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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".]
Carl and his dad I stonecarvers. Carl can cut the stone in five days. With his father''s help he can carve it in two days. How long would take his father to carve it alone. Bob c
Express the answer as an integer, simplified fraction, or a decimal rounded to two decimal places.
x+3=2 What is x?
how many does a rhombus have
``A car dealer has 22 vehicles on his lot. If 8 of the vehicles are vans and 6 of the vehicles are red, and 10 vehicles are neither vans nor red, how many red vans does he have on
How do you find perpendicular line equations?
{5x-4y=-21} {-2x+4y=18}
-6k+7k=
37/k-2-k-30
the sum of three consecutive odd integers is -195. find the three integers.
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