SOLUTION: Hi Please can someone help 10. If u = ax + by and v = bx - ay, a and b constants, obtain du/dx and dv/dy. By expressing x and y in terms of u and v, obtain dx/du and dy/

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: Hi Please can someone help 10. If u = ax + by and v = bx - ay, a and b constants, obtain du/dx and dv/dy. By expressing x and y in terms of u and v, obtain dx/du and dy/      Log On


   

Question 385546: Hi
Please can someone help
10. If u = ax + by and v = bx - ay, a and b constants, obtain du/dx and dv/dy. By expressing x and y in
terms of u and v, obtain dx/du and dy/dv and deduce that
du/dx.dx/du = a^2/a^2+b^2 and dv/dy.dy/dv = a^2/a2+b2
Thank you very much
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
To find du/dx, first note that y is constant in this case. Therefore, du/dx = a, likewise dv/dy = -a. The rest of the problems immediately follow, to find dx/du, assume all of the variables except u are constant.