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03-31-2004, 05:17 AM
Anyone know calculus??? I think theres guys that know their computers in here, and maybe computer knowledge=math knowledge? I don't think the problems are that hard, but I'm not that sure on it and I need to get this stuff 100% correct. If anyone can help me out with any of the following it would be much appreciated. Thanks in advance:
1) Find the point in the plane 1x-2y+5z=15 that is closest to the origin.
2) Let P(x,y)=x^2y^2-xy+1 be the pressure at point (x,y) in a pool, measured in pascals. Let position be measured in meters.
a) find the gradient of P (I got this part)
b) a fish is located at (1,2), and wants to move in the direction of maximum decrease in pressure. Which direction is taht? Express answer as unit vector.
c) What is the maximum instantaneious rate of decrease in pressure at (1,2), measured in pascals per meter?
3) Let f(x,y)=xy(1-x-y).
a) find all critical points of f(x,y).
4) Let R(t)=<t^2,t,2t> parametrize a curve C. Let P be a plane parametrized by x+y-3z=-6. Find all points of itnersection of the curve and plane.
1) Find the point in the plane 1x-2y+5z=15 that is closest to the origin.
2) Let P(x,y)=x^2y^2-xy+1 be the pressure at point (x,y) in a pool, measured in pascals. Let position be measured in meters.
a) find the gradient of P (I got this part)
b) a fish is located at (1,2), and wants to move in the direction of maximum decrease in pressure. Which direction is taht? Express answer as unit vector.
c) What is the maximum instantaneious rate of decrease in pressure at (1,2), measured in pascals per meter?
3) Let f(x,y)=xy(1-x-y).
a) find all critical points of f(x,y).
4) Let R(t)=<t^2,t,2t> parametrize a curve C. Let P be a plane parametrized by x+y-3z=-6. Find all points of itnersection of the curve and plane.