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# Rate of production of eggs

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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

https://brainmass.com/math/calculus-and-analysis/rate-production-eggs-3507

#### Solution Preview

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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

The expert finds the derivative of equation to determine maximum value. A machine produced eggs at a constant rate are given.

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