4. For the cylinder with patch (a) Find the normal vector U. (b) The Gauss X(u, v) = (R cos u, R sin u, v), equals 0. map is G(u, v) = U. Find the derivative dG of the Gauss map. (c) Verify that the shape operator S(Xu) = −Vxu U equals 1 Xu and S(Xv) = -VXv U R (d) From the previous part, you know a matrix for the shape operator is s- (- / 0) S= R 1 H = = trace(S). 2 Use this information to find the Gauss curvature K = det(S) and the mean curvature

Q: Find the equation of this quartic that goes through the point (0, - 2). ا 3 2 1+ 0 -1 2 -5 -x

A:

Q: Solve step by step in digital format please 5. Prove analytically that the midpoint of the…

A:

Q: 3. Find the solution of the given initial value problem. d'y 3dy dx +2y = 2x, y(0) =y'(0)= %3D dx…

A: if we do the part A then part B will also be completed, as we need solution in part A which we can…

Q: 7. Graph a quadratic that has a vertex of (2,-4) and passes through the point (4,8). all the other…

A: Introduction: The standard form of the quadratic equation is given by, y=a(x-h)2+k Where (h,k) is…

Q: What are the coordinates of the vertex for the given equation in standard form? y=x^2+6x+5

A:

Q: Write the standard equation for the circle of radius 2v3 and centered at point (-2, 4)

A:

Q: Hi, i am having a hard time on sketching the plan 4x1+2x2+x3-8=0, could someone give me a help…

A: Sketch the plane of the given equation

Q: What is the equation of the parabola that has a max of (2,3), and passes through point (, -1)?

A:

Q: 1. Plot the data below in the grid of squares provided. You will have two data sets, one for men and…

A: Answer : • The graph of choice should be a scattered diagram.• This graph will help you to show a…

Q: Bx + (5x^2)/2 + (5y^2)/4 + y/(sqrt(2)) + 1 = 0 Check the alternative that contains ALL values ​​of…

A:

Q: 2) Find the Cartesian coordinates of the following : Зл. -), (5,7) ,(10,5) , (3.5) , (-2, 5) , (4.-)…

A:

Q: Determine the vertex of a parabola y=-2x^2+15x using calculus (use first principles to solve)

A:

Q: and x>0 2) lincar equationi in standard form

A: Solution:- solve by intregrating factor

Q: hello, can you explain how it is symmetric in more detail?

A: The given relation is symmetric. The explanation is provided below.

Q: What is this quadratic in vertex form? Please show solving steps

A:

Q: Express point P- 3,- into Cartesian coordinates with an aid of a suitable diagram.

A:

Q: Determine an equation for the parabola whose vertex is (- 2, 3) and goes through the point (4, - 6)

A: Given (h, k)=(-2, 3) and parabola passes through (4, -6).

Q: The number of houses that can be served by a water pipe varies directly as the square of the…

A: Given that, The number of houses that can be served by a water pipe varies directly as the square of…

Q: what quadrtant is the point (-3,2)

A: Point (-3,2) Here x axis is negative and y axis is positive

Q: 5) Write equation of the line -5-4-3-2-10 A Y

A: