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# Rate of production of eggs

Eggs are produced at a rate of R(t)eggs per hour,where t=0 represents 12:00 midnight and R(t)(in thousands of eggs) is :-

R(t)= -10cospi/12t+10

a)how many eggs are produced in one day.

b)When are the eggs produced at the fastest rate

c)A machine can produce eggs at a constant rate. At the end of 1 week the same number of eggs are produced by the machine . What rate is the machine producing eggs in terms of R(t).

d)Each chicken produces the same amount of eggs on one 24hr period.how many chickens are there if each chicken can produce 20 eggs per day

#### Solution Preview

The signs etc are preserved in the word file. Take a look in the word file.
Eggs are produced at a rate of R(t)eggs per hour,where t=0 represents 12:00 midnight and R(t)(in thousands of eggs) is :-

R(t)= -10 cos pi/12 t+10

a)how many eggs are produced in one day.

No of eggs produced can be found by integrating R(t) from time t=0 to t=24

0 &#8747;24 R(t) dt= 0 &#8747;24 (-10 cos (pi /12) t+ 10 ) dt

=[ -(10 sin (pi /12) t)/ (pi /12) ...

#### Solution Summary

Finds the derivative of equation to determine maximum value.

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