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Suppose you are given twelve coins all identical in appearance. You are told that one coin is counterfeit and weighs a slightly different amount from the remaining 11. You are given a simple two-arm balance to weigh the coins. Determine which coin is the counterfeit coin in as few weightings as possible. Does your method also allow you to state whether the counterfeit coin is heavy or light?
Do not explain your answers in English. Please find system of equations questions in your textbook or MML for us. Try your best to solve.
He has 790 feet of fencing available to complete the job. What is the largest possible total area of the four pens?
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A rancher has 30,000 linear feet of fencing and wants to enclose a rectangular field and then divide into four equal pastures with three internal fences parallel to one of the rectangular sides. What is the maximum area of each pasture?
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Suppose payments were made at the end of each month into an ordinary annuity earning interest at the rate of 6%/year compounded monthly. If the future value of the annuity after 12 yr is $65,000, what was the size of each payment?
A metal storage tank with a mximum volume of 500 m^3 is to be constructed in the shape of a right circular sylinder surmounted by a hemisphere. What radial and height dimensions will require the least amount of material?
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