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Solve the simultaneous equations: y = x - 2 and y^2 + x^2 = 10

y = x - 2 y 2 + x 2 = 10 Subsitutute the top equation into the second equation: (x-2) 2 + x 2 = 10 Expand out the brackets and simplify: x 2 - 4x + 4 + x 2 = 10 2x 2 - 4x - 6 = 0 x 2 - 2x - 3 = 0 Factorise t...
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Answered by Iman R. • Maths tutor
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How do I differentiate (2x+1) / (3x^2 - 5)?

This is a typical example where the quotient rule is required to answer the question. This is clear because the function is made up of two other functions of x, one is the numerator and the other is the deno...
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Answered by Sophie T. • Maths tutor
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A geometric progression has first term 3 and second term -6. State the value of the common ratio.

3/-6 = -2
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Answered by Elizabeth H. • Maths tutor
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The probability distribution of the random variable X is given by the formula P(X = x) = 0.09+0.01x^2 for x= 1,2,3,4,5 ). Find E(X).

The expected value of a discrete variable is defined as: E(X) = ∑x*P(X=x) (for all possible values of x, in this case x = {1,2,3,4,5} ) (next, we will expand the summation and substitute in the values given,...
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Answered by Robin H. • Maths tutor
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Integrate cos(2x)

The intergral for cosx is sinx, but '2x' must be considered. When differentiating a sinx/cosx function, the '2x' would be differentiated separately and placed in the front (multipling). So when intergating y...
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Answered by Gold O. • Maths tutor
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