Problema Solution
The number of tickets sold each day for an upcoming performance of Handels Messieah is given by N(x)=-0.6x^2+18x+11, where x is the number of days since the concert was first announced, When will daily ticket sales peak and how many tickets will be sold that day?
When will daily ticket sales peak ----------
How many tickets will be sold that day------
Answer provided by our tutors
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The given equation:
N(x)=-0.5x^2+11x+13
is a parabola that opens downward -- because the coefficient associated with the x^2 term is negative. So, if you find the "vertex" it will give you the maximum.
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Finding the "axis of symmetry" will give you the "number of days" after announcement that the ticket sales reached its peak:
x = -b/(2a)
x = -11/(2(-0.5))
x = -11/(-1)
x = 11 days
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To find the number of tickets sold, plug in the value above back into:
N(x)=-0.5x^2+11x+13
N(11)=-0.5(11^2)+11(11)+13
N(11)=-0.5(121)+(121)+13
N(11)=-60.5+134
N(11)=73.5
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Ticket sales will peak 11 days after the concert was first announced. The number of tickets sold on that day will be 73.