Q: parametric
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Q: EXAMPLE 9 Find the tangent plane to the surface with parametric equations x = u2, y = v2, z = u + 2v…
A: Given parametric equation x=u2 , y=v2 , z=u+2v
Q: Find two different sets of parametric equations for y = 2x O x(t) = t, y(t) = 2t – 7 O x(t) = 2t,…
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Q: Find a set of parametric equations for the tangent line to the curve of intersection of the surfaces…
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Q: 25) Show that the curve with parametric equations x = tcos(t) , y = tsin(t), lz = t ies on the cone…
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Q: Find a parametric curve r(t) that represents the curve of intersections of the semi ellipsoid…
A: We will find the curve r(t) that represents the curve of intersections of two surfaces.Below find…
Q: A circular helix in xyz-space has the following parametric equations, where θ ∈ R. x(θ) = 4 cos θ…
A: Arc length in 3d We want to determine the arc length of a curve given by parametric equation ,…
Q: 2 Sketch the parametric surface x = Vi u +v ,y = u, z = v.
A: We will sketch the parametric surface x=u2+v2, y=u, z=v. Notice that x2=u2+v2⇒x2=y2+z2.
Q: Describe the set in cylindrical coordinates. y^2 + z^2 ≤ 9, x ≥ y
A: Let x=rcosθ, y=rsinθ and z=z. And the given equation is x ≥ y ⇒ cosθ ≥ sinθ
Q: The equation of the tangent plane to the parametric surface x = u, y = v², z = uv at the point where…
A: This question can be solved using the concept of finding the tangent plane when the parametric…
Q: Find a point on the ellipsoid x² + 2y2 + z2 = 19 where the tangent plane is perpendicular to the…
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Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…
A: To find a parametric equation of the line tangent to the curve of intersection of the surfaces at…
Q: Consider a spatial curve in three-dimensional space given in parametric form by x(t) = cos t, y(t)…
A: Introduction :
Q: Find the distance between the point (1, −2, 4) and the line given by the set of parametric equations…
A: The given point is M=(1, −2, 4) The direction vector of the line is =s=(2,1,2) A point on the line…
Q: What is the rectangular equivalence to the parametric equations? z (8) = 4 cos 0 + 2, y (8) = 2 sin…
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Q: I am working with cal 3. How do I find the parametric equations of the line for the intersection of…
A: The parametric equations of a line through the point (x0, y0, z0) and parallel to the direction…
Q: Determine the total distance covered from t = 1 to t = 3 from the given parametric equations: x =…
A: Let's find the total distance covered. = d
Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y? = 8,…
A: Given: The parametric equations for the line tangent to curve of intersection of the surfaces…
Q: Find a parametric equation for the line tangent to the curve of the intersection of the surfaces at…
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Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² + ¹/² = 4…
A: We need to obtain a set of parametric equations for the curve of intersections of the cylinders:…
Q: Find the surface area of the parametric surface †(u, v) = (u + sin(v), v+ sin(u), u – v) where…
A: According to the given information, it is required to find the surface area of parametric surface.
Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…
A: Here we have to find the equation of the tangent line.
Q: Find an equation of the tangent plane to the given parametric surface at the specified point. r(u,…
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Q: iminate the parameter in the parametric equations x(f) = 5t – 8 and y(t) = Vt – 5 to find a…
A: Given: The parametric equations are xt=5t-8 and yt=t-5 Given query is to find the Cartesian…
Q: Find a set of parametric equations for the curve of intersection of the cylinder (x − 1)² +: 4 the…
A: We will use trigonometric identity sin2t+cos2t=1 and parametric form of standard ellipse to find…
Q: Find the distance from the point (3, 2, 5)to the line with parametric equations x=t,y =l +t ,z = 2 +…
A: The equation of the line in matrix form: xyz = 012 +…
Q: S is the surface with parametric equations x = 3u+v, y = 3u – v, z = uv for (u, v) in the region D…
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Q: x = 3 + 2t y = 9– 3t 1<t<4 about y-axis
A: We have to find the surface area of parametric curve.
