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Given that y is directly proportional to square root of x and that y = 20 when x = 49 find an expression to represent x and y.

y = k √x20 = k √49 20/7 = ktherefore y = 20/7 √x

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Two ordinary fair dice are rolled. Work out the probability that both land on a value less than 4.

The probability of an event= Number of ways an event can occur/ Total number of possible outcomesBoth dices land on values less than 4. This means they both can be 1,2 or 3. Therefore, number of ways the ...

Answered by George S. • Maths tutor

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g(x) = ( x / (x+3) ) + ( 3(2x+1) / (x^2 + x - 6) ). Show that this can be simplified to: g(x) = (x+1) / (x-2).

Step 1: The denominator of the right-hand fraction is quadratic, so we can factorise this to (x+3)(x-2). This looks similar to the denominator of the left-hand fraction, suggesti...

Answered by Amar S. • Maths tutor

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A curve has the equation: x^2(4+y) - 2y^2 = 0 Find an expression for dy/dx in terms of x and y.

First of all expand the brackets in the equation. Then you can differentiate each term with respect to x. As one of the terms will be a product of x and y the product rule must be used to find the differe...

Answered by Carlotta M. • Maths tutor

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Prove that, if 1 + 3x^2 + x^3 < (1+x)^3, then x>0

(1+x)^3 = x^3 + 3x^2 + 3x + 1 (Can be calculated straight away by binomial method or by multiplying brackets individually)
if (1+x)^3 > 1 + 3x^2 + x^3then: x^3 + 3x^2 + 3x + 1 > 1 + 3x^2 +...

Answered by Vigneswaran T. • Maths tutor

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