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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".]
The following equalities can be used to make conversion factors. 2.54 cm = 1 inch 12 inches = 1 foot 1 mile = 5,280 feet 100 cm = 1 m 1000 m = 1 km 36 inches = 1 y
YOU EARN 15N DOLLARS FOR MOWING N LAWNS.HOW MUCH DO YOU EARN FOR MOWING ONE LAWN? SEVEN LAWNS?
In previous section we looked at the two functions f ( x) = 3x - 2 and g ( x )= x/3 + 2/3 and saw that ( f o g ) ( x ) =(g o f )( x ) =
-5t=-45
2x^2+7x+3/x^2-2x-15
The population of a city was 141 thousand in 1992. The exponential growth rate was 1.6% per year. Find the exponential growth function in terms of t,where t is the number of years
#question.3000 board feet of maple lumber for making their classic and modern maple rocking chairs. A classic maple rocker requires 15 board feet of maple, and a modern maple rocke
using T for term- p T-1,2,3,4,5,6 = 8,16,24,32,40. Formula is T x _ +_=8, T x_+_=16 etc same 2 numbers must be used. how do i figure this out? an brackets be used or minus?
x+y=0 x=y+4
carly spends $5 for n notebooks.w
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