Set up the triple integral in cylindrical coordinates for the right circular cylinder whose base is the circle r = 2sin(theta) in the xy plane and whose top lies in the plane z = 4 - y. Use the order (dz)-(r)(dr)-(d-theta)

Q: Let S be the surface of revolution of the curve C: z? + (y+ 5)² = 4. (a) Find a parametrization of…

A: Consider the given information: Let the surface is given by, z2+(y+52)=4

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: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: Find the arc length function s(t) for r, (t) = (e' sin(t), e' cos(t), e) where t 2 0. Then…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Transform (4, 7/3, ) from spherical into cylindrical form (here o is any angle).

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Q: Suppose F(x, y) = (2y, — sin(y)) and C' is the circle of radius 5 centered at the origin oriented…

A: The given vector field is F→x, y=2y, -sin y. The curve C is the circle of radius 5 centered at…

Q: A sodium ion (Na+) moves in the xy-plane with a speed of 2.90 ✕ 103 m/s. If a constant magnetic…

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Q: (a) A filament is formed into a circle of radius a, centered at the origin in the plane z = 0.…

A: For Biot-Savart law dH=μ04πIdl×rr3=μ0Idlsinθ4πr2 gives the magnetic field produces at a point due to…

Q: For the vector fleld G = (ye" + 3 cos(3r + y))i + (re + cos(3a + y)) j, tind the line integral of G…

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Q: 1. Let R and b be positive constants. The vector function r(t) = (R cost, R sint, bt) traces out a…

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Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

Q: A car travels over the hill having the shape of a parabola. When the car is at point A, it is…

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Q: Kepler's Third Law states that the ratio T/a³/2 is equal to a con- stant C for all planetary orbits…

A: Given :        Ta32 = C , where T is the period and a is the semimajor axis.

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

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Q: l a parametrization of the surface x³ + 5xy + z² = 10 wh 1 2, y = ,z = 0. e symbolic notation and…

A: In this question, the concept of the equation of the tangent plane is applied. The Equation of…

Q: Let S be the surface obtained by revolving the plane curve 2x=sqrt(9−y2) about the y-axis.Obtain a…

A: Given- Let S be the surface obtained by revolving the plane curve 2x = 9 - y2 about the y-axis. To…

Q: H=pz coup ap te'sing a4 tp'ar At point (1, ,0)

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Q: The position vector for a particle moving on a helix is c(t) = (3 cos(t), 2 sin(t), t²). (a) Find…

A: The position vector for particle moving on helix is ct=3cost, 2sint, t2. To find the speed of the…