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Prove algebraically that (4n + 1)² − (2n − 1) is an even number for all positive integer values of n.

First of all expand the brackets and simplify the expression given:(4n+1)(4n+1)-(2n-1)= 8n²+8n+1-2n+1= 8n²+6n+2= 2(4n²+3n+1). Since the expression can be factorised with 2...

Answered by Shiv M. • Maths tutor

9963 Views

If a particle of mass m is launched vertically upwards from the ground with velocity u m/s, how long will it take to return to the ground in terms of m, u and g?

Taking upwards to be positive, and using the 'suvat' equation s=ut+1/2at² we know that u=u, a=-g and s=0 when the particle returns to the ground. Then we solve for t:
0=ut-1/2gt²

Answered by Jackie V. • Maths tutor

2985 Views

How to recognise and make the link between probability and the algebraic demands of this question?

While I doubt students will ask this exact question, think it provides the basis for what are usually the most difficult questions in GCSE papers, and students would usually be unsure where to start. My i...

Answered by Neeraj K. • Maths tutor

2723 Views

Use the substitution u=x^2-2 to find the integral of (6x^3+4x)/sqrt( x^2-2)

First use the substitution to find du/dx which is 2x. From this we now know that dx= du/2x (just re-arranging.) Substituting that into the integral we now get (6x³+4x)/ (sqrt (u) x 2x) du. Canc...

Answered by Khalil S. • Maths tutor

9353 Views

Let f(x)=x^3 - 2x^2 + 5. For which value(s) of x does f(x)=5?

Although it can be tempting to dive straight into such a question, its always useful in mathematics to take a step back and assess the question before scribbling down panicked answers.

For inst...

Answered by Jed G. • Maths tutor

3280 Views