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A cuboid of height 5 cm has a base of side 'a' cm. The longest diagonal of the cuboid is 'L' cm. Show that 'a' = SQRT[ (L^2 - 25)/2]

A cuboid is made of squares and rectangles, with the diagonal 'L' connecting opposite corners of the 2 square faces. As the cuboids corners are all right angles, all the diagonals form right angled triang...

Answered by Joshua P. • Maths tutor

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A conical vase of base radius 5cm and height 20cm is filled with 200ml of water, how high is the water level? Give your answer to 3 significant figures.

Answer: 2.96 cm

Equations used: Volume of a cone = (base area x height) / 3 ; Base Area = pi x radius²

Volume of whole vase = (pi x 5² x 20)/3 = 523.6 cm³

Answered by Ian C. • Maths tutor

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Factorise the following equation: 2x^2 + 8x + 8

The first step in factorising is to look for a 'common factor'. A common factor is a number or letter that all the values have in common.

All the integers (numbers) in this equation can be divided...

Answered by Ellen K. • Maths tutor

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How do I find the roots of a quadratic equation?

There are a few methods you can use. Here are two methods: 1) Inspection. Say we have the equation x²+4x+3. We can find two numbers which multiply together to make 3 but add together to make 4....

Answered by Daniel E. • Maths tutor

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