how can i solve this problem? The number of tickets sold each day for a upcoming peformance of Handel's Messiah is given by N(x)=0.4x^2+8x+11, where x us 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.
Your School Subject is Math, not "college."
since you labeled it "college" I will assume you know Calculus.
N(x)=0.4x^2+8x+11
N'(x) = .8x + 8
= 0 for a max/min of N
.8x + 8 = 0
x will be a negative, so your problem makes no sense.
your function is an upwards parabola so it has a minimum, not a maximum.
perhaps you have a typo and the first term is -.8x^2
then the above result becomes
-.8x + 8 = 0
x = 10
and N(10) = -.8(100) + 80 + 11
= 11
11 tickets sold ????
There are more people singing Hallelujah.
Apart from the subject, that equation isn't going to peak for x > 0. I think you may have an error in the question.
To find out when the daily ticket sales will peak and how many tickets will be sold that day, we need to determine the maximum point of the given function. This can be achieved by finding the vertex of the quadratic equation represented by the function N(x).
The vertex of a quadratic equation in the form of ax^2 + bx + c can be calculated using the formula x = -b / (2a). In our case, a = 0.4 and b = 8.
Let's substitute these values into the formula to find the x-coordinate of the vertex:
x = -8 / (2 * 0.4)
x = -8 / 0.8
x = -10
The x-coordinate of the vertex is -10, which represents the number of days since the concert was first announced. However, since the concert was announced in the future, the value of x = -10 is not relevant for determining the peak ticket sales. Instead, we need to find the positive root of the equation, which represents the number of days after the announcement.
To determine the number of tickets sold on the day of the peak, we can substitute the x-coordinate of the vertex (which we found as -10) into the equation N(x).
Let's calculate the number of tickets sold on the day of the peak:
N(-10) = 0.4(-10)^2 + 8(-10) + 11
N(-10) = 4(100) - 80 + 11
N(-10) = 400 - 80 + 11
N(-10) = 331
Therefore, the number of tickets sold on the day of the peak will be 331.
To summarize:
- The daily ticket sales will peak on the day that is 10 days after the concert was announced.
- On that day, a total of 331 tickets will be sold.