A university is trying to determine what price to charge for tickets to football games. At a price of $27 per ticket, attendance averages 40 comma 000 people per game. Every decrease of $3 adds 10 comma 000 people to the average number. Every person at the game spends an average of $6.00 on concessions. What price per ticket should be charged in order to maximize revenue? How many people will attend at that price?

ticket price is 27 -3(3)= $18 , and Number of people = 40,000+10,000(3)=70,000 .

Step-by-step explanation:

We start the equation with (27-3x).  We don't know how many times we're subtracting $3 from the price.  This is multiplied by (40,000+10,000x). 

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This represents the amount of money for tickets multiplied by the amount of people.  We still need to add the amount of concessions.  Since (40,000+10,000x) represents the number of people, we multiply that by $6.00.This gives us:

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Differentiating this w.r.t x :

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⇒

⇒ ,

⇒ , { Rounding off }

So, ticket price is 27 -3(3)= $18 , and Number of people = 40,000+10,000(3)=70,000 .

answer: sine

step-by-step explanation:

we have three similar triangles, because each has a right angle and shares an angle.   let's write the angles in order: opposite to short leg, long leg, hypotenuse.

cab similar to bad similar to cbd

or as ratios,

ca: ab: cb = ba: ad: bd = cb: bd: cd

we also know

ac = ad + cd

(ad+cd): ab: cb = ba: ad: bd = cb: bd: cd

(ad+cd)/cb=cb/cd

we have cb=6, ad=5 and seek x=cd.

we reject the negative root and conclude x=4

answer: 4