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The center of a national park is located at (0,0). A special nature preserve is bounded by by straight lines connecting the points A at (3,2), B at (5,1), C at (8,4) and D at (6,5) in a parallelogram. The yearly rainfall at each point is given by RF(x,y) =x2-xy+y2 in inches. Transform this into a rectangle in v - r space using the Jacobian theory we studied and determine the following.
1. Find the average rainfall per year for the entire region.
2. Suppose that we desire to constract a weather station at a point in order to report a number on a regular basis that might represent the average rainfall for the entire preserve. Assuming we pick the center of "mass" of the rainfall density function for this point, find the location of the weather station in the (x,y) system
Let f : R 3 → R be de?ned by: f(x, y, z) = xy 2 + x 3 z 4 + y 5 z 6 a) Compute ~ ∇f(x, y, z) , and evaluate ~ ∇f(2, 1, 1) . b) Brie?y
A graph G has 21 Edges, 3 vertices of degree 4 and other vertices are of degree 3. Find the number of vertices in G. Ans: It is specified that graph G has 21 edges, so total
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Cross Product In this last section we will look at the cross product of two vectors. We must note that the cross product needs both of the vectors to be three dimensional (3D
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PROBLEMS RELATED TO APPLYING OPERATIONS : Some of us were testing Class 4 children with addition and subtraction problems. We gave them sums that were written horizontally and th
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Dividing Whole Numbers: Example: Divide 347 by 5. Solution: Beginning from the left of the dividend, the divisor is divided into the
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Since we are going to be working almost exclusively along with systems of equations wherein the number of unknowns equals the number of equations we will confine our review to thes
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