Legend tells of a Roman general who was so successful in his campaigns that the
ID: 3186343 • Letter: L
Question
Legend tells of a Roman general who was so successful in his campaigns that the emperor oftered the general his choice of reward. The general asked the emperor for all the silver that he could carry out of the imperial treasury in one month. The emperor agreed, but offered two conditions. On the first day, the general would receive 1 silver denarius. On the second day, he would turn in the previous day's coin and receive a coin valued at 2 denari. Each day, the general was to come to the treasury turn in the previous day's coin and the treasurer would mint a special coin that would be twice as heavy and worth twice as much as the coin the general got a day earlier. One denarius coin weighed about 0.006 kg. The largest object the general could carry or roll without help could weigh no more than 300 kg.Explanation / Answer
a. the value of coin= v(x)
day 1 v(1)=1
day 2 v(2)=21 = 1*2
day 3 v(3)=22 = 1*2*2
value of coin day x= v(x)= 2x-1
B. weight of coin =0.006kg
weight of coin day1 =0.006*1
weight of coin day2=0.006*21
weight of coin day3=0.006*22
weight of coin day x= 0.006*v(x)
in the question given that
=w*v(x) ? 300
=0.006*2x-1 ? 300
=2x-1 ? 300/0.006
=log 2x-1 ? log50000
=(x-1)log2? log50000
=(x-1)? log50000/log2
=x-1? 15.56
=x? 16.56
domain is 1?x?16
2. M(x)=mass of coin
m(1)=0.006
m(2)=0.012
m(16)=0.96
domain of m(x)= 0.006?x?0.96
3.(A) inequality of mass of coin M(x)
=x?0.006 and x? 0.96
=[0.006?x0.96]
4.
TOTAL value of coin = v(x)*total weight
= 16*300= 4800
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