A school council is planning a battle of the bands. They expect that 700 tickets will be sold if the ticket price is $5. A survey shows that if the ticket price is raised by $0.50, 50 fewer tickets will be sold. The situation can be modelled by y = -25p^2 + 100p + 3500, where y represents the revenue from ticket sales in dollars and p represents the number of times the ticket price is increased by $0.50.What is the maximum revenue the student council can make?

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

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answer: i literally just answered this question but they want me to do it again

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i believe the answer is 323 ft

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