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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".]
a3=8,a5=2, n=6 what is the sum
Taylor is 7 years younger than Lisa Lila is 3 x Lisa''s age if Lisa''s age is represented by x create an expression that represents the total age of all three girls
45
use the given matrix to preform the operation R1+2R2 and select the correct option. 3, -2, 1 1, -3, 4 1, -2, 0 a. 3, -2, 1 5, -8, 9 1, -2, 0 b. 3, -2, 1 2, -6, 8 13,
no questions help me
An artifact was found and tested for its carbon-14 content. If 86% of the original carbon-14 was still present, what is its probable age (to the nearest 100 years)? (Carbon-14 has
20 (4k+26) E k=1
Log(8)10 Find the approximation and exact value. log(5)317 Find the approximation and exact value
rectangular coordinate system
The sum of digits of a number is 9 If the digits of the number are reversed the number increases by 45 What is the original number?
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