Question 305284: Word problem: The number of tickets sold each day for an upcoming performing of Handel's Messiah is given by N(x)=-0.4x^2+8.8x+13, 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?
Ticket sales will peak _____ days after the concert was first announced.
The number of tickets sold on that day will be ______. (round to the nearest integer).
I don't understand what they want me to do or the formula to fill out this problem.
Found 2 solutions by Theo, ikleyn:
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! This formula is a quadratic equation of the form:
n(x) = ax^2 + bx + c
The specific equation is:
n(x) = -.4x^2 + 8.8x + 13
This makes:
a = -.4
b = 8.8
c = 13
You solve this by finding the min/max point of the curve.
The min/max point of a quadratic equation is determined by the formula:
x = -b/2a.
Since b = 8.8 and a = -.4, this equation will become:
x = -8.8 / (2*(-.4) which becomes x = -8.8 / -.8 which becomes x = 11.
The max / min point will be at x = 11.
When x = 11, the value of n(x) will be determine by your equation of:
n(x) = -.4x^2 + 8.8x + 13 which will become:
n(11) = -.4*(11^2) + 8.8*11 + 13 which will become:
n(11) = 61.4
A graph of your equation of n(x) = -.4x^2 + 8.8x + 13 with the min/max point of y = 61.4 is shown below:
I placed a horizontal line at y = 61.4 in the graph to show you that the min / max point is at (11,61.4)
This min/max point is a max point because the sign of the coefficient of the x^2 term is negative.
Since y or n(x) represents the number of tickets sold, and since x = the number of days since the tickets went on sale, then the maximum number of tickets sold was 61.4 and this occurred on the 11th day.l
The question to be answered was:
Word problem: The number of tickets sold each day for an upcoming performing of Handel's Messiah is given by N(x)=-0.4x^2+8.8x+13, 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?
The answer to the question is:
Ticket sales will peak __11__ days after the concert was first announced.
The number of tickets sold on that day will be __61__. (round to the nearest integer).
Answer by ikleyn(52899)  (Show Source):
You can put this solution on YOUR website! .
Word problem: The number of tickets sold each day for an upcoming performing of Handel's Messiah is given
by N(x)=-0.4x^2+8.8x+13, 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?
Ticket sales will peak _____ days after the concert was first announced.
The number of tickets sold on that day will be ______. (round to the nearest integer).
I don't understand what they want me to do or the formula to fill out this problem.
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The problem is posed in a blatantly illiterate manner, as for many days
the formula yields non-integer quantities of tickets sold.
From a mathematical perspective and from common sense point of view, this is nonsense.
Meaningless problems cannot be solved; they must be appropriately corrected or thrown in the trash.
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