SOLUTION: The number of tickets sold each day for an upcoming performance of handel's messiah is given by N(x)=-0.3x^2+6x+10, where x is the number of days since the concert was first announ

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: The number of tickets sold each day for an upcoming performance of handel's messiah is given by N(x)=-0.3x^2+6x+10, where x is the number of days since the concert was first announ      Log On


   



Question 329394: The number of tickets sold each day for an upcoming performance of handel's messiah is given by N(x)=-0.3x^2+6x+10, 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?
Found 2 solutions by stanbon, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The number of tickets sold each day for an upcoming performance of Handel's messiah is given by N(x)=-0.3x^2+6x+10, 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?
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N(x)=-0.3x^2+6x+10
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max occurs when x = -b/2a = -6/(2*-0.3) = -6/-0.6 = 10 (max sales on day 10)
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N(10) = -0.3(10)^2+6*10+10 = 40 tickets will be sold on day 10
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Cheers,
Stan H.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
The minus sign in front of the x%5E2 term tells me
that the curve has a max at the top, not a min at the
bottom. What is needed is to find the point MAX(x,N)
For an equation of the form y+=+a%2Ax%5E2+%2B+b%2Ax+%2B+c,
x%5Bmax%5D is at -b%2F%282a%29. For the given equation:
N%28x%29+=+-.3x%5E2+%2B+6x+%2B+10
b+=+6
a+=+-.3, so
x%5Bmax%5D+=+-6%2F%282%2A%28-.3%29%29
x%5Bmax%5D+=+10
Now I need to find N%5Bmax%5D
N%28x%29+=+-.3x%5E2+%2B+6x+%2B+10
N%5Bmax%5D+=+-.3%2A100+%2B+6%2A10+%2B+10
N%5Bmax%5D+=+-30+%2B+60+%2B+10
N%5Bmax%5D+=+40
Ticket sales will peak on the 10th day and 40 tickets will be sold that day
Here's a graph of equation:
+graph%28+500%2C+500%2C+-1%2C+20%2C+-5%2C+50%2C++-.3x%5E2+%2B+6x+%2B+10%29+