Suppose we want to form a conic container by rolling up a circular sector of radius 10. We want to find the central angle (theta) such that it maximizes the volume of the cone. Find the radius and the height of the cone and then express the volume as a function of theta. Make sure you state the domain.

Q: Without using a graphing utility, sketch the surface with equation x2 + y2 − z2 = 0.

A: Surface with the equation

Q: Describe and graph (using a computer) the surfaces d) 4y² + z² − x − 16y - 4z + 20 = 0 e) x² - y² +…

A: The given surfaces are: d  4y2+z2-x-16y-4z+20=0e x2-y2+z2-2x+2y+4z+2=0f  fx,y=1x-y2 We have to…

Q: The following hyperbola has a vertical transverse axis: (x+2)² (+7) _ =1. 17 16

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: 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: In the automobile assembly company; There is a robotic arm on an assembly line in charge of placing…

A: The given diagram is                 The given coordinates of B is So the distance of AB=5(x…

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: Find the points on the cone 22 = x2 + y? that are closest to the point (1,3,0)

A:

Q: 3. Use calculus (derivative and C.N.) to find the area of the largest rectangle that can be…

A: This question is related to conic section .solve in step 2.

Q: Find the equation of each sphere based on the information provided. Show your work and do not expand…

A: Let's find equation of sphere.