Find an equation for the projection of the curve on the xz plane. (Hints: First, figure out from which point does the curve start. Do not forget that we consider only t > 0.) z = 3sin x ; X > 0. y=3 cos x z = 2sin x ; x > 0. z = 3 cos x ; x 2 0

Q: x = t + t and y = t* + 2t²

A: If the parametric equation of a curve are x=f(t) and y=g(t), then the slope of the tangent line at…

Q: Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t),y = 2…

A:

Q: A. Sketch the two curves: 1. r1 = 3 cos 0. 2. r2 = 1+ cos 0.

A: Use polar system to sketch this curve.

Q: 5. Given that r(t) = 3i + e* sin tj + e cos tk Find equations of the normal plane and osculation…

A: We have to  find equation of normal and oscillating plane of above curve.

Q: Q11:- Consider the parametric equations x(t) = 2et and y(t) = t- Find the arc length of e2t %3D the…

A:

Q: 6. Find the parametric equations of the line along which the following planes intersect. t: x +y +…

A:

Q: Q2 - A) Find the parametric equations for the line that is tangent to the given curve : r(t) = (a…

A: To find The parametric equations for the line that is tangent to the given curve

Q: III. Find the parametric equations of normal line to the surface given by f(x, y) = tan 2 V + y? at…

A:

Q: Q2/ Identify the symmetry of the curve r= sin e + cos e. Then sketch the curve in xy-plane.

A: Given: r=sin θ+cos θ The symmetry tests for polar graphs. 1. Symmetry about the x-axis: If the point…

Q: 5. Find the length of the parametric curve x = t + y = v12t +5, 1<t<2. %3D

A: We have to find the curve length.

Q: Eliminate the parameter t from the following. x = 4 sin t, y = 4 cos(t) Sketch the graph of the…

A: The given question has been solved in detail

Q: find the equation of the plane perpendicular to the curve

A: Given, We have to find the equation of the plane perpendicular to the curve: , at

Q: 9. Given the parametric equations x = et and y = te-t, vt. dy (a) Find dx (b) Find dx2 d?y (c) For…

A:

Q: A curve is given by the parametric equations x(t)=t2-4t and y(t)=t2+2t-3. The line tangent to the…

A:

Q: 5 Find the length of the curve r= e", - n<0 sa given in polar coordinates. V5 a) sinh(27) b)V5…

A: Given curve is r=e2θ and −π≤θ≤π We have to find the length of the given curve. The length of the…

Q: Find of the parametric curve x = sect, y = tant, at t = dx? Select one: -3V3 -1 3V3 3y3 1 3v3 O none

A: Here we find the double derivatives value at t=π/3

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: 2. Consider the parametric equation r(t) = (1 – t°, t(1 – t)) where –1 <t < 1. (a) Plot this curve…

A: The solution is given as follows

Q: 3. Consider the parametric equations x = 1+ cos(t), y = -2+ sin(t), 0S <2M. 3.1. Find an equation…

A:

Q: 1. Let S be the surface generated by the curve z² + y +4= 0 when it is revolved about the r-axis.…

A: To find the parametric equation for S. To find the equation of the normal line to S at 1,532,52.

Q: (a) By eliminating the parameter, sketch the trajectory over the time interval 0 ≤ t ≤1 of the…

A: Given- x=cosπt, y=sinπt To sketch- (a) The trajectory over the time interval 0 ≤ t ≤1 of the…

Q: Curves C and C2 are parametrized as follows: C, is (x(t), y(t)) = (t,0) for – 1<t<1 and C2 is (x(t),…

A: Given that curves C1 and C2 are parametrized as follows:   C1 is (x(t),y(t)) =(t,0) for -1&lt;= t…

Q: Find the exact value of x²y³z ds, where C is the curve with parametric equations x = e-t cos(5t), y…

A:

Q: A curve is defined by the parametric equations cos z dz, sin z dz, t > 1. X= y= Find the length of…

A: Use the formula for the length of curve in parametric form.

