Deduce from the orbit equation (1 + e)r 1 + e cos 0 that a planet is closest to its sun when 0 = 0 and show that r = n at that time.

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

A:

Q: In  the given  equation as  follows , find the arc length of the curve on the given interval :-…

A: Consider the given parametric equations x=t , y=t510+16t3  And the given interval is, 1≤t≤2 Now,…

Q: The arc length of the curve r= cos 30 with 0<0<n is

A:

Q: Suppose an object moves in an elliptical orbit parametrized byx = 4 cos t and y = 7 sin t, where t ≥…

A:

Q: Find the equation of the plane perpendicular to the curve r(t) = (sin(2t), t, cos(2t)) at the point…

A:

Q: A curve is defined by the parametric equations a(t) = 2 cos(5t) and y(t) = -7 sin(-10t). Find .

A:

Q: 5. Eliminate the parameter to find a Cartesian equation of the following curves. et (a) x = vt+1, y…

A: Eliminate parameter t.

Q: 3. Deduce from the orbit equation (1 + e)ro 1 + e cos 0 that a planet is closest to its sun when 0 =…

A:

Q: Find the speed at t = π/4 of a particle whose position at time tseconds is c(t) = (sin 4t, cos 3t)

A:

Q: A particle is moving in space with position function R(t) = (cos(4t), sin(4t),5 - 3t) %3D Find the…

A:

Q: The curve graphed below has the parametrization C = {(v 4 %3|

A: Introduction: A parametric equation is one in which the dependent variables are defined as…

Q: A slime mold grows in a spiral pattern with polar radius r=θ3r=θ3. If the mold grows by continuing…

A:

Q: 35. Calculate || 9x*+4y* dx dy, where D is the interior of the ellipse (G) + (4)' =

A: Given:

Q: Find the equation of the tangent line to right branch of the hyperbola π π ㅠ x = sect, y = tant, st≤…

A:

Q: Show that the parabolas $r=c /(1+\cos \theta)$ and $r=d /(1-\cos \theta)$ intersect at right angles.

A:

Q: Sketch the plane curve r(t) = a cos3 ti + a sin3 tj and find its length over the given interval [0,…

A: The curve is r(t)=a cos3ti + a sin3tj   Interval is 0, 2π

Q: 11. dy/dx = -x/y, y(0) = 4 %3D

A: Given: Let's sketch the isoclines and their direction markers, then sketch a few solution curves,…

Q: Consider a particle traveling clockwise on the elliptical path                              x2/ 100…

A: Given: x2100+y225=1  or  x2102+y252=1 Leaving point of the particle from the orbit (−8,3)

Q: 4. Find the slope of the curve r = cos 20 at the origin 5. A particle moves along a path whose…

A:

Q: 13. dy/dx = 2x, У (0) 3D —1

A: Solution: dy/dx =2x  ,    y(0)=-1

Q: 3. Draw a hyperbolic orbit with of a =1.0, eccentricity of at (x, y) = (-1,0). the semi major oxis…

A: Solution:   Equation of hyperbola is given by (x-h)^2/a^2 - (y-k)^2/b^2 = 1 focii is at (h ± ae, k)…

Q: Parametrize the following curve: y = tan−1(x2 + 1)

A:

Q: Express the equation z = rroot2 cos2tita, which is given in cylindrical coordinates, in…

A:

Q: Find the length of the following two-dimensional curve. π 3 r(t) = (3 cos ³t, 3 sin ³t), for Osts- 4

A:

Q: Draw the isoclines with their direction markers and sketch several solution curves, including the…

A:

Q: Find the length of the arc of the curve having the parametric equations x = t³ and y = 2t2 from t =…

A:

Q: Deduce from the orbit equation r=(1 + e)r0 /(1 + e cos u) that a planet is closest to its sun when u…

A:

Q: (c) (d) Determine the exact length of the curve of the conic section from 0 = 0 to 0 = π/6. Explain…

A:

Q: Find the equation of the osculating plane of the helix: r(t) = sin(3t), y(t) = 2t, 2(t) = cos(3t)…

A: Given the equation of the helix:     x(t)=sin(3t), y(t)=2t, z(t)=cos(3t) So, rt=sin3t,2t,cos3t. Find…

Q: Suppose an object moves in an elliptical orbit parametrized by x = 4 cos t and y = 5 sin t, where t…

A:

Q: Find the length of the curve whose parametric equations are x = 3t^2 and 3t^3, from t = 0 andt = y =…

A:

Q: Find the length of the arc of the curve having the parametric equations x = t³3 and y = from t = 0…

A:

Q: Find the arc length of the curve on the given interval. Parametric Equations x = 5t + 5, y = 7- 2t…

A: The parametric equations of the given curves are   x=5t+5,  y=7-2t and the given interval is -1≤t≤3…

Q: ) Suppose that the parametric equations x = 1, y = r', 12 0, model the position of a moving object…

A: Given

Q: The x and y coordinates of particle P, executing simple harmonic motion, are [x = A cos wt, y = A…

A: Given statement is "The x and y coordinates of particle P executing simple harmonic motion, are…

Q: The arc length of the curve r = cos 30 with 0<0<n is

A:

Q: A curve has an equation of 9x2 + 25y2 = 225. Compute the second eccentricity of the curve. %3D 1.33…

A:

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

A:

Q: Find the curva tuie For He Curve 2+); +(6 cos 2t) + 5¢ K %3D

A:

Q: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

A: Give a parametrization of the left half portion of the polar curve described by the equation r = 3.

Q: Find the isogonal trajectory of the family of curves y + 2xy – x² = k where tan a = 1

A:

Q: Find the length of the parametric curve x = sin-1t,y = In V1– t² for 0 <t<-

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: Q3/|A:- Verify that dV = p² sin o dp do dp when using spherical coordinates. %3D

A:

Q: The area of the rotational surface resulting from rotating the arc of the curve x=cos^3 t, y=sin^3 t…

A:

Q: Find the orthogonal trajectory of y=c cos x.

A:

Q: Consider the plane curve given by the parametric equations x = t² + 22t - 23 y = t² + 22t - 5 What…

A: