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(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 polar coordinates. Then compute the Laplacian using the cylindrical polar form. Show that your answer here is the same as your answer from (a).
(c) For this section take u(x,y,z) =x ^2, Convert the formula for u into a formula for u involving spherical polar coordinates. Then compute the Laplacian using the spherical polar form. Check that your answer is 2.
Matrices have a number of interesting mathematical attributes, such as their dimensions, how they can be derived from linear systems, and the kinds of operations that can be performed on them.
Provide a coefficient matrix corresponding to the system of linear equations.
q1. develop the estimated regression equation that relates line speed the number in defective parts found. q2. use the equation to forecast the no. of defective parts found for a line speed of 50 ft /sec. line speed no. of defective parts 18 21 19 19..
Explain under what circumstances each method would be preferred over any of the other methods. Give an example for each circumstance.
What lump sum should be invested today
Solving Systems of Equations:-What are the three methods for solving systems of equations?-Do they all produce the same answer?
If a,b are positive integers with greatest common divisor d and least common multiple m, show aZ+bZ=dZ and aZ intersect bZ=mZ
the volume of a rectangular prism is given by the formula v lwh lengthbullwidthbullheight. what are the length width
solve the following system of inequalities by graphing.5x - 4y ge -203x - 2y le -8y ge
A parachutist and her parachute have a combined mass of 80 kg. She steps out from an aircraft travelling horizontally at 90m s-1 at a height of 300m above the ground, and falls for 5 seconds before instantaneously opening her parachute.
Is the perimeter of a composite figure greater than, less than, or equal to the sum of the perimeters of each figure separately? Explain. Draw a composite figure followed by a parallelogram and a trapezoid.
Find the equation of the resulting function
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