# Search results

1. ### Principal root of a complex number

Thank-you. So it is how I though. As for the latter question, we can ignore that since I understand it now. Thank-you.
2. ### Solve a differential equation for the initial conditions,

Edit: What (s)he was trying to state is that y = 0 is an equilibrium solution of the differential equation. What would this imply about the equation?
3. ### Principal root of a complex number

Evaluate the integral of ∫\Gamma f(z) dz, where f(z) is the principal value of z1/2, and \Gamma consists of the sides of the quadrilateral with vertices at the pints 1, 4i, -9, and -16i, traversed once clockwise. I understand how to compute this for the most part. I'm just not 100% confident...
4. ### Principal root of a complex number

Homework Statement I am doing a problem of a contour integral where the f(z) is z1/2. I can do most of it, but it asks specifically for the principal root. I have been having troubles finding definitively what the principal root is. Anyplace it appears online it is vague, my book doesn't...
5. ### Verify that the Stokes' theorem is true for the given vector field

This is a problem from an old final exam in my Calc 3 class. My book is very bad at having examples for these types of problems, and my instructor only went over one or two. Help would be much appreciated. Homework Statement Verify that the Stokes' theorem is true for the vector field...
6. ### Use Lagrange multipliers to find the max & min

Ah! Yes, I know this function. I just didn't know it's name. Thank-you for reminding me of it!
7. ### Use Lagrange multipliers to find the max & min

I am sorry, but can you elaborate more on what a Hessian is? Currently we have only covered Lagrange multipliers.
8. ### Use Lagrange multipliers to find the max & min

Homework Statement Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x,y) = exy; g(x,y) = x3 + y3 = 16 Homework Equations ∇f(x,y) = λ∇g(x,y) fx = λgx fy = λgy The Attempt at a Solution ∇f(x,y) = < yexy, xexy > ∇g(x,y) = <...
9. ### Find symmetric equations for the line of intersection of the planes

I assumed it because of how y and z cancel each other out. Plus i kinda knew that x held constant and y & z covers all integers =P (oops)
10. ### Find symmetric equations for the line of intersection of the planes

5x - 2y - 2z = 1 4x + y + z = 6 So, for z = 0, 5x - 2y = 1 4x + y = 6 5x - 2y = 1 + 8x + 2y = 12 13x = 13 x = 1 4 + y + z = 6 y + z = 2 y - 2 = -z Thanks =D So just set up a simple system of equations? I thought I tried that -.- I must have set it up wrong. Thank-you though!
11. ### Find symmetric equations for the line of intersection of the planes

It's what the chapter & lesson is about. x = -1 y = 1
12. ### Find symmetric equations for the line of intersection of the planes

I fixed it, thank-you. We're apparently supposed to be using the cross product of the two normal vectors of the planes (which gives the same vector as the intersection line, just parallel). It doesn't give me a point, and I can't figure out how they got that specific answer. Would that be...
13. ### Find symmetric equations for the line of intersection of the planes

Homework Statement Find symmetric equations for the line of intersection of the planes The planes: 5x - 2y - 2z = 1 4x + y + z = 6 Homework Equations r = r0 + tv x = x0 + at y = y0 + bt z = z0 + ct The Attempt at a Solution I have attempted this in many different manners and would like...
14. ### Vectors - Boat & Stream problem

This is from Stewart 7E Calculus textbook in Chapter 12 section 2 problems. It is over vectors; this is the first problem I came across in the practice questions I had issues with, mainly because I'm a bit rusty on my solution from a Physics standpoint.
15. ### Vectors - Boat & Stream problem

Thank-you bossman, and you solved it the way they probably wanted (or in a similar fashion). This is from a chapter about vectors etc. This shall help me whenever I come across anything similar to this...I kinda feel stupid that I didn't figure it out though.
16. ### Vectors - Boat & Stream problem

Homework Statement A boatman wants to cross a canal that is 3 km wide and wants to land at a point 2 km upstream from his starting point. The current in the canal flows at 3.5 km/h and the speed of his boat is 13 km/h. (a) In what direction should he steer? (b) How long will the trip take...