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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".]
how do you factor 8y^2-23y+15
Example 2 Solve out following systems of equations. 3x + y - 2z = 2 x - 2 y + z = 3 2x - y - 3z = 3 Solution Firstly write down the augmented matrix for this syst
81x^5-49x^3=0
Two cars are 500 miles apart & directly moving towards each other. One car is at a speed of 100 mph and the other is at 70 mph. Supposing that the cars start at the same time how
Solving the following inequalities. Give both inequality and interval notation forms of the solution. -2 ( m - 3) Solution Solving out single linear inequalities follo
find the percent up or down: 75 to 110
I need to do a coursework for math but do not know what to do?
I do not know how to do this
Write the equation of the circle in standard form. Find the center, radius, intercepts, and graph the circle. ??2+??2+16??-18??+145=25.
The difference of two numbers is 18. The larger number is four more than twice the smaller. What are the numbers?
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