N(x)=-0.6^2+15.6x+12, 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 peak-
number of tickets sold-
assume you mean:
N(x)= -0.6 x^2 + 15.6 x + 12
+0.6 x^2 - 15.6 x = -N + 12
x^2 - 26 x = -1.6666 N + 20
x^2 - 26 x + 169 = -1.6666 N + 189
(x-13)^2 = -1.6666 N + 189
(x-13)^2 = -1.6666 (N - 113.4)
13 days and 113 tickets
If you know calculus
dN/dx = 0 at max = -1.2 x + 15.6
1.2 x = 15.6
x = 13
To find the day when daily ticket sales peak and the number of tickets sold on that day, we need to analyze the given equation.
The equation provided, N(x) = -0.6^2 + 15.6x + 12, represents a quadratic function. The general form of a quadratic function is f(x) = ax^2 + bx + c, where a, b, and c are constants.
In our equation, the coefficient of the x^2 term is -0.6^2, which simplifies to -0.36. The coefficient of the x term is 15.6, and the constant term is 12.
The peak of a quadratic function occurs at the vertex of the parabola. To find this vertex, we can use the formula x = -b/2a. In our case, a = -0.36 and b = 15.6.
x = -15.6 / (2 * -0.36)
x = 21.67
Rounding this value to the nearest whole number, we find that the peak of the ticket sales occurs on the 22nd day since the concert was first announced.
To determine the number of tickets sold on that day, we substitute x = 22 into the N(x) equation:
N(22) = -0.6^2 + 15.6 * 22 + 12
N(22) = -0.36 + 343.2 + 12
N(22) = 354.84
Therefore, on the 22nd day, the ticket sales would peak, and approximately 355 tickets would be sold on that day.