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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".]
if log a-b/2=1/2 (log a + log b) show that a*a+b*b=6ab
Activity 1: Graphing To fill an order for Sizzlin'' Sauce sauces, you bought 1050 green peppers and 1200 hot chili peppers. • Write and graph a system of inequalities to represent
how solve the 2, x>-3
Find g(f(h(-3))). f(x) = 2x -- g(x) = -3x+4 -- h(x) = -2x-8
50 units for 580 dollars a month, rent increase 625.00 now only 47 units occupied
To find the calorie density (D) in calories per ounce of food that contains c carories and weight w ounces is given by D=C/w
3x/4 = 2
Working together Jack and Bob can clean a place in 30 minutes. On his own, Jack can clean this place in 50 minutes. How long does it take Bob to clean the same place on his own?
Aubrey is 5 years younger than her brother is and three years ago the sum of their ages was 23 years. How old is each now?
Prove that cosets of an ideal I in a ring R are disjoint or equal
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