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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 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
3.4% as a decimal
A company makes and sells notebook computers. The company’s cost function in thousands of dollars is C(x) = 0.3x + 100, and the revenue function in thousands of dollars is R(x) = 0
i need help on quadraics formulas
In the earlier two sections we've talked quite a bit regarding solving quadratic equations. A logical question to ask at this point is which method has to we employ to solve a giv
if there are 12 boys how many girls will it be
Example Evaluate each of the following logarithms. (a) log1000 (b) log 1/100 (c) ln1/e (d) ln √e (e) log 34 34 (f) log 8 1 Solution In order to do
How do you do out a substitution problem and then graph it?
3/8=n/12
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