Give a parametric description for a cylinder with radius a andheight h, including the intervals for the parameters.

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

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Q: Which of the following is the surface area of the solid body created by rotating the given…

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Q: Let a = a(t) be a parametric curve. The value to in which the curve has a velocity vector equal to…

A: Consider the given information.

Q: Give a parametric description for a cone with radius a and heighth, including the intervals for the…

A: We can parameterise the same as following: Assume s & t as two parameters radius = a and height…

Q: find the areas of surfaces generated by revolving the curves about the given axes

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Q: Find the arc-length of the segment of the curve parametric

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Q: Show that the cylindrical equationr 2(1 − 2 sin2 θ ) + z 2= 1is a hyperboloid of one sheet.

A: The cylindrical co-ordinates is converted into rectangular co-ordinate as x=rcosθ         ⋯⋯1y=rsinθ…

Q: Find an arc length parametrization of r(t) = (et sin t,et cost,et)

A: Given that, rt=etsint, etcost, et       ...(1)

Q: osen y

A: Is it sen y =x

Q: Which lines or line segments or rays must be drawn or con- structed in a triangle to locate its a)…

A: (a) The orthocentre is the point where all the three altitudes of the triangle cut or intersect each…

Q: and the plane - 3 X + Z Intersect along a line. Find Parametnic desenetion of this la

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Q: . Sketch the curve parametrized by r(t) = (ltl + t, ltl - t)

A: The given curve is rt=t+t, t-t. Sketch the graph of the above curve as shown below.

Q: Is the below statement True or False? The parametrization for a given curve is unique.

A: No. Parametrization of a curve is not unique. For example y = x2 can be written as (t,t2) or…

Q: Sketch the set (described in cylindrical coordinates). r = 4

A: GIVEN r=4 we need to sketch the cylindrical coordinates

Q: Express the plane  z = x  in cylindrical and spherical coordinates.

A: it is merely z-x=0.

Q: Evaluate ∫W z dV, where W is the first-octant portion of the solid sphere of radius 2 centered at…

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Q: Use the parametric equations of an ellipse x = acos(theta), y = bsin(theta) on the interval[0,2pi]…

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Q: Find a parametrization for the following curve. a.) The circle centered at (2,1) of radius 3.

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Q: )2. Find the paramehic from the cuve check whether the cure is a repulor cuve. Alo reparzmetije the…

A: We have to find the parametric form of the curve

Q: Surface at 0 = 30° and r = 10 is a.. Cylinder Cone Circle Plane

A: Solve

Q: Use cylindrical coordinates to evaluate Vio-ri-p2xy dzdydx

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Sketch the set (described in cylindrical coordinates). θ = π/3

A: Given: θ=π3

Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: 2r find the moment with respect to the wavic of the area hounded by the parabola v - Av-172 and v

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Q: Find a parametrization of the circle of radius 6 in the XY-plane, centered at the origin, oriented…

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Q: Find the length of the parametric y = 2 , - V3sts V3. curve x = 1+

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Q: 2. By changing to cylindrical coordinate, evaluate So 1-x²1542x² dzdydx

A: Introduction: Sometimes, a triple integral given in the rectangular coordinate system is very…

Q: . Find a parametrization for the circle (x – 2)² + y² = 1 starting at (1, 0) and moving clockwise…

A: Consider the equation of circle

Q: where B is the ball with center at the origin and radius 1

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Q: Write a formula for the curvature of a plane curve with equation y= f(x)

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Q: Sketch a Saccheri quadrilateral in the spherical model of double elliptic geometry with the…

A: To sketch: A Saccheri quadrilateral in the spherical model of double elliptic geometry with the…

Q: Find the curvature of a superellipse defined by the parametric equations…

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Q: Give a parametric description for a sphere with radius a, includingthe intervals for the parameters.

A: We will use the spherical coordinates for parametrization. Where ρ= radius= a And,

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: The equation of a sphere of radius 3. centered at the origin in cylindrical coordinates is + = 9.…

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Q: Find the length of the arc of the curve having the parametric equations x = from t = 0 to t = 1. t…

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Q: The area of the rotational surface resulting from rotating x² + y2 = a² about the x axis is? the arc…

A: Given : x2 + y2 = a2

Q: .Estimate vu in cylindrical form, in the orthogonal curvilinear coordinates

A: Given: We consider elliptic in cylindrical form .

Q: Sketch the reglon enclosed by the given curves. Dedde whether to iIntegrate with respect to or y.…

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Q: Find a parametrization for the curve described below. the line segment with endpoints (4,1) and…

A: The line segments between  (xo , yo)  and  ( x1, y1)  can be expressed as:x(t) = (1 − t)xo + tx1…

Q: Find a plane curve a(s) endowed with a unit-speed prametrization by SE (-0, 0) such that its signed…

A: The curvature of the curve αs is given by: αs=∫s0scos(θ(u))du, ∫s0ssin(θ(u))du-----(1) in which…

Q: Show that the geodesic on the surface of a right circular cylinder is a segment of a helix

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Q: Sketch the cardioid curve r = 1 + cos θ.

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Q: What is the solid body surface area formed by rotating the given parametric curve around the y-axis?

A: Given x=costy=sint+t0≤t≤π2

Q: Flnd the parametric equation of the line of ntersection of the planes and

A: First find normal vector then take cross product and use formula

Q: What is a parametrization of a curve in the xy-plane? Does a function y = ƒ(x) always have a…

A: Parametrization of a curve in the xy-plane:Parametrization of a curve consists of both equation and…

Q: Determine the radius of the curvature of the plane curve given by y In sec x at the || point (0,0).

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Q: Determine the area bounded by the conic sections y = x² – 6² and y = 6² – 2². O 576 O 183 O 281 O…

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Q: ) Evaluate x²dzdydx by switching to cylindrical coordinates.

A: To solve this problem we use her Cylindrical Coordinate .  x=r cos(theta)  y= r sin(theta) z=z

Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.