3. What are the rectangular coordinates of the point with polar coordinates (r, 0)= ( 2, ? 4 (x, y) (V2, v2)< -incorect trig ab b a (O)

Q: Use the integration capabilities of a graphing utility to approximate the area of the surface formed…

A:

Q: 7. (a) Find a spherical coordinate equations; for the sphere x²+y²+(z-1)²=1 and the surface…

A: To convert a point from Cartesian coordinates to spherical coordinates, use equations…

Q: What is the rectangular equivalence to the parametric equations? z (0) = 4 cos 0+2, y (0)=2 sin 0-5,…

A:

Q: Describe how the surface with spherical equation p²(1 + A cos² ¢) = 1 depends on the constant A.

A: Given : ρ2(1+Acos2ϕ)=1To describe: How the surface with spherical equation  ρ2(1+Acos2ϕ)=1depends on…

Q: 9. Calculate lim (2,y,2)→(0,0,0) x² + y² + z² by converting to spherical coordinates.

A:

Q: Which of the following sets of parametric equations is for the surface obtained by rotating th curve…

A:

Q: Match the surface to its corresponding equation in spherical coordinates. 37 4 -3 -2 -1 0 1 2 3 3…

A: To solve this we have to find the relation of equation

Q: 4. Find the parametric equations for the tangent line to the curve of intersection of the y? z1…

A:

Q: 9. Approximate the surface area of the surface generated by revolving the polar curve given below…

A: I have appended the formula used in the solution part

Q: III. Find a set of parametric equations for the curve of intersection of the cylinder (x-1)² + ² x²…

A:

Q: 15. Find the radius of curvature at 0 = -n of the parametric equations x = 3(0 + cos 0), y = 3(1 –…

A: For the parametric curve x=x(θ), y=y(θ)Curvature K=|x'y''-y'x''|[(x')2+(y')2]32Radius of…

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x - 1)2 + y2/4 = 1…

A: Given: The equation of cylinder is: x-12+y24=1 .....(1) The equation of paraboloid is: x2+y-22=z…

Q: Find parametric equations for the intersection of the planes 2x + y − 3z = 0 and x + y = 1

A: Two planes lying in 3-Dimensional plane can intersect each other at any point and that point can lie…

Q: 2. Find parametric equations for the line tangent to the curve of intersection of the surfaces at…

A:

Q: Find an equation of the form p = ƒ (0, 4) in spherical coordinates for the surface z = 16 (Use…

A: The equation in spherical coordinates for the surface is determined as shown below

Q: Use spherical polar coordinates to evaluate LLEN V4-x2 x² + y2 + z² dz dy dx. -V4-x2

A: Solution is given below:

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: Use the integration capabilities of a graphing utility to approximate the area of the surface formed…

A: Given r=4cos2θ and 0≤θ≤π4 To find the area of the surface formed by revolving the polar equation…

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 1st  and 2nd Derivate of y with respect to x from parametric equations. Complete solution…

A:

Q: 4. Find the equation of the plane that passes through the point (5, –1,0), and is per- pendicular to…

A: Let's find.

Q: 9. Show that for a ± 0, the equation p = 2a sino cos 0 in spherical coordinates describes a sphere…

A: Given :  The equation ρ = 2 a sin ϕ  cosθ  .   To determine: The equation ρ = 2 a sin ϕ  cosθ  in…

Q: 1.Find the area of the triangle in the xy-plane with vertices A(n,n2, n3),B(m,m2,m,),C(r..). 2.…

A:

Q: 1. Eliminate the parameter to find a Cartesian equation of the curve with parametric equations z =…

A:

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: Identify the surface whose equation in spherical coordinates is given by p= 8 cos o

A:

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: 8. Find a Cartesian equation for the surface whose spherical equation is p= 2 sin() sin(0).

A: Solve the following

Q: Find an equation for the paraboloid z = x2 + y2 in spherical coordinates. (Enter rho, phi and theta…

A: The equation of the paraboloid z = x2+y2                                       ........(1) To…

Q: 1. Convert the point (-1,1, v2) from Cartesian to spherical coordinates. (a) (VZ. VZ) (b) (1., vZ)…

A: To convert the point (-1,1,√2) from cartesian coordinates to spherical coordinates.

Q: 18. Find the acute angle between the plane x+2y-z=8 and the line with parametric equations x =1, y…

A:

Q: 6. Find parametric equations for the line of intersection of the planes 2x – y + z = 4 and 3x + y +…

A:

Q: Consider the curve with polar equation r= 6 sin where 0 <0<. Without finding the Cartesian equation,…

A: Given: The given polar equation is : r=6sinθ where 0&lt;θ&lt;π. To find: We have to determine the…

Q: Find the number of points of intersection of the polar curves r=2cos0 and r=1+2sin0. O 1 3 O 2

A: Number of point of intersection of polar curves r=2cosx and r=1+2sinx

Q: 9. (a) Find the equation of the cone 3.x2 +3y2 in spherical polar coordinates. (b) Use spherical…

A: Given

Q: 9. The Whitney umbrella surface is given parametrically by I= uv, y = v, 2= u. A picture of this…

A:

Q: Find an equation for the paraboloid z = x2 + y² in spherical coordinates. (Enter rho, phi and theta…

A:

Q: What is the rectangular equivalence to the parametric equations? x(θ)=2sinθ+1,y(θ)=3cosθ−2 , where…

A:

Q: What is the rectangular equivalence to the parametric equations? z (0) = 4 cos 0+2, y (0)=2 sin 0-5,…

A:

Q: 2. Use parametric equations to derive the formula for the lateral surface area of a right circular…

A:

Q: Find a set of parametric equations for the curve of intersection of the paraboloid x² + 4y² − z = 0…

A: To find the parametric equations for the intersection of given surfaces.

Q: Find a set of parametric equations for the curve of intersection of a paraboloid x² + (y − 2)² = z…

A:

Q: Find the area of the surface obtained by rotating the curve of the following parametric equations…

A: We need to find surface area.

Q: # 2. Let C be the curve that is the intersection of the cylinder x²-2x+4y2 = 0 with the plane z-x…

A: The cylinder x2-2x+4y2=1 and a plane z-x=3. We have to find the parametric equations for the…

Q: 5. Find parametric equations for the line of intersection of the planes x + y = 1 and y +z = 1.

A:

Q: i need to convert below z=64-4*x^2-4*y^2 and above the xy-plane into polar coordinate however i am…

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Q: 11.) Find a rectangular equation for the Surface whose Spherical equation is a sin ($) Sin (e)

A:

Q: Find the distance between the point (4, −1, 5) and the line given by the set of parametric equations…

A: The point is: P(4, −1, 5) The line is: x = 3, y = 1 + 3t, z = 1 + t The line is: &lt;3, 1, 1&gt; +…

Q: The parametric equations for the line tangent to curve of intersection of the surfaces x? + y² = 8 ,…

A: