Example: Find the surface area of the curve described by x = t³, y = t², 0

Q: Describe a surface of revolution in your own words.

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. 2 + 2)3/2, 1s ys…

A: The curve x=13y2+232 revolved about x-axis on 1≤y≤4

Q: Determine the area bounded by the ellipse satisfying:(101x+ 10y)2+ (20x+ 2y)2= 1.

A:

Q: Use the parametric equations of an ellipse, x = 5 cos(0), y = 3 sin(0), 0 ≤0≤2π, to find the area…

A:

Q: Sketch the surface created by 4.r2 + 9y? + 3622 = 36. %3D

A: Given,4x2+9y2+36z2=36 Simplify equation (i) as x29+y24+z21=1  .....(i) Intercepts along x,y,z…

Q: Convert to standard from and give the center and radius: x^2+ Y^2 - 2x +6y - 1=0

A: x-h2 +y-k2 =r2 (h , k) is centre and r is radius .

Q: explain the geometric relationship between the answer found in part b and the surface defined above

A: In part (b) we calculated gradient of F at (0, 1, 2).

Q: What is a trace of a surface?

A:

Q: Explained every step

A: The given equation of the surface is  x2 + 2y2 + z2 − 4x + 4y − 2z + 3 = 0.   The general equation…

Q: Explain what it means for a surface to be orientable.

A: They are the surfaces for which we can define clockwise consistently. e.g. Cylinder and spheres are…

Q: Explain the concept and provide an example of Parametric and Nonparametric tests.

A: Introduction - Two types of hypothesis testing Parametric test Non parametric test  Parametric…

Q: Karla is running along a circular race track that has a radius 3.3 km long. She starts at the…

A: O : Center of the park A : Karla's starting point B : The point where Karla passes Gabriel C : The…

Q: x = z? + y? Name of the surface

A: x=z2+y2 We need to name the surface.