Q: The figure displays a portion of the curve e described by the parametric equations: x(t) = 3 In(t +…

A: "Since you have posted a question with multiple subparts, we will solve first three subparts for…

Q: 2) Draw a plane curve of the parametric function below, then prove algebraically that it has an…

A:

Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t 2 0. Find an equation for the projection of…

A: Equation of projection of curve on xy plane will not contain the term of z.

Q: The parametric curve x = 3 sin 2t and y = 8 cos 2t, where 12n traces the ellipse x2 y? + = 1 9. 64 O…

A:

Q: 29. Find parametric equations for the tangent line to the cur ve of intersection of the paraboloid z…

A: Given paraboloid is z=x2+y2 ellipsoid is x2+4y2+z2=9 and the point (1,-1,2) find the parametric…

Q: The astroid curve below is defined by the parametric equations x(t) = 2 cos' t, y(t) =2sin't.…

A:

Q: Suppose parametric equations for the line segment between (2, 8) and (– 2, 0) have the for s ¤(t) =…

A:

Q: Match each of the following parametric Equations with a plane curve : x(t) = 3 + 5cos(t), y(t) = 4 +…

A:

Q: 5. Find the length of the curve r = e", - n<0 < n given in polar coordinates. V5 sinh(2z) b)V5…

A: The arc length of polar curve r=fθ between θ=a and θ=b is given by the formula L=∫abr2+drdθ2dθ We…

Q: (a) Find the exact length of the curve (i) r = 1+ sin 0, (ii) r = 2(1+ sin 8), 0<0< 27, 0<0< 2n.…

A: We have to find arc length of give curve after that we have to find relationship between their…

Q: Consider the curve described parametrically by X = 3cos(t) , y = 3sin(t) , 0<t< 57/4 tch the curve,…

A: Given parametric Curve x= 3cos(t), y=3 sin(t), 0≤t≤5π4

Q: 3. The two curves r,-1-cose and razcose are intersecting at angles: A. (-5. B. (. c.).

A: Explanation of the answer is as follows

Q: Consider the following. x = sin(t), y = csc(t), 0 < t < A/2 %3D %3D (a) Eliminate the parameter to…

A:

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

A:

Q: The parametric representation of a curve is given as 3 3 r(t) = (V i+ + k. 12 12 (a) Eliminate the…

A: We are given that r(t)=32ti+t312+1tj-312t3k. From this, we get x=32t, y=t312+1t, and z=312t3. From…

Q: Consider the following. x = tan?(0), y = sec(@), -x/2 < 0 < x/2 %3D (a) Eliminate the parameter to…

A:

Q: 1. The line parametrized by x 7, y = 5t, z = 6+t is parallel to the x-axis. 2. The parametric curve…

A: (1)

Q: 6. The curve C: 3*-1 + xy - y? +5 = 0. show that at points (1,3) can be writien in the form -In(ue)…

A: Solve the following

Q: The curve C have the parametric equation: x(t) = t² + 1 and y(t) = t³ – 1 a) Make a sketch of curve…

A: In the Cartesian coordinate system, the parametric equations use a third variable(usually "t") to…

Q: 4. Consider the circular helix given by 7(t) = (3 cos t, 3 sin t,4t). Give an equation for the…

A:

Q: 1 If the parametric equatioms are: x= sin-t and y= cos,t, 1 %3D - nstSn 2 then the Cartesian…

A: Given x=sint2, y=cost2, -π⩽t⩽π

Q: A curve in the plane is defined parametrically by the equations written below. An equation of the…

A:

Q: (i) Find a Cartesian equation of the curve C. Hint: square the equation for y and replace the…

A:

Q: Find 2 for the parametric curve c(t) = (3r³, 3r² – 3) at the point t = 4. (Use symbolic notation and…

A: Consider the parametric curve  ct=3t3,3t2−3 To find : dydxt=4