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 If n (A) = 6 and n (B) = 9, then the maximum number of elements in AB is

Find the inverse Laplace Transform of the following functions:

a) s/(s²-4)

b) 10/(s-2)²+4

c) 10s/(s+1)²+10

d) 2/s²+6s+8

e) 1/s(s-2)

f) 1/s²(s²+1)

show that the equation has exactly one real root 2xcosx0

Slyvia likes playing badminton with her friends. Her utility function for playing badminton
every week is given by
U(t) = 11t - 21^2 ( 21 raised to 2)
where t is measured in hours. They play on a badminton court, which they can rent per
hour. Suppose the current price to play on the badminton court is $2.50 per hour.

1.How many hours should Fang play if she wishes to maximise her utility?

2. Explain what we mean by the principle of diminishing marginal utility. Does the
principle apply in Fang's case? Explain why.

3. In a diagram with income in pound sterling on the horizontal axis and quantity
on the vertical axis, show the relationship between Fang's budget and the
number of hours that would maximise her consumer surplus.

Half of the pens at a stationary shop are blue. 1/8 of the remaining pens are red, while the remaining pens are black. If there are 210 more black pens than red pens, how many pens are there altogether?