For the given curves, write equations in both rectangular and polar form. Please show which formulas/properties are used and explain steps taken.
1. The horizontal line through (1,3)
2. The circle with center (3,4) and radius 5
3. The circle with center (5,-2) that passes through point (1,1)
Convert the equation to polarcoordinates and simplify.
1. a. xy = 1
b. (x^2 + y62)^2 = 2xy
Express the equation in rectangularcoordinates.
2. a. r = 3sin(t)
b. r = 4cos3(t)
r^2 = 4sin2(t)
r = 4/(2 + cos(t))
Consider the solid bounded above by the plane Z = 4 and below by the circle
X^2 + Y^2 = 16 in the XY-plane.
a) Write the double integral in rectangularcoordinates to calculate the volume of the solid.
b) Write the double integral in polarcoordinates to calculate the volume of the solid.
c) Evaluate part a or part b
Please assist with the attached problem.
(a) Calculate the Laplacian of function u(x,y,z) = x^3 - 3xy^2 + z^2 in 3D Cartesian coordinates.
(b) Convert the formula for u into formula for u involving cylindrical polarcoordinates. Then compute the Laplacian using the cylindrical polar form. Show that your answer here is the same