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find dy/dx at t, where t=2, x=t^3+t and y=t^2+1

We know from simple fraction rules that dy/dx=(dy/dt)/(dx/dt). dy/dt=2t, dx/dt=3t^2+1. Therefore, dy/dx=2x2/12+1=4/13
NO
Answered by Niamh O. • Maths tutor
6492 Views

A curve has equation x^2 + 2xy – 3y^2 + 16 = 0. Find the coordinates of the points on the curve where dy/dx =0

We would do this by differentiating everything individually so to differentiate x 2 we multiply the x 2 by the power which is 2 and then take the power down by 1 to make 2x. To differentiate 2xy we would use...
TK
Answered by Tom K. • Maths tutor
5488 Views

What is a stratified sample?

