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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".]
x=y=3 , 2x-y=5
graph and identify the conic section and describe the graph and its lines of symmetry then find the domain and range 3y^2 - x^2 = 25
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
1/4-12
a^4b+a^2b^3
I am finishing a quadratic equation problem and I am left with 3 plus or minus the square root of 361 all over 2. what next?
Actually here we're not going to look at a general cubic polynomial. Here we are jsut going to look at f ( x ) = x 3 . Really there isn't much to do here other than only plugging
Not every linear system along with three equations and three variables utilizes the elimination method exclusively therefore let's take a look at another instance where the substit
what is 2+2?
How much of a 50% alcohol solution should we mix with 10 gallons of a 35% solution to get a 40% solution? Solution Let x is the amount of 50% solution which we need. It me
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