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anonymous
 one year ago
The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars each:
P(n) = 250n^2 + 2,500n  5,250
Part A: What are the zeroes of the above function, and what do they represent? Show your work.
anonymous
 one year ago
The following function represents the profit P(n), in dollars, that a concert promoter makes by selling tickets for n dollars each: P(n) = 250n^2 + 2,500n  5,250 Part A: What are the zeroes of the above function, and what do they represent? Show your work.

This Question is Closed

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1What does n represent?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1precisely, n, is a price per ticket.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1What does P(n) represent?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Yes, when P(n) is 0, that means that the profit is zero (i.e. made nothing), right?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1The xintercepts of this function are the values of n (or the value of the price per ticket) with which the P(n) (or the profit) is 0. (There are going to be 2 xintercepts)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, if you find the xintercepts, you are going to find the 2 possible values of a price per ticket with which the promoter will NOT profit (but will not lose).

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, do you see what these xintercepts would mean?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Ok, now you have to solve for these xintercepts.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the x intercepts are 3 and 7?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So, when the ticket costs 3$ or 7$ , then the promoter doesn't gain or lose.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1when the *average* ticket I should say

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Well, all you had to do is to find these zero (these xintercepts), and to then say what these xintercepts represent in your situtation.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1you found x=3, and x=7 ((( and that is correct ))) now you have to say what do these intercepts mean/do/represent?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1just say what we have agreed on in the beginning.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0can you help me with part B?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I can try my best with it:)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Part B: Find the maximum profit by completing the square of the function P(n). Show the steps of your work.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1``` SIDE  NOTE: Most people would say that this question requires calculus, but in a case of a parabola (a quadratic does not). (this what most people say is a mistake). ``` ALL YOU GOT TO DO: You have to write your P(n) in a vertex form, and the vertex is going to be the maximum.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1Let me see.... i wil be typing, and if it is right I will post the work, and if it is not, then I will ask you to redo it and follow along with me.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1hope that is fair.

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large\color{black}{ \displaystyle P(n) = 250{\rm n}^2 + 2,500{\rm n}  5,250 }\) \(\large\color{black}{ \displaystyle P(n) = 250({\rm n}^2 10{\rm n})  5,250 }\) \(\large\color{black}{ \displaystyle P(n) = 250({\rm n}^2 10{\rm n}+2525)  5,250 }\) \(\large\color{black}{ \displaystyle P(n) = 250({\rm n}^2 10{\rm n}+25)+(250)(25)  5,250 }\) \(\large\color{black}{ \displaystyle P(n) = 250({\rm n}^2 10{\rm n}+25)+1000 }\) \(\large\color{black}{ \displaystyle P(n) = 250({\rm n}5)^2+1000 }\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes, that is correct

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1oh, you graphed it... good, but it is very good (I would insist that even required) to know that without graphing.... in any case though, lets do a little review of what you have actually found just now,

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the axis of symmetry would be 5 right? (Thats part C)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yes part C is correct

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1now the review of what does the vertex of (5,1000) actually mean in this case.

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thats the maximum about of profit the promoter can make?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1that is you are refering to the point to a 5 or a 1000 ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.01000 makes more sense 1 think

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1and what does 5 mean, can you tell me?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the amount the tickets cost?

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1So when the average ticket costs 5$, you get a maximum profit of 1000

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1A quite small, if not miserable profit in a real life situation... but won't be talking about a real life situation because such situations are never modeled with quadratics in real life....

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1yeah, so you got any questions regarding any of the PARTS ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0as usual you're the most helpful person on the whole site. Thanks!

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1\(\large{\bbox[5pt, cyan ,border:2px solid black ]{ \rm Thanks! }}\)

SolomonZelman
 one year ago
Best ResponseYou've already chosen the best response.1I wouldn't say I am most helpful, but won't deny some use.; you are always welcome!
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