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Q15 from Senior Mathematical Challenge 2018: A square is inscribed in a circle of radius 1. An isosceles triangle is inscribed in the square. What is the ratio of the area of this triangle to the area of the shaded region? (Requires Diagram))

Radius = 1, therefore diameter = 2Let x be the length of one side of the square.Using Pythagoras,x² + x² = 2²2x² = 4x = sqrt(2)Area of isosceles triangle = side...

Answered by Thomas H. • Maths tutor

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Solve e^(2x) = 5e^(x) - 6, giving your answers in exact form

Solve e^2x = 5e^x- 6e^2x - 5e^x+ 6 = 0(e^x)² - 5e^x<...

Answered by Thomas H. • Maths tutor

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Writing your UCAS Personal Statement...how can my application stand out from the crowd? (part 2)

I have been confronted with the power of autoimmune diseases first handed. I witnessed the vulnerability in my family, as they faced these conditions, desperately hoping for a cure that is yet to be disco...

Answered by • Personal Statements tutor

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Writing your UCAS Personal Statement...how can my application stand out from the crowd?

One of the most important generators of academic evolvement is doubt. As a student of the German School in Budapest, I have been exposed to a multicultural environment that challenged me to think more cri...

Answered by • Personal Statements tutor

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How many molecules of water are present in 5g sample?

In order to measure the amount of water molecules, we need to use following equation:
n = m / M where n is the amount of water molecules in molesm is the mass in grammesM is the molecular mass of wat...

Answered by • Chemistry tutor

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