The profit function, y, for selling x shirts is given by the equation y=-0.1x^2+10x. what is the maximum value of the profit, y?

24: 56

step-by-step explanation:

24 can be divided into 3 and 56 can be divided into 7, where as all the other ratios can't.

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