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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+3/4=41/3
Describe the property used to convert the equation from one line to the next: 8y-(8+6y)=20
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
what is the range of f(x)=2x+2
how do i solve 18=c+5 2
1/3h-4(2/3h-3)=2/3h-6
The United States is becoming more health conscious, and as a result,the problem of obesity has gotten more attention.The Body Mass Index (BMI), relates a person’s height and weigh
A toy manufacturer develops a formula to determine the demand for its product depending on the price in dollars. The formula is , where P is the price per unit and D is the number
-3t^2+15t-18
Simplify 3(x-2)to the second -2(x+1)
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