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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".]
A student rented a bicycle for a one-time fee of $12.00 and then a charge of $0.85 per day.She paid $28.15 for the use of the bicycle. How many days did she keep it?
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
Now let's move into the next technique for solving systems of equations. As we illustrated in the example the method of substitution will frequently force us to deal with fraction
9x^4-x^2=0 step by step
how do you factor 8y^2-23y+15
(f(x+h)-f(x))/h
If the rational number x= b/ c is a zero of the n th degree polynomial, P ( x ) = sx n + ...........+ t Where every the coefficients are
the sudbrook school play has a maximum of 700 tickets to sell.at least 300 tickets must be sold in advance. Advance tickets will be sold for $20.00 while the tickeys at the door wi
Question 1 [7 marks] The reduced row echelon form of ? ? ? ? ? ? ? ? ? ? ? ? 3 4 17 22 1 2 5 row a b A is equal to ? ? ? ? ? ? ? ? ? ? ? ? 0 0 0 0 0 0 1 2 1 2 0 3 R . (a) What can
__5n^2)_______ multiplied __(3)____ (3n^2) (n)
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