Top answers

A curve is defined by parametric equations: x = t^(2) + 2, and y = t(4-t^(2)). Find dy/dx in terms of t, hence, define the gradient of the curve at the point where t = 2.

dy/dx = (dy/dt)/(dx/dt) y = t(4-t 2 ), then using differentiation of y with respect to t, dy/dt = 4 - 3t 2 x = t 2 + 2, then using differentiation of x with respect to t, dx/dt = 2t Find dy/dx by dividing dy...
MW
Answered by Micah W. • Maths tutor
5917 Views

What is the process of mitosis?

A useful mnemonic to remember the stages of mitosis is PMAT. Don’t forget that the cell spends most of its time in interphase, the phase where the DNA is replicated, before moving to mitosis.Prophase- chromo...
CH
Answered by Caroline H. • Biology tutor
3326 Views

Express 3sin(2x) + 5cos(2x) in the form Rsin(2x+a), R>0 0<a<pi/2

Start by expanding out Rsin(2x+a) using the addition formula for sin, sin(A+B) = sin(A)cos(B)+cos(A)sin(B). Substituting 2x = A and a= b, we get that Rsin(2x+a) = R(sin(2x)cos(a) + cos(2x)sin(a)) = Rcos(a)si...
MF
Answered by Michael F. • Maths tutor
10441 Views

Explain how the theme of love is presented in Shakespeare's "Much Ado About Nothing"

This is an essay question that could come up in A Level based on the syllabus' I have looked at; there is not time or space to write out the full essay here, so I have gone for three key bullet points I woul...
NT
Answered by Nathan T. • English tutor
3458 Views

Solve the simultaneous equations: y=x+1, x^2+y^2=13

We already have an expression for y, so we can substitute this in:x 2 +(x+1) 2 =x 2 +(x+1)(x+1) = x 2 +x 2 +2x+1=2x 2 +2x+1 and hence 2x 2 +2x+1=13 and so 2x 2 +2x-12=0Now look for common factors. Here we ca...
LC
Answered by Lauren C. • Maths tutor
7857 Views