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Perplex is building a skyscraper in New York City. Every story of the building has the same height, except for the first floor.
The height of the skyscraper is 66.3m after 20 stories have been completed, and 95.1m after 29 stories have been completed.
- [4]
Find the height of each regular floor, and the height of the first floor.
The current tallest building in New York is 541m tall.
- [2]
Determine the number of stories Perplex will need to break this record.
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A king tells Sissa to pick his prize for inventing the game of chess. Sissa asks for 1 grain of rice on the first square on the board, 2 grains of rice on the second square, 4 grains of rice on the third square, and so on for every square on the 8×8 board.
The king laughs at him for picking a small reward for such a brilliant game.
- [2]
Write an expression for the number of grains of rice on the nth square of the board.
- [2]
Determine how many grains of rice Sissa asked for in total. Give your answer in the form c×10k, where 1≤c<10 and k∈Z.
6796 grains of rice costs $1, and a kilogram of gold costs $110,365.64.
- [2]
Find the mass of gold whose value equals that of the rice requested by Sissa.
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James is 65 and immortal. He has $2,000,000 in an investment account with an annual interest rate of 8%, compounding monthly.
James plans to withdraw $P every month forever.
Find the maximum possible value of P.
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Jim and Joanne each own their own personal computers, worth $1200 and $2500 respectively.
Jim's computer depreciates at a rate of 7% per year. It is also known that after 2 years, Joanne's computer is expected to be worth approximately $1800.
- [2]
Show that the annual depreciation rate of Joanne's computer is 15%.
Jim and Joanne's computers become equivalent in value n years after they are purchased.
- [2]
Determine, to three significant figures, the value of n.
- [1]
Comment on the validity of your answer to part (b).
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