3. During the week, a local car wash station has a happy hour special when clients get the most popular exterior wash for a special fee based upon car size. For compact cars, the charge is $8.00. For full-sized cars, the charge is $10.00. For SUVS, the charge is $12.00. For vans, the charge is $15.00. For trucks, the charge is $20.00. Part A: Explain how you can represent this situation with a piecewise- defined function.

no i do not : ( what is it?

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