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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
4853 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
5505 Views

The roots of the equation z^3 + 2z^2 +3z - 4 = 0, are a, b and c . Show that a^2 + b^2 +c^2 = -2

If the roots of this cubic equation are a, b and c, then the equation can be written(z - a)(z - b)(z - c) = 0multiplying this out gives:z^3 - az^2 - bz^2 - cz^2 + abz + acz + bcz - abcgrouping terms with z t...
EH
7473 Views

Prove that sum(k) from 0 to n is n(n+1)/2, by induction

Proof by induction involves making an assumption, and using that assumption to prove that the consecutive case follows the pattern. The key to this is realising that most questions follow the same structure,...
NR
8731 Views

What is a complex number?

A complex number is a number that consists of two parts, a real part, like any number you have been dealing with since you started learning maths, and an imaginary number, often tagged along with a i or a j,...
PB
4670 Views