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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.
1. give a scenario that could be modeled like a logarithmic function and explain why it is logarithmic.2. compare and
Write a quadratic equation in the variable x having the given number as solutions. Type the equation in standard form, ax^2+bx+c=0 Solution:5, only
Conics translations
Comparison of charges.
Prove that the equivalence relation modulo m where m is an integer, forms a ring. Also, does this same equivalence relation form a field and why?
Suppose a consumer price index of a country is decreasing at the rate of 4.3% per year. Use the approximate half life formula to estimate its half life.
Explain how we could change the codomain of the mapping in part B so that the mapping would no longer be onto.
In general, what can you say about the usefulness of these area formulas? What other methods could be used to find the area and surface areas of objects?
The book gives for v2= (0,0, 1)^T, and for V3, he added to use formula (A-2I)^2 v =0 to find v3 to be v3= (0,1,0)^T.
Pythagorean Quadratic - Buried treasure. Ahmed has half of a treasure map,which indicates that the treasure is buried in the desert 2x + 6 paces from Castle Rock. Vanessa has the other half of the map.
Find the value of n such that the expression is a perfect square trinomial, then factor it. Solve the equation by completing the square and applying the square root property
In a certain year, solar and wind energy generation totaled 1000 24 trillion BTUs. Wind generated 52 trillion BTUs more than eight times that generated by solar energy. How much was generated by each source?
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