Top answers

The element of a cone has length L. For what height H (with respect to L) will the volume of the cone be the largest?

This is a good exercise to introduce student to the idea of derivatives and their possible practical use. Firstly, I should draw the cone and notice that its volume is equal to 1/3 pi H*R 2 (where R - radius...
MK
Answered by Max K. • Maths tutor
4547 Views

Differentiate y=(3x-1)/(2x-1)

First, recognise that the function is a fraction and recall the quotient rule. y=u/v dy/dx=(vu'-uv')/v 2 , where u' and v' is the derivative of u and v respectively. Then, apply the rule. u=3x-1, v=2x-1 u'=3...
MM
Answered by Martin M. • Maths tutor
8155 Views

let y=6x^-0.5+2x+1, find dy/dx.

dy/dx = -6(0.5)x^-1.5+2 = -3x^-1.5+2
RL
Answered by Rodger L. • Maths tutor
4260 Views

Integrate the following fraction w.r.t. x: (sqrt(x^2 + 1)-sqrt(x^2 - 1))/(sqrt(x^4 - 1))

Notice the denominator can be factorised as the difference of two squares. The fraction can then be simplified by cancellation. The resulting fraction(s) can then be solved using the list of integrals in you...
TD
Answered by Tutor80072 D. • Maths tutor
4865 Views

Express (3 - sqrt(5))^2 in the form m + n*sqrt(5), where m and n are integers.

Layout the problem in a more recognisable form such as (3 - sqrt(5))(3 - sqrt(5)) . Notice that this looks a lot like a factorised quadratic equation , where sqrt(5) can be treated as a variable like x . The...
AP
Answered by Anselmo P. • Maths tutor
9315 Views