Q6 - Tf the position vecter of aPartick P is Vt) = <3 Cost.5 Sin t.4 Costy 1- Show the Speed of the Particle is an Constant. 2. At what Points does the Purbicle P Puss through Hhe YZ- plane ?

Q: A particle moves along the x-axis with velocity v(t) = (6t 2 - t) mis.Find the particle's position…

A: Given: vt=(6t2-t)ms, s2=4m we know that for position function we have to integrate given velocity…

Q: The velocity of the body is given by: v(t) = 2t, 1≤t≤5 = 5t² + 3, 5<t≤ 14 where t is given in…

A: Given : vt =2t , 1≤t≤5       =5t2+3  ,5&lt;t≤14 Find : a. Trapezoidal Rule where n=2          : b…

Q: Find T, N and B for the curve 7(t) = (4 cos(2t), 4 sin(2t), 2t) at the point t = 0 %3D Give your…

A: given that                                          r→(t)=4cos(2t), 4sin(2t), 2t at t=0…

Q: The vertical stress increment (Aơ) due to a point load acting on the surface of linearly elastic…

A:

Q: 18. The length of the curve y = r* from r = 0 to r = 2 is | V1+2® VItz® dz B. | V1+3x2 dx A. C. D.…

A: Question 18 is solved. Solving more questions are against the policy of bartalby. In question 18 ,…

Q: find the speed at the given value of t. r(t) = (cosh t, sinh t, t), t= 0

A: r(t)=⟨cosh t, sinh t, t⟩ at t=0

Q: Q3 Point out the singularity and is ty pe of follo wing fune tions 22 () d) Sin t2 24

A: Singularity

Q: 5. T'he surface of a pice of bubble wrap is given by the function f(r, y) = cos(r) sin(3). In which…

A: Given: The surface of the bubble wrap:fx,y = cosxsiny--------------------------------To find: The…

Q: Find the length of the curve. r(t) = cos(6t) i + sin(6t)j + 6In(cos(t)) k, 0 <t< n/4

A:

Q: Q6 Evaluate Sl(2xy* – y? cos x)dx + (1 – 2y sin x + 3x²y²)dy] where C is the arc of the parabola 2x…

A:

Q: S(t)=t°-3tー+5 find accelercstuon of the purticle at t=1.

A: Here s(t)=t6-3t2+5 We have to find the acceleration at t=1.

Q: Assuming that C is the curve with parametrization r(t) = ti + t²j+t°k, O0sts1, find numerical value…

A: First I have written a short note about line integral , along a curve in parameterization form, just…

Q: is maving with Ithe given the particle. data. Find the positionof a/t) =3 cost-2 sint is(0)o and…

A: Given: a(t) = 3cost -2sint , s(0) =0, v(0)=4 We know that a(t) = ddtv(t) ⇒vt = ∫a(t) dt

Q: 5. Do the following tasks using Mathematica. i) Find the length L of the curve y = 1 In a, 1<¤< 2…

A:

Q: Determine the length of the curve 7(t) = (3t, sin t, cos t) on the interval 0 < t < 2n. %3D А. L =…

A: As we know that, The expression for the length of the vector-valued curve is: L=∫abx't2+y't2+z't2dt…

Q: 2 zy ら- Let Los 63 Z), find the Wニ Value of d at the point (!, Ln2, o) on the curve x = Cost , y =…

A: To find.  The value of dw/dt at the point(1, ln2, 0) on the given curves.

Q: particle moves along the curver(t)=(t2−1)i+(2t3+3)j+(3t−4)k.Find the speed of the particle at t=1.

A: Position vector of the particle is Velocity vector of the particle at any time t is At t=1,…

Q: Consider the following. x = sin(2t), y = -cos(2t), z = 8t; (0, 1, 47) Find the equation of the…

A:

Q: The curves C,:x=t, y=t, z=t, t20 and C,: x= sint, y 1+cost, z=1, 120 have intersection at the point…

A:

Q: Find the length of the curve 7 (t) = (3 cos(4t), 3 sin(4t), 4t) for –5 <t< 8 Give your answer to two…

A:

Q: Q.18 A curve 'C'is defined as x= a cos³0, y = a sin°0 in [O, t/2]. What will be the point P on curve…

A: Explanation of the answer is as follows

Q: Q:Find the that is POT HOh of the curve area of the suoface generated by revolving the Y=x² between…

A: Using area formula we have

Q: Find the length of the curve. r(t) : cos(8t) i + sin(8t)j + 8 In(cos(t)) k, 0 stS T/4

