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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".]
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
How did they get an answer of 4.24899(-6) the question isc=4d(-1)/3.b. I now i substitute 23,245 for d and 13.5 for b, but don''t understand how they got this answer?
we are going to fence into a rectangular field & we know that for some cause we desire the field to have an enclosed area of 75 ft2. We also know that we desire the width of the fi
.1.Write your birth date or the birth date of someone in your family as mm/dd/yy. (Example: March 13, 1981 is written 3/13/81, and November 7, 1967 is written 11/7/67). ?Now le
6x^3+3x^2-18x
the weight of a body above the surface of earth varies inversely with the square of the distance from the center of the earth. if maria weighs 125 pounds when she is on the surface
how can we solve if the given is negative?
In this definition we will think of |p| as the distance of p from the origin onto a number line. Also we will always employ a positive value for distance. Assume the following num
what is the sum of 7/9 - 1/3
64n^2-1
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