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solve the simultaneous equation 2y + x = 8 and 1 + y = 2x

The aim of the question is to work out the values for x and y in order to make both equation correct. Therefore the best approach is to try to isolate one of the letters first. step 1. rearrange both equatio...
DE
Answered by Dina E. • Maths tutor
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A particle of mass m moves from rest a time t=0, under the action of a variable force f(t) = A*t*exp(-B*t), where A,B are positive constants. Find the speed of the particle for large t, expressing the answer in terms of m, A, and B.

First, we need to find a formula for the speed of the particle, v, at a given time, t. Relate the speed, v, to the force f, using Newton's 2nd Law: f(t) = m dv/dt (remembering that acceleration is the time-d...
Answered by • Maths tutor
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How can you factorise expressions with power 3 or higher?

The key to factoring big and complicated expressions into simpler forms is to remember the factor theorem . The factor theorem says that if we plug a number k into our expression and it comes out as 0, then ...
CD
Answered by Christopher D. • Maths tutor
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Prove by contradiction that there is an infinite number of prime numbers.

The 'by contradiction' tells us we need to assume the opposite to begin with: 1) Let's assume there is a finite number of prime numbers2) Let P be the largest prime number (the last one) 3) if we multiply al...
CL
Answered by Charlotte L. • Maths tutor
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What are the necessary conditions for a random variable to have a binomial distribution?

There can only be two possible outcomes, 'success' and 'fail' (e.g heads or tails) There is a fixed number of trialsThe probabilities of 'success' and 'fail' are constant and stay the same in each trial (e.g...
JT
Answered by Julie T. • Maths tutor
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