Q: Describe the set of all points P = (x, y,z) satisfying x^2 + y^2 ≤ 4 in both cylindrical and…
A: Given, x2+y2≤4
Q: Evaluate ⌠⌠(x+y)ds, where S is the cone whose parametric equations are x=ucosv, y=usinv, z=2u,…
A: Given cone whose parametric equations are x=ucosv, y=usinv, z=2u, 0≤u≤3, 0≤v≤π/2 we find the given…
Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z = x²…
A: Given :- The curve of intersection of the paraboloid z = x2 + y2 and the ellipsoid x2 + y2 + z2 =6…
Q: x =9+2t² y = 4t 0St<2 about x-axis
A: SURFACE AREA OF PARAMETRIC CURVE: Consider the parametric curve given by…
Q: 3. Consider the parametric vector equation of a cone r(u, v) = u cos vi + u sin vj + uk with 1<u < 2…
A: The volume of a cone with radius r and height h is given by V=13πr2h. Given a function…
Q: ) Consider an object moving in the plane according to the parametric equations x = 26te z – 676e , y…
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Q: Find an equation of the tangent plane to the given parametric surface at the specified point. x = u…
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Q: Consider the line perpendicular to the surface z=x^2+y^2 at the point where x=3 and y=2. Find a…
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Q: Find the surface area of the parametric surface F (и, v) — (2 сos(2и) + vcos(u), 2 sin(2u) +…
A: Here, we need to find the surface area of the parametric surface r→(u,…
Q: Find
A: We find surface area of given region.
Q: Find a parametric representation of the cone z = /3x + 3y² in terms of parameters p and 0, where (p,…
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Q: Show that the parametric equations x a cosh u cos v, y b cosh u sin v c sinh u represent a…
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Q: Calculate the area of the parametric surface given by: r(u, v) = 2 sin u cos vi + 2 sin u sin vj + 2…
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Q: Sketch the plane curve represented by the parametric equations x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π…
A: Given x = 6 cos t, y = 4 sin t, π ≤ t ≤ 2π
Q: Let P(r, y, z) be the point at which the line with parametric equations x = -t, y=3+2t, z=1-t te R,…
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Q: Of the curve lying in the plane XZ-, (x - a) ^ 2 + z ^ 2 = r ^ 2 in R ^ 3 The region created by…
A: Given that the region is being created by rotating x-a2+z2=r2 in ℝ3 around the z-axis. To find the…
Q: 2. Use parametric equations to derive the formula for the lateral surface area of a right circular…
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Q: 1. Identify the parametric surface S given by: r(u, v) = 3 cos ui+ vj + 3 sinu k where 0 <u < 2n and…
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Q: Find an equation of the tangent plane to the parametric surface + = Z= Note: Your answer should be…
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Q: Find the area of the surface obtained by rotating the curve of parametric equations: 6 x = 6t – t, y…
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Q: Which of the following sets of parametric equations is for the surface obtained by rotating the…
A: For a fixed value of z, that is surface cut by a plane z=k it is a Circle, of radius 1/(10+k^2).
Q: Sketch the plane curve represented by the parametric equations x = 5 cos t, y = 2 sin t, 0 ≤ t ≤ π…
A: x=5cost, y=2sint Now,…
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- Write parametric equations for a cycloid traced by a point P on a circle of radius a as the circle rolls along the x -axis given that P is at a maximum when x=0.Find the distance from the point (3, 2, 5)to the line with parametric equations x=t,y =l +t ,z = 2 + t.Sketch the plane curve represented by the given parametric equations x = 4 cos t + 2, y = 4cos t - 1. Then use interval notation to give relation’s domain and range.
- Derive the parametric equations of the line of intersection of the two planes: II : x – 2y + z =1 and II, : 2x – 2y – 4z = 4 - -Find parametric equations for the line through the point (0, 1, 2) that is perpendicular to the line x = 1 + t, y = 1 – t, z = 2t and intersects this line.Find the distance between the point (2, 3, 2) and the line given by the set of parametric equations x = 1- , y = 1+1, z= - 31.
- Find a parametric function for the intersection of r – 3y + 4z = 0 and a? + y² = 9.find the distance between the point (2,2,3) and the line of parametric equations x=1-2t, y=1+t, z=-tFind the parametric equations of the line tangent to the curve of intersection of the surfaces x² + y² = z and x² + y² = 4 at the point (√2, √2,4).
- The parametric equations for the line tangent to curve of intersection of the surfaces x? + y? = 8,x + y? -z = 0 at the point (2,2,8) is X-. ., y and z is known.Find the distance between point A(3, 4, 4) and the line of parametric equations x = -1-t, y = -t, z = 2, tER.Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t, and x = 2 + 2s, y = 5 + 14s, z = -2 + 5s. Submit Answer