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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".]
In a certain Algebra class there is a total 350 possible points. These points come through 5 homework sets which are worth 10 points each and 3 hour exams that are worth 100 points
How do you find y & x equal with -4x+y=6 and -5x-y=21
how to use the factor theorem
1. Construct a truth table for the following Boolean expressions: a) ABC + A'B'C' b) ABC + AB'C' + A'B'C' c) A (BC' + B'C) 2. Simplify the following expressions:
Graphing and Functions Graphing In this section we have to review some of the fundamental ideas in graphing. It is supposed that you've seen some graphing at th
r+7= r=3
We can also indicate a strict mathematical/formula definition for absolute value. It is, It tells us to look at the sign of p & if it's positive we just drop the absolute
3_-1 x+2 --- 1+_2 x+2
y = 5x, solve for x
a rectangular table is five times as long as it is wide. if the area is 45ft2, find the length and width of the table..
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