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A motile cell is placed at the point (x0, y0) on a square shaped dish filled with a "nutrient bath". The concentration of nutrient at any point (x, y) in the dish is given by
N(x, y) = 10 - 2x2 - 4y2.
Cells are typically known to move, in a continuous fashion, in the direction of maximum increase of this nutrient. Furthermore, it is observed that each cell moves with a velocity proportional to the gradient vector at each point (where k is the constant of proportionality).
(a) Show that the parametric equations that represent the motion of the cell over time are given by
x(t) = x0e-4kt, y(t) = y0e-8kt.
[Hint: you may need to look up a method for solving first order ordinary differential equations, known as "separation of variables".]
solve simultaneous equations by drawing graphs 3x+4Y=5 2X-Y=3
It is probably the easiest function which we'll ever graph and still it is one of the functions which tend to cause problems for students. The most general form for the constant
2x^2+7x+3/x^2-2x-15
27x^2+3x+5
Horizontal Shifts These are quite simple as well though there is one bit where we have to be careful. Given the graph of f ( x ) the graph of g ( x ) = f ( x + c ) will be t
exammples
a farmer has a garden with 2 sides at right angles and the third side is 423ft.long.find the perimeter of the garden. if the angle between the shortest and the longest side is 58''
I have a 12.2 bottle of mustard. I use 1/20 of mustard per serving per hot doog. How much mustard do I have left after 4 servings of hot dogs.
Sketch the graph parabolas. g ( x ) = 3x 2 - 6 x + 5 Solution For this parabola we've obtain a = 3 , b = -6 and c = 5 . Ensure that you're cautious with signs while id
4(3x-2) -5(x+1)=6-(4x-3)
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