Two ships are sailing in the sea on the two sides of a lighthouse. The angle of elevation of the top of the lighthouse is observed from the ships are 30 degree and 45 degree respectively. If the lighthouse is 100 m high, the distance between the two ships is:

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if m=7-$4\sqrt{3}$,then find the value of $\sqrt{m}+\frac{1}{\sqrt{3}}$

Solve the following Mathematical Problems

A finance company declares that, at a certain compound interest rate, a sum of money deposited by anyone will become 8 times in 3 years. If the same amount is deposited at the same compound rate of interest, then in how many years will it become 16 times?

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In a cricket match, Team A scored 232 runs without losing a wicket. The score consisted of eves, wised and runs scored by two opening batsmen: Rick and Stew. The runs scored by the two batsmen are 26 times wide. There are 8 more byes than wide. If the ratio of the runs scored by Rick and Stew is 6 : 7, what were the runs scored by Rick?

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A group of students hired a bus for TK. 3000 for going to a picnic. They had an understanding that each participant would share the charge is equal amounts. But because of 10 students were not turning up, the charge per student increased by TK. 10 over the initial estimate. What was the number of students who originally registered for the picnic?

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After traveling 108 km, a cyclist observed that he would have required 3 hours less if he could have traveled at a speed 3 km/hr more. At what speed did he travel?