The number of tickets sold each day for an upcoming performance of Handel's Messiah is given..........? by N(x)=-0.3x^2+8.4x+10, where x is the number of days since the concert was first announced. When will daily tickets sales peak and how many tickets will be sold that day? Ticket sales will peak days after the concert was fist announced. The number of tickets sold on that day will be .
.3 x^2 -8.4 x = -n + 10
x^2 - 28 x = -3.33 n + 33.33
x^2 - 28 x + 14^2 = -3.33 n + 33.33 + 196
(x-14)^2 = -3.33 n + 229.33
so x = 14 days
then
3.33 n = 229.33
n = 69
To find the day on which daily ticket sales will peak and the number of tickets sold on that day, we need to determine the vertex of the quadratic equation N(x) = -0.3x^2 + 8.4x + 10.
The vertex of a quadratic equation in the form of y = ax^2 + bx + c is given by the x-coordinate of the vertex, which is given by the formula x = -b / (2a).
In this case, a = -0.3 and b = 8.4. Plugging these values into the formula, we get:
x = -8.4 / (2 * -0.3)
x = -8.4 / -0.6
x = 14
So, the number of tickets sold will peak 14 days after the concert was first announced.
To find the number of tickets sold on that day, we substitute x = 14 into the equation N(x):
N(14) = -0.3(14)^2 + 8.4(14) + 10
N(14) = -0.3(196) + 117.6 + 10
N(14) = -58.8 + 117.6 + 10
N(14) = 68.8
Therefore, the daily ticket sales will peak 14 days after the concert was first announced, and the number of tickets sold on that day will be 68.8 tickets.
To find out when daily ticket sales will peak and how many tickets will be sold on that day, we can use the given equation N(x) = -0.3x^2 + 8.4x + 10.
The peak of the function occurs at the vertex of the parabolic equation. The x-value of the vertex can be found using the formula x = -b/2a. In this case, a = -0.3 and b = 8.4. Plugging these values into the formula, we get:
x = -8.4 / (2 * -0.3)
x = -8.4 / -0.6
x = 14
So, the peak of the ticket sales will occur 14 days after the concert was first announced.
To find out how many tickets will be sold on that day, we need to plug the x-value (14) back into the equation N(x):
N(14) = -0.3(14)^2 + 8.4(14) + 10
Now, we can calculate the value:
N(14) = -0.3(196) + 117.6 + 10
N(14) = -58.8 + 117.6 + 10
N(14) = 68.8
Therefore, on the day that daily ticket sales peak (14 days after the concert was first announced), approximately 68.8 tickets will be sold.