Describe the motion of a particle with position ( x, y) as t varies in the given interval 0 stS2n. x = 10 + 4 sint, y = 8 cost OA. (x – 10)2 y? Moves once anticlockwise along the ellipse 100 = 1 starting and ending at (4,8). 64 OB. Moves once clockwise along the circle (* - 10)" + (8y) = 16 starting and ending at (0,8). OC. Moves once clockwise along the ellipse (x – 10) y 16 64 =1 starting and ending at (10,8). OD. Moves once clockwise along the ellipse (x – 10)? y? 100 64 starting and ending at (0,8). OE. Moves once anticlockwise along the ellipse (x – 10)? y? 1 100 64 starting and ending at (10,8).

Q: Find the arclength of the curve z 9 cos(9t), y = 9 sin(9t) with 0 <t< 36

A:

Q: Find the point on the curver(t) = (12 sin t)i - (12 cos t)j + 5t k at a distance 13p units along the…

A:

Q: Find the solutiTon of followina ordfnarg differentral equation -2x

A:

Q: Identify the length of the arc having parametric equations x = t3 and y = 2t2 from t = -2 to t = 0

A:

Q: cos(3t), y = 6+ sin(3t) on 0 <t <

A: Please see the explanation below

Q: Find a parametrization of the right branch (x &gt; 0) of the hyperbola(x/a)2−*(y/b)2= 1 using cosh…

A: Given that. xa2-yb2=1     ...(1) Need to evaluate parametrize form of (1).

Q: a) Find the arc length parametrization of the line x = t, y = t that has the same orientation as the…

A: a)The given line is x = t, y = t.We can write it as a vector valued function as r(t)→ =x(t) i^ +…

Q: The area of the surface generated by revolving the curve y = V9 - x,-2 s xS 2 about the x-axis is…

A:

Q: Find the gardientoff at the indicatedpoint. frx,y)=D5sin x+Cos3y ;

A: Given: f(x,y)=5sinx2+cos3yπ2,0

Q: ind a parametrization for the ray (half line) with initial point (2,3) when t=0 and (-1,0) when…

A:

Q: te the line integral c 3 == 1 from A=(2, 0) to (0, -1) Jax + 2xyay where is the arc on the ellipse

A:

Q: Find the point on the ellipse x = 2 cos t, y = sin t, 0 … t … 2pi closest to the point (3/4, 0).…

A: To Find: Point on the ellipse x=2cost, y=sint, 0≤t≤2π, closet to the point 34,0. Concept: Distance…

Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2,4) and (-…

A:

Q: Find the arclength of the curve a = 8 cos(3t), y = 8 sin(3t) with 0 < t<. 9

A:

Q: 9) Find the area of the surface generated by rotating about the y-axis y = x' between (0,0) and…

A:

Q: Find the arc length of the curvex (y² + 2)3/2 from y-0 to y=1

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Starting from the point (3, 1, –1), reparametrize the curve x(t) = (3 + t, 1 – 2t, –1 – 2t) in terms…

A: We need to reparametrize the given curve in terms of arclength. The solution is given below.

Q: cos(2t), y = 4+ sin(2t) 0 <t< on 2

A:

Q: Find the arclength of the curve y = (x² − 4)² on [2,4].

A:

Q: Find the arclength of the curve x= 4cos(6t), y= 4sin(6t) with 0 less than or equal to t less than or…

A:

Q: Find the value of Jsinydx+ (xcosy-siny)dy, where Cis any curve from (2,0) to (1,n). Ca.2 Cb1 none of…

A: Green's theorem: ∫C Pdx+Qdy =∬D ∂Q∂x-∂P∂y dA where P and Q have continuous first order partial…

Q: Starting from the point (0, 4, -2) reparametrize the curve r (t) = (0 – 2t) i + (4 – 2t) j + (-2 +…

A:

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: Consider the parametrization x(t) = e2t +1 and y(t) = e2t – 1. (a) Find the equation of the tangent…

A:

Q: 4 Find the arc length of the curve the interval 2≤+ ≤ 5 3 given parametrically by x= 3 + ² y = + ²,²…

A: To find out the arc length of the curve.

Q: The position of a particle moving in the xy-plane is given by the parametric equations x(t) =…

A:

Q: Obtain the center of gravity of the skin of the rotating object that occurs if the arc y = √9 - x2;…

A: As per the question we are given the arc : y = √(9-x2)  for  0≤x≤3 And the surface obtained by…

Q: Q2. A particle moving along the curve R(t)=(cost +1 sint)i + (sint -t cost)j,find acceleration…

A: Solution:

Q: Find the arc length of the curve y = (ex + e-x)/(2), 0 ≤ x ≤ 2.

A:

Q: Find the arclength of the curve r(t)=⟨10(2)^(1/2)t,e10t,e−10t⟩, 0≤t≤1 I am stuck on the…

A: Solution

Q: V9, 0< y< 4 Find the area of the surface generated by revolving the curve x = about the у-ахis.

A: We have to find the surface area.

Q: Find the Sufface arca 0f the soid of revolution Obtained bu rotatig y=+2x With TtxE2 around メーaxis、…

A:

Q: (iii) dz< 22 + 2 where here y parametrises the straight line segment from 0 to 1- i.

A:

Q: Differentiate parametrically to find x=3t², y=6t dy dx in terms of t:

A:

Q: Find the exact arc length of the curve 2xy = y² + 4 over the interval 2 ≤ y ≤ 4. Find the area of…

A: Given: 2xy=y2+4 over 2≤y≤4 to find the arc length of the curve and given the another equation is…

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: Starting from the point (2, –1, 2), reparametrize the curve r(t) = (2 – 2t, -1+ 2t, 2 – 3t) in terms…

A:

Q: Find the arclength of the curve z = 7 cos(3t), y = 7 sin(3t) with 0 < t< 12

A:

Q: x = sin´t, y = cosʻt, 0<t<3™

A: Given x=sin2t, y=cos2t, 0≤t≤3π

Q: Let r(t) = -6t2 î+ (t² +3) ĵ + 7 k for t > 1. Reparameterize in terms of the arc-length parameter.

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: In the figure to the​ right, the equation of the solid curve is y equals StartFraction secant…

A:

Q: Find the arc length over the domain 0<t<5 7t 1 10) x= V-7t – 2, y=- + | 4 2

A:

Q: 3. Find the arc length of the curve æ = 5 + y3/2 between y = 0 and y = 2.

A:

Q: (2? – y) dæ + (y² + æ) dy] - where C is the parabolic arc Y = x2 from (1, 1) to (0, 0). Oo None of…

A:

Q: Starting from the point (-3, –1, 1) reparametrize the curve r (t) = (-3+ 3t) i+(-1+2t)j+ (1+ 3t) k…

A:

Q: ind the equation of the tangent line to right branch of the hyperbola == sec t, y= tant, 2 - sts at…

A: Topic:- application of derivatives

Q: The 35-kg boy is sliding down the smooth spiral slide such that his z coordinate decreases 2 m per…

A: Solution is in step 2

Q: Find the arclength of the curve æ = 5 cos(4t), y = 5 sin(4t) with 0 < t s 4

A: