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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".]
what is 500 times 70
The average U.S. citizen consumes about 2.5 × 102 L of water per day for various uses. In 2013, there were about 3.16 × 108 U.S. citizens. About how many kiloliters of water were c
7w+2=3w+94
-2(x-4)+3(2x-1)
A college student invested part of a $25,000 inheritance at 7% interest and the rest at 6%. If his annual interest is $1,670 how much did he invest at 6%? If I told you the answe
How many ways can five people line up if two of them cannot sit together?
is 55 an integer
Also, as x obtain very large, both positive & negative, the graph approaches the line specified by y = 0 . This line is called a horizontal asymptote. Following are the genera
if a-b equals 73 what is a
five years ago,you bought a house for $151,000, with a down payment of $30,000, which meant you took out a loan for $121,000. Your interest rate was 5.75% fixed. You would like t
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