Find the surface area of helioid equation (spiral ramp vith vector r Cu,v) = LucosV, usinv, v). %3D

Q: Find the area of the surface generated by revolving the curve = V¤ + 3, 4 < y <7

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Q: Describe the surfaces r = R in cylindrical coordinates and ρ = R in spherical coordinates.

A: Given cylindrical and spherical coordinates.

Q: Find the point where the helix r(t) = (cos(t), sin(t), t) intersects the plane z = (х, у, 2) %3D

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Q: At how many point(s) does the helix with vector equation r(t) : (cos t, sin t, t) intersect the…

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Q: Find the surface area of the torus obtained by rotating the circlex 2 + (y - b )2 = r 2 about the…

A: Given the equation of the circle  x2+(y-b)2=r2. We need to find the surface area of the torus…

Q: Find the area of surface that is generated by revolving the portion of the curve 9 – y² , – 2 < y< 2…

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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: Explain Cylinder Surface?

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Q: A curve is given in polar coordinate as r=R(f). What is its curvature? Find it in terms of R,R' and…

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Q: Describe the surface with cylindrical equation r=6

A: We have to describe the surface with cylindrical equation r=6.

Q: The vector equation r(u,v)=ucosvi+usinvj+vk, 0≤v≤4π, 0≤u≤1, describes a helicoid (spiral ramp). What…

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Q: Change from rectangular to cylindrical coordinates. (a) (3, 3, 4) (r, 0, z) =

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase.…

A: (a)From given information, x(t)=16cos5(2π)=16cos(10πt) y(t)=16sin5(2π)=16sin(10πt) z(t)=50t…

Q: In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase.…

A: Given information: The radius of the spiral is 29 feet and height is 60 feet that makes 6…

Q: The centroid of an obtuse triangle is outside the triangle. true or false?

A: solution ======== The centroid is the concurrent point of the three medians in a triangle. It is the…

Q: Determine the area of the surface generated by rotating around the "y" axis, the curve described by:

A: Here, the given parametric curve is: x=t33, y=t+1; 1≤t≤2⇒x'(t)=t2, y'(1)=1 Now, the surface area…

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

A: Solve

Q: Surface at θ = 40⁰ and r = 20 is a     plane    cirlce   cone

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Q: Find the area of the surface generated by revolving the curve

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Q: What cross-section cannot be formed by intersecting a plane with a right cylinder? Campbol OM…

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Q: Point W is the centroid of triangle TRV. VX = 204 and RW = 104. The length of RY = ____.

A: We have the given triangle as It is given that Point W is the centroid of triangle TRV. VX = 204 RW…

Q: consider surtace S with paramtrization. Gcu,v) = cu,V,uv) , tuts of s also compute the surface areu

A: Given that  G(u,v) = &lt;u,v,uv&gt; , u2+v2≤1 Surface area is given by, S=∫∫D|Gu×Gv|du dv To find Gu…

Q: A curve has a vector equation r = ti+ 4 sin(t)j + 4 cos(t)k. Find the curvature, K.

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Q: Identify the surface whose equation in spherical coordinates is given by P=6 cos o O Paraboloid O…

A: We will identify the given surface.

Q: Let S be the surface parametrized by R (u, v) =< u, uv, uv

A: It is given that, the parametrized surface is R(u,v)=u, uv, uv2, 0≤u≤2, 0≤v≤3.  We have to calculate…

Q: Find the coordinates of the center of gravity of the homogeneous wire showen below. The portion on…

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Q: Find the area of the helicoid (or spiral ramp) with vector equation r(u, v) = ucos(v) i + usin(v) j…

A: The area of the Helicoid with vector equation r(u,v)=(ucosv)i^+usinvj^+vk^ in limits a≤u≤b  and…

Q: The vector equation r (u, v) = u cos vi + u sin vj + vk, 0 < v < 5n, 0 < u < 1, describes a helicoid…

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Q: Find the orthogonal trojectories of y(sx +c) = 1.

A: Given query is to find the orthogonal trajectories to y (3x+c) = 1.

Q: Use triple iutegral in reitanqular coordinates +to tindd te nass of. sphere with den a ensing S こス…

A: mass = density * volumem        = massδ         = densityV        =…

Q: Use the polar coordinates to find the volume of a sphere of radius 3.

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Q: Surface at 0 = 40° and r = 20 is a.. Cylinder Plane Circle Cone

A: Given:  r=20, θ=40°

Q: Identify the surface whose equation in." spherical coordinates is given by p = 8 cos ø Cone O…

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Q: Describe the surface whose equation in cylindrical coordinatesis z= r

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Q: Calculate the area of the surface of rotation created by rotating the curved segment about the…

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Q: Use Spherical coordinates to evaluate Cx*+ ya+22)² dV where Bis the B. ball with anter at the ongin…

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Q: he normal vector to the tangent plane for the surface point (1, 2, -1) is: Select one: None of them…

A: topic:- application of derivatives

Q: In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase.…

A: Formula: The parametric equation for the helical path having radius r feet and height h feet that…

Q: Find the area of surface that is generated by revolving the portion of the curve x = /9 – y? , -2 <…

A: We will find out the surface area of revolution.

Q: Find the area of the surface generated by revolving the curve about each given axis. x = 2t, y = 3t,…

A: TO FIND THE AREA GENERATED BY THE REVOLVING BELOW SURFACES x =2t y =3t ,   0≤t≤9 FORMULAS USED (a)…

Q: A conical surface is defined as 0 = 30°,0 < y< 2n,0<r< 2, the lateral surface area is what?

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Q: - In cortesien coordina te system is dx dy da. Infer the differentia polar coordinate system ?

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Q: Use  inertia  to  classify  the  quadric surface  given by equation. x2 + y2 + 2z2 − 2xy − 4xz − 4yz…

A: We have to use  inertia  to  classify  the  quadratic surface  given by equation. x2 + y2 + 2z2 −…

Q: Find parametrization of the horizontal circle of radius 4 with center (5, -2, 6). r(t) = %3D

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Q: Enter the equation of the clrcle with the glven center and radlus. Center: (6, 0); radius: /7 The…

A: The equation of the circle with center (h,k) and radius r is   (x-h)²+(y-k)²=r²