Trash collection from music festivals
the number of tickets sold for a music
festival, x, is linearly related to the number
of pounds of trash, y, that must be cleaned
up afterwards. the organizers of an
upcoming music festival expect to sell
approximately 1,000 tickets.
pounds of trash
approximately how much trash will need to
be collected after the music festival?
00 200 300 400 500 600 700 800 900 1000
number of tickets sold

answer: sorry i can't you.

step-by-step explanation:

what is the original number? you forgot to add it.

answer: 204

step-by-step explanation:

we are told that the revenue is

x⋅(4080−10x)=−10x^2+4080x

this is a quadratic function, so to maximize it we should find the x-value of its vertex. recall that the x-value of the vertex of the parabola ax^2+bx+c is given by the formula −b/2a.

so in this case, we have a=−10 and b=4080, so the x-value of the vertex is

−b/2a= −(4080)/2(−10)=204

step-by-step explanation:

we have

using a graphing tool

see the attached figure

this is a quadratic equation (vertical parabola) open up

the vertex is a > vertex

the domain of the function is all real > interval (-∞,∞)

the range of the function is the > [-6.125,∞)

the function has two x->   and

the function is increasing over the > (0.25,∞)

the function is decreasing over the > (-∞,0.25)