Equations - July 2007, Stage 4&5

Problems

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Matchless

Stage: 3 and 4 Challenge Level: Challenge Level:2 Challenge Level:2

There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value, can you find that x, y pair ?

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Gutter

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

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Reasonable Algebra

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.

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Equation Attack

Stage: 5 Challenge Level: Challenge Level:1

The equation a^x + b^x = 1 can be solved algebraically in special cases but in general it can only be solved by numerical methods.

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Production Equation

Stage: 5 Challenge Level: Challenge Level:2 Challenge Level:2

Each week a company produces X units and sells p per cent of its stock. How should the company plan its warehouse space?

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Resistance

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Find the equation from which to calculate the resistance of an infinite network of resistances.