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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 Fritzes are buying a house that sells for $185,000. The bank is requiring a minimum down payment of 15% for a 30-year mortgage at 5.2% interest. Find (a) the amount of the down
a stack of disks is 0.5cm thick.how many disk each at 0.125cm thick are in a stack?
whats the answer to y=4-9x
(M^1/4n^1/2)^2(m2n3)^1/2
what is 2+2?
how to find hcf easily
r-17
2 bicyclist riding on a circular track start at the same time. one can make it around the track in 8 min. the other takes 10 min. how long will it take the faster bicyclist to catc
$2.350 is invested in account paying 9% compound semiannually. how much will the account be worth after 8yrs
3x+y=-2 6x+2y=10
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