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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.
The perimeter of a rectangle or field is 340 yards. The length is 50 yards longer than the width. Find the dimensions.The smaller of the two sides is_?_many yd.
The economies of many countries in the rest of the world go into recessions.
if it is known that determinant of A, det(A) = alpha*delta - beta*gamma > 0, and that the trace of A, Tr(A) = alpha + delta
Exponential equation by isolating the natural logarithm.
Use the function to predict the salary
Find the slope intercept equation
write the polynomial in standard form identify the degree of the polynomial identify the leading coeffcient and then
For n = 32 in A, B, and C, plot the results overplotting a Gaussian determined by estimating the amplitude and width by eye for the histogram of the result. Do the histograms seem to be Gaussian?
Find the vertex and intercepts of function f(x)=x2+x-2. Graph the linear equation y=2/3(x)-2. Find the x and y intercepts of 4x+3y=-12.
Please solve in lowest terms with parenthesis if necessary:
Find the addition
An investment advisor invested a total of $10,000, part at 5% annual simple interest and part at 3.5% annual simple interest. The amount of interest earned for 1 year was $437. How much was invested at the 5% rate and how much was invested at the ..
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