A: Solution is given as below:

Q: Find the slo pe of the Para bola y=X at the Point PC2,4).write an equation for the tangent to the…

A:

Q: For which values of a E R the tangent plane to the graph of f(r, y) = 1+ sin(ar + y?) at the point…

A: Given a curve  f(x,y)=1+sinαx+y2 We have to give value of Alpha such that the tangent plane to given…

Q: 3 For which values of a € R the tangent plane to the graph of f(x, y) = 1 + sin(ax + y²) at the…

A: The given graph is                                f(x,y)=1+sin(αx+y2)

Q: C: 1- Find for the function: X²+ Siny =X.y² 2- Find the mnd dy por the fur etion - for the fum…

A: 1) Given: x2+siny=xy2 On differentiating the given function on both sides with respect to x,…

Q: C. A simply supported beam has the bending moment, M given by M = 15x – 29 (x - 0.5)? %3D 4 where x…

A: We can find the value of 'x' for M=0 as below

Q: O with n=4, 20timaste S°(ax-)dx using the Trapezeidal -3 Approxi a i mation and Simpsen's Ru le .…

A: Answer

Q: r(t) = (cost, sin t,In (cos t)) from t = 0 to t= %3D (5) Find the length of the curve

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Q: der the following. x = t - 2 sin(t), y = 1 - 2 cos(t), 0≤t≤ 7″ an integral expression that…

A: We are asked to find the length of the curve

Q: dA When the radius r of a sphere increases with time t, the change in area is dt O a. dr 4a r dt O…

A: Surface Area of sphere = 4πr2  r= radius of sphere

Q: .4. The approximate value of y=V4+sin.x at x=0.12, obtained from the tangent to the graph at x = 0,…

A: 14)  y=4+sin xy=4+sin x12 Differentiate with respect to 'x' As,  dxndx=n xn-1d sinxdx=cos x…

Q: hIf the velocity of a particle at a time t iS 9lven by tle initlal value problem Find the partiche…

A:

Q: Find the length of the curve F(t) = (4 cos(3t), 4sin(3t), 3t) for -8<t< 10 Give your answer to two…

A:

Q: A particle is moving with the given data. Find theposition of the particle.   v(t)  =Sint -Cost…

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Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< t/4

A:

Q: Q6 Evaluate S[(2xy – y? cos x)dx + (1– 2y sin x + 3x?y?)dy] where C is the arc of the parabola 2x =…

A:

Q: A particle is moving along the x-axis with a velocity of v(t) = 8 cos (). The particle is at %3D x =…

A: Given : v(t)= 8*cos(t/2)  At t=0, partical is at x=2

Q: Q2: Gruph the nector fundion Tt)= Find the equat in for the tanget f functron fexy) = SinCxy) at…

A: a) Given,  rt=cost, sint, t Here  xt=cost,yt=sint,zt=t

Q: mos t Y Using accurate centered li ff. fommula approximate error in and then słate the approxi mahin…

A: Please check step 2 for the solution.

Q: Q3: A cylindrical tank of radius R = 1.5 m and height H = 3 m initially filled with water. At the…

A:

Q: Compute the length of the curve r(t) = 8t cos(t), 8t sin(t), 2t over 0 st < 2n. Hint: V? + a2 dt = +…

A: Given

Q: B) The position of a particle in the plane at time t is 1 i+ V1 + t2* '1+ t² r(t) : Find the…

A:

Q: Q6 Evaluate Sel(2xy' - y? cos x)dx + (1 – 2y sin x + 3x?y)dy] where Cis the arc of the parabola [12]…

A: Evaluate ∫c[(2xy3-y2cosx)dx-(1-2ysinx+3x2y2)dy] where c is the arc of parabola 2x=py2from (0,0)to…

Q: ds The velocity of a particle moving back and forth on a line is v = = 6 sin(2t) m/sec for dt all t.…

A:

Q: The position of a baseball (in ft) is represented by r(t) = 45 2ti + (2 + 45/2t - 16t2)j. Find the…

A:

Q: 2. The velocity v of a falling parachutist is given by v = m (1 – e-c/m)t) where g = 9.81 m/s?. For…

A: The velocity of a falling parachutist is given by v=gmc1-e-cmt Given that g=9.81, c=15, v=36, t=10.…

Q: Find the length L of the curve R(t) = 4 cos(5t) i – 4sin(5t) j + tk over the interval [3, 6]. L =…

A: Given:

Q: *:VP+o* dt =+ o? + n(* + vP + o*). (Round your answer to one decima Compute the length of the curve…

A: