Identify the surface whose equation is given. p = sin(8) sin(4) O a sphere of radius - centered at (0,, 0) sphere of radius 1 centered at (0, 0, 0) O a sphere of radius centered at (0, 0, o) 2 O a sphere of radius 1 centered at (0, 1, 0 a sphere of radius - centered at (0, 0, 0) 2

Q: Identify the surface whose equation is given. p = sin(0) sin(4) (0, 0, 0) O a sphere of radius…

A: We have to identify the given surface.

Q: Question 14 Solve the problem. Find the equation for the tangent plane to the surface z = 8x2 - Sy2…

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Q: Consider the equation yux – uu, = x. (a) Write a parametric representation of the characteristic…

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Q: 2. Solve Laplace's equation inside the circular annulus given in the polar coor- dinates by the…

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Q: Find an equation of the tangent plane to the given surface at the specified point. z = 6(x - 1)2 +…

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Q: (a) If a > 0, find the area of the surface generated by rotating the loop of the curve 3ay = x(a –…

A: The graph of the function 3ay2=x(a-x)2.

Q: Find parametric equations for the path of a particle that moves along the circle described by x2 +…

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Q: 1-4 Find the area of the surface generated by revolving the given curve about the x-axis. . 1. y =…

A: Surface area is 7✓55 π

Q: 2. Consider the two surfaces zx = x² + y? and z³ = 4(x² + y³) They have a curve of intersection C…

A: a) The two surfaces are zx=x2+y2 and z3=4x2+y2. To find the curve of intersection of these two…

Q: ssume you are given the surface S with equation æ² + + = 1. = 1. 9

A: We can use distance formula to solve the problem

Q: Find an equation for the projection of the curve on the xz plane. (Hints: First, figure out from…

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Q: √1-x² Evaluate x²(x² + y²)² dydx. (evaluating this using rectangular coordinates is nearly hopeless)

A: As per our guideline, we are supposed to solve only first question. Kindly repost other question as…

Q: Find an equation of the plane tangent to the following surface at the given points. z= 2 cos (x- y)…

A: The given function: z=f(x, y)=2 cos(x-y)+2 The given points: To find the equation of tangent plane:…

Q: Solve the problem. Find the equation for the tangent plane to the surface z=-3x2 - Sy2 at the point…

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Q: Solve the problem. Find the equation for the tangent plane to the surface x2 + 10xvz + y = -8z2 at…

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Q: Find a parametric equations representation for the curve (x + 3)² + (y – 2)² = 9 x = 9cost + 3, x =…

A: You know the trigonometric identity:

Q: Find parametric equations and a parameter interval for the motion of a particle that starts at (–…

A: Given a particle starts at -a,0 and trace the circle x2+y2=a2 We have to find the parametric…

Q: Mathematical oncologists sometimes approximate tumors with the bumpy sphere model given by the…

A: Hi! You have posted multiple questions. As per norms, we are solving only the first question. If you…

Q: 1-4 Find the area of the surface generated by revolving the given curve about the x-axis. I 1. y…

A: We know that curved surface area revolving about the x-axisSurface area = 2π∫abf(x) 1+ f'(x)2 dx…

Q: Describe the graph of the equation. r = 2 cos t i - 9 sin t j + k O An ellipse in the plane z = 1,…

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Q: Consider the surface S of equation 2 = x² + y*" An equation for the tangent line tangent to S at…

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Q: Find an equation of the tangent plane to the surface x³ + 2z?ey-² = 136 at point P = (4, 5, ). (Use…

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Q: 2) Suppose you need to know the equation of the tangent plane to a surface S at the point (2,1,3).…

A: Step:- 1  Let S be the surface in ℝ3 say z= f(x,y), and let A=a1,a2,a3 is a point on S then a plane…

Q: 1. Find parametric equations for the following curves in R°. (a) The great circle on the sphere x² +…

A: The objective is to find the parametric equations for the curves in R3.   (a) It is given that, the…

Q: Find parametric equations for the path of a particle that moves along the circle x2 + (y − 1)2 = 9…

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Q: z = sin(2x) cos(y) 1. Construct a grid for x and y going from (0, 0) to (4, 6). 2. Use this grid to…

A: Using the Geo Gebra software I have plotted all these three problem in 3d graph. 1. The grids are…

Q: ind an equation of the tangent plane at P = ( 2,3, - 3 |to the given surface. 10x? + z?e"-* = 49…

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Q: Find an equation of the tangent plane at P = ( 2, 3, to the given surface. 8x? + z?e"-* = 41…

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Q: The following equation is an equation of a surface of revolution obtained by rotating a curve C…

A: The given equation of surface of revolution is x2+y2+z2=1. This equation can be written as:…

Q: #3. Find the point on the surface x2 + 2y + z = 3 that is closest to the point P = (-1,3,2). You can…

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Q: Find an equation for the plane that is tangent to the given surface at the given point. z=√√y-x…

A: Introduction: The formula of the tangent to the plane F(x,y,z)=0 at the point a,b,c is given by,…

Q: Problem Consider the surface defined by f(x, y) = ln(5y – 7.x). Find the equation of the tangent…

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Q: 4:- Consider the image of the sphere r(0; Ø) = (a cos 0 sin Ø; a sin 0 sin Ø; a cos Ø) where 0 0…

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Q: 2. Eliminate the parameter to find a description of the shape graphed by the para- metric curves…

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Q: x^2+y^2=4   The part of the circle in region 1 is rotated around the line x + y = 2. the area of…

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Q: d a set of parametric equations for the tangent line to the curve of intersection of the surfaces at…

A: Given surfaces are z=x2+y2 and z=16-y at the point 4,-1,17. To find a set of parametric equations…

Q: Question 1. Consider the surface S given by the implicit equation 2° – xy + yz + y³ =1. (a) Find the…

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Q: 8. The tangent line to the curve r(t) = Li+ej=t'k 2-t at the point P(1,1, -1) intersects the line…

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Q: 3. (a) The surface f(x, y, z) = 1+y - 2 = 0 and g(x, y, z) = x+2-4 0 mect in an ellipse E. Find the…

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Q: Describe the graph of the equation. r = 4 cos t i – 14 sin t j + k O An ellipse in the plane z = 1,…

A: Here, the given parametric equation is: r=4 cos t i-14 sin t j+k⇒r(x(t),y(t),z(t))=(4cos t, -14 sin…

Q: 4) Assume you are given the surface S with equation x? + + = 1. (a) Find the equation of the tangent…

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Q: 1-6 Find an equation of the tangent plane to the given surface at the specified point. 1. z = 3y² –…

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Q: Describe the graph of the equation. r = 8 cos t i – 18 sin t j + k O An ellipse in the planex = 1,…

A: Equation in the vector form

Q: as engineer design a cooling tower in the shape of hyperboloid of one sheet. The horizontal cross…

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Q: Consider the equation of the surface S given by 3x-3y®z7-2xy = 8, where a is an odd number and B is…

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Q: 4. points] Find the equation of the tangent plane to the surface a? 2yz + z3 = 0 at (1, 1, 1).

A: This question is based on 3-d Geometry.

Q: (a) Circle: x = h +r cos 0, y = k + r sin 0 (b) Ellipise: x = h + a cos 0, y = k + b sin 0 (c)…

A: We have to find out in rectangular form

Q: 3. Find a rectangular equation to represent the plane curve. x = 3 tan t, y= 2 sect %3D

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Q: Describe the graph of the equation. r = 7 cos t i - 16 sin i j+k O An ellipse in the planex = 1,…

A: We have to describe the graph of the equation.