Convert the equation of the sphere :   Into:   Cylindrical coordinates (An implicit equation is OK.)

Q: The following are the parametric equations for the motion of an object:

A: This question is taken from the calculus in which we have to find the slope from the given…

Q: Match the surface to its corresponding equation in spherical coordinates. 4 2 3 4. %3D 2 1 а. -1 -2…

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Q: Write the equation of the sphere in standard form. x2 + y2 + z2 + 12x - 4y + 4z + 35 = 0 Find its…

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Q: Convert the following point from cylindrical to rectangular coordinates: 11T ,4.5 6 10,

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Q: Consider the sphere r? + y? + 22 = 9. Please find the equation of the plane tangent to this sphere…

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Q: Show that the parametrization of the ellipse by the angle 0 is ab cos e Va? sin? e + b2 cos2 0 ab…

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Q: - Draw the graph of the following parametric equations, and find the Cartesian equations. 1) x = 6t…

A: Apologies. We only answer one question at a time. We will answer question 1 as the exact one wasn't…

Q: Identify and sketch the surfaces described by the given equations. Explain.

A: our objective is to sketch the surface.

Q: 4. For each equation of a surface given in spherical coordinates, sketch the surface and describe it…

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Q: Eliminate the parameter t to find a Cartesian equation for: 3D² y = 3 + 5t The resulting equation…

A: Given that: x=t2…

Q: 1.3 Show that the following equation represents a sphere, and find its center and radius. x? +y? +…

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Q: Convert the rectangular equation to an equation in cylindrical coordinates and to an equation in…

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Q: Given a point in spherical coordinate (5, ) find its equivalence in cylindrical coordinate. Draw the…

A: Introduction: Apart from the rectangular coordinate systems, there are two other coordinate systems…

Q: Convert the coordinates as indicated (3,TT/3, -4) from Cylindrical to Cartesian.

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Q: (a) ρ%3D2. (b) ¢ = 7. (c) ρ =D COs

A: In a spherical coordinate every point P is represented as ρ, θ, ϕ, where ρ is the distance between…

Q: Convert the following quadric surface into spherical coordinates.

A: Convert the quadric surface into spherical coordinates.

Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation x2…

A: We have to convert the given equation x2+y2=16 into spherical coordinates

Q: If æ (t) = -2sin t and y(t) = 3cos²t, eliminate the parameter to write the parametric equations as a…

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Q: Eliminate the parameter in the parametric equations a(t) = –8t – 9 and y(t) = –32t + 9 to write a…

A: Given parametric equations, x(t)=-8t-9 y(t)=-32t+9

Q: Write the equation of the sphere in standard form. x2 + y2 + z2 + 8x - 4y + 4z + 15 = 0 Find its…

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Q: cribe the surface with equation 2 +y +? + 8x + 6y + 2z - 10 = 0 surface is a sphere with center ( i…

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Q: For each equation of a surface given in cylindrical coordinates, sketch the surface and describe it…

A: Given: a) r = 7 b) θ =π2 c) z = 2

Q: Write the parametric equations x = 2t – t°, y = 4 – 2t - in the given Cartesian form.

A: We are given the equation of the function in parametric form and we need to find the cartesian form…

Q: C) Convert the equation 5x2 + 2y2 = 3z to spherical coordinates. %3D

A: Use the relation between and spherical coordinate and cartesian coordinates.

Q: Find an equation in spherical coordinates for the equation given in rectangular coordinates. x² +y²…

A: Explanation of the answer is as follows

Q: Write the equation for the sphere of radius 1 centered at the prigin in the each of the following…

A: The general equation of a sphere in cartesian coordinates is: x-a2+y-b2+z-c2 = r2 Here, r is the…

Q: Find the rectangular coordinates of the center of the sphere p = 2 sin w (cos 0 – 2 sin 0).

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Q: Find the rectangular coordinates of the point, whose cylindrical coordinates are given. (a)    (8,…

A: ρ, θ, z=8, π4, 3⇒ρ=8, θ=π4, z=3  Now rectangular coordinates are, x=ρcosθ, y=ρsinθ, z=z⇒x=8cosπ4,…

Q: Write the equation of the sphere in standard form. x2 + y2 + z? + 6x – 2y – 2z = 14 Find its center…

A: Consider the equation of a sphere : where a,b,c are coordinates of the center of circle from the…

Q: Eliminate the parameter t to rewrite the parametric equations as a Cartesian equation Į x(1) = (t –…

A: Given equations x(t)=(t-1)2 y(t)=e3t To convert given equations into cartesian equation we need to…

Q: Sketch and describe the shape that is defined by the spherical coordinate equation p = ¢

A: It is a semicircle

Q: Eliminate the parameter in the parametric equations #(t) = 2t + 5 and y(t) = 8t equations. Provide…

A: In this question we will simply eliminate parameter t and get an equation between x and y. Solution…

Q: What Cartesian equation is equivalent to the given parametric equations? {x(t)=4sin(t)…

A: For x=a.cos(t) and y=b.sin(t) the Cartesian equation is written as: xa2+yb2=cos2t+sin2t=1.

Q: Find the solution set in parametric form of the following system: I + 211 + -211 I3 + 214 %3D

A: We have to find the parametric form of the given set of equations.

Q: Part a) Convert the equation z = 3x2 + 3y2 to spherical coordinates. Part b) Describe in plain…

A: Given equation z=3x2+3y2

Q: Convert (5, t/6, t14) from spherical to rectangular coordinates.

A: Solution is given below

Q: Classify and sketch the surface 12x? – 3y? + 4z? = 12 What are the 3 traces? Show equations of the…

A: A quadratic surface is a hypersurface. It is nothing but the generalization of a conic section in…

Q: Identify and sketch the surfaces described by the given equations. Explain.

A: The given equation is the y^2 + z^2=1

Q: Find the rectangular coordinates of the point, whose cylindrical coordinates are given. (a) (4, T/4,…

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Q: 1.3 Show that the following equation represents a sphere, and find its center and radi x2 + y2 + z2…

A: Given,          x2+y2+z2-6x+8y-10z+25=0We know that,           The standard equation of the sphere…

Q: Write the parametric equations x=2sinθ,y=9cosθ,0≤θ≤πx=2sin⁡θ,y=9cos⁡θ,0≤θ≤π in the given…

A: Given information: The parametric equations are x=2sinθ            y=9cosθ             Can be…

Q: Convert the rectangular equation y = 4 to an equation in (a) cylindrical coordinates and (b)…

A: y=4 a). rsinθ=4   ∵x=rcosθ,  y=rsinθ,  z=z⇒r=4sinθ⇒r=4cscθ

Q: Find a spherical coordinate equation for the sphere x² + y? + (z – 1)² = 1

A: All real numbers can be represented on a line called the number line. The number zero corresponds to…

Q: Eliminate the parameter t to find a Cartesian equation in the form x = f(y) for: %3D Sa(t) = 4t2…

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Q: C) Convert the equation 5x2 + 2y2 3z to spherical coordinates. %3D

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: Convert the rectangular equation x2 + y2 = 4y to an equation in (a) cylindrical coordinates and (b)…

A: Given- x2+y2=4y To find- An equation in (a) cylindrical coordinates and (b) spherical coordinates.…

Q: Eliminate the parameter t to find a simplified Cartesian equation of the form y = mx + b for Sa(t) =…

A: We have to eliminate the parameter t to find a simplified cartesian equation of the form y = mx+b.…

Q: Convert the following point from spherical to rectangular coordinates: (17) - 4 4 (x, y, z) =

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Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

A: This is a problem of change from spherical to cartesian and polar to cartesian.