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The equation of a curve is y = x^2 - 5x. Work out dy/dx

This is an example of differentiation. This can be useful in many concepts, one being finding the gradient of a line or curve at a certain point. To differentiate these types of equations, the rule is to mul...
VL
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Prove by induction that 11^n - 6 is divisible by 5 for all positive integer n.

Let P( n ) be the statement that 11 n - 6 is divisible by 5. BASE CASE : L et n = 1. This gives 11 1 - 6 = 5 , obviously divisible by 5, therefore we know that P(1) is true. HYPOTHOSIS STEP : Assume that P( ...
SH
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What is the complex conjugate?

The complex conjugate of a complex number is a number for which the real part is the same and for which the imaginary part has the same magnitude but opposite sign. e.g. the complex conjugate of 6+7i is 6-7i...
ES
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Find the displacement function if the acceleration function is a=2t+5. Assume a zero initial condition of displacement and v=8 when t=1.

Integrating the acceleration function gives the velocity function v, as below: v = t 2 +5t +C 1 , where C 1 is a constant. Integrating the velocity function gives the displacement function x, as below: x = t...
JH
4890 Views

Given that the equation x^2 - 2x + 2 = 0 has roots A and B, find the values A + B, and A * B.

There are two obvious approaches here: 1. Solve the equation x 2 - 2x + 2 = 0 to find A and B and then calculate the required values. 2. Or we can use the quicker method of analysing what it means for the ex...
SP
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