Explore BrainMass

Explore BrainMass

    Rate of production of eggs

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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

    © BrainMass Inc. brainmass.com December 24, 2021, 4:43 pm ad1c9bdddf
    https://brainmass.com/math/calculus-and-analysis/rate-production-eggs-3507

    SOLUTION This solution is FREE courtesy of BrainMass!

    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 ∫24 R(t) dt= 0 ∫24 (-10 cos (pi /12) t+ 10 ) dt

    =[ -(10 sin (pi /12) t)/ (pi /12) + 10 t ]0 24

    The first term is a sine function between o and 2 pi . Hence its value will be zero. The second term will give a value of 240.
    Thus 240,000 eggs will be produced in one day. ( The value of R(t) is in thousands of eggs)

    b)When are the eggs produced at the fastest rate .

    The maxima and minima can be found by differentiating the rate with respect to t and equating it to zero.

    d/ dt (-10 cos (pi /12) t+ 10 )=0

    or 10 sin (pi /12) t =0

    This is satisfied at t=0 and at t=12
    At t=0
    R(t)= (-10 cos (pi /12) X 0+ 10 )=0
    This is the minimum value.
    At t=12
    R(t)= (-10 cos (pi /12) X 12+ 10 )= -10 cos pi + 10= -10(-1) +10=20

    This is the maximum value.
    At noon (t=12) the eggs are produced at the fastest rate. (20, 000 eggs per hour)

    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).

    The machine is producing 240,000 eggs per day= 240,000/24= 10,000 eggs per hour
    R(t)= 10 t
    Where R(t) is in thousands of eggs per hour.

    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.

    Total no of eggs produced in a day=240,000
    Each chicken produces 20 eggs per day
    No of chicken= 240,000/20=12,000

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    © BrainMass Inc. brainmass.com December 24, 2021, 4:43 pm ad1c9bdddf>
    https://brainmass.com/math/calculus-and-analysis/rate-production-eggs-3507

    Attachments

    ADVERTISEMENT