ 4 sin(t)j + 4 cos(t)k. Find the curvature, K.

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Q: A plane travels from point A on a bearing 150° to a point B 10 km from A as illustrated above. How…

A: We are given the following information. We need to find AC.

Q: a. The perpendicular bisector of JK is the perpendicular to f that passes through P. b. Draw an arc…

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Q: Use triple iutegral in reitanqular coordinates +to tindd te nass of. sphere with den a ensing S こス…

A: mass = density * volumem        = massδ         = densityV        =…

Q: A marble of radius r, o<re4, 1s dropped into a cohtainer having the shape of a circular Cylinder.…

A: A marble of radius r , where 0&lt;r&lt;4is dropped into a container having the shape of a circular…

Q: dø What is the curvature of the circle, x2 + y² = 36 ? hint: k %3D %3D ds change in angle of circle…

A: Given that : Equation of Circle x2 + y2 = 36   To find :- Curvature. Curvature :- The arc rate of…

Q: Evaluate fc (2 +x 2y ) ds, where is the upper half of the unit circle x2 y2 =1

A: We have to evaluate ∮C2+x2ydS   where C is the upper half of the unit circle x2+y2=1

Q: A beam whose centre of gravity divides it into two portions, a and b, is placed inside a smooth…

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Q: 8. PT is tangent to circle O at P If mNP = 90°, and mMXP : 186°, find %3D %3D X/ d. mZ4 e. mZ5 f.…

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Q: 12.The temperature at each boint of a metel plate i given by the functien %3D :) In What disection…

A: The temperature function is given by Tx,y=excosy+eycosx the Temperature rise will be given by…

Q: H.w/ Findthe forthes tand closest paints.ah the sphere x+y+2'=36 from p(l2,2).

A: I used Lagrange Multiplier to solve this.

Q: Eliminate the Parametor t townite the farametric sauation as a Cartosian cuetion =4 Sin Lt) 3D

A: From both equations, we find sin(t) and cos(t)

Q: Consider the paraboloid paremterized by o(u, v) = (u, v, u² + v²). 1. Find the second fundamental…

A: Consider the given equation of circle, γt=sint,cost,1 The formula for normal curvature is defined…

Q: 5-) blas) what is squore 6 corner ABCA with coordina tes')

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Q: 4) Given the Torus x(e,0)=((R+rCose) Coso, (R+rCose) Sind.rSine), O<O< 2 , OSOA2, r<R. a) Find the…

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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: Consider the curve y(2) = sin z. Which one of the following statements is true? O The curvature at =…

A: Here to find curvature of curve, y(x)=sin(x) Curvature of curve is given as,…

Q: Consider the non-right triangle below. у ст ZCAB T cm Suppose that m/CAB = of this triangle? 61°,…

A: Given,

Q: 1) Calculate the curvature of the position vector 7(t) = sin tax + %3D 2cos tay + V3 sin tāz is a…

A: In this question we have to find curvature and radius of curvature.

Q: Consider the plane curve parametrized by F(1) -i+ (In(com(1)J, Find curvature s(4).

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Q: a) [12 pts] C1 is the path along the arc of the unit circle from z = 1 to z = -i. Provide a sketch…

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