1.Given dy = (y + 2)(y 3), answer the following questions: dx a) Identify the eq

Question

1.Given dy = (y + 2)(y 3), answer the following questions: dx

a) Identify the equlibrium values. Which are stable and unstable. (Equilibria are y = 2, 3, where 2 is stable and 3 is unstable)

b) Construct a phase line. Identify the signs of y and y.

c) Sketch several solution curves.

2.There are 8 performers who will present their comedy acts this weekend at a comedy club. How many different ways are there to schedule their appearances?
3.You volunteer to help drive children at a charity event to the zoo, but you can fit only 6 of the 14 children present in your van. How many different groups of 6 children can you drive?

Explanation / Answer

setting dy = (y + 2)(y 3) = 0, we get equilibrium values as  y = 2, 3

y = 2y-1

y"<0 for y = -2 hence it is stable

y">0 for y = 3hence it is unstable

2) answer is 8*7*6*5*4*3*2*1

3)C(n,r) = (n!)/(r!(n-r)!)

C(14,6) = (14!)/(6!*(14-6)!)

C(14,6) = (14!)/(6!*8!)

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