the number of tickets for an upcoming concert is given by N(x)=-0.5x^2+14x+10 where x is the number of days since the concert was announced. When will the tickets peak and how many tickets will be sold that day?
If you are in a Calculus class, then find the derivative, set it equal to zero and solve.
If not, then you will have to complete the square
let me know which method you will need help with.
I am in Algebra Thank you for your help
To find out when the tickets will peak and how many tickets will be sold on that day, we need to determine the maximum value of the function N(x)=-0.5x^2+14x+10. This can be done by applying techniques from calculus.
Step 1: Identify the coefficient values of the equation N(x)=-0.5x^2+14x+10.
- The coefficient of x^2 is -0.5
- The coefficient of x is 14
- The constant term is 10
Step 2: To find the x-coordinate of the peak, you can use the formula x = -b/2a, where a is the coefficient of x^2 and b is the coefficient of x in the equation N(x)=-0.5x^2+14x+10.
- Substitute the values into the formula: x = -(14) / (2*(-0.5))
- Simplify: x = -14 / -1
- Final result: x = 14
Step 3: To determine the number of tickets sold on the day of the peak, substitute the value of x (14) into the equation N(x)=-0.5x^2+14x+10.
- Substitute x = 14 into the equation: N(14) = -0.5(14)^2 + 14(14) + 10
- Simplify: N(14) = -0.5(196) + 196 + 10
- N(14) = -98 + 196 + 10
- N(14) = 108 + 10
- Final result: N(14) = 118
Therefore, the tickets will peak on the 14th day since the concert was announced, and 118 tickets will be sold on that day.