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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".]
Alex lives .4 miles from the park, beth lives .8 miles from the park. To run equal distances Alex runs 8 times around the park and Beth run 6 times around the part. Write an equati
Ask questionteachme how to graph points convert fractions to deciams #Minimum 100 words accepted#
A cyclist bikes 12 blocks south and 5 blocks east, and rides back along a diagonal path. what is the total distance that he travled? show the work
has a y-intercept of 5 and a slope of 2/3. solve for the standard equation
(2 X2)3 BY BB
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Express commuter train #12 leaves the downtown station and travels at an average speed of miles per hour towards the north-side station, which is miles away. Express commuter train
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2x-1=10 I got 9/2 but i''m not sure if that is really right
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