CPhill

Correct, Tiddle  !!!!

tan 3x = 1

The tangent is equal to 1 at pi/4, 5pi/4, 9pi/4, 13pi/4, 17pi/4 and  21pi/4

Dividing each by 3 we have

pi/12, 5pi/12, 9pi/12 (3pi/4), 13pi/12, 17pi/12 and 21pi/12

Yeah......ya' gotta' watch them sneaky teachers..........!!!!!

I can't even say that fast one time, jilllybean !!!!

-3 x +12>-6    subtract 12 from both sides

-3x > -18        divide both sides by -3 (remember that we have to "reverse" the inequality sign when we divide by a negative !!!).....so we have......

x < 6

Or that you can't have a negative value under an even root........

OK...so we have

2.5 = 10(1 - e^k5)   divide both sides by 10

.25 = 1 - e^k5          rearrange

 e^k5    =  1 -.25

e^k5  = .75     take the ln of both sides

ln e^k5   = ln .75      and by  log property, we can write

k5  = ln.75            divide both sides by 5

k =ln.75 / 5 = -.0575

For $700 of expenditures, we have

S = 10(1 - e^(7*-.0575) ) =  about 3.3135 or about 3314 units

(Actually...I rounded "k"....the answer is really about 3315 units !!)

I don't see any thing "tricky" about it, either..... (???)

With one gallon it travels 10 * 5280 ft = 52800 ft

One ounce is 1/128th of a gallon, so it travels 1/128th of 52800ft = 412.5 ft

I like that, Melody........I'm gonna' steal that one from you....!!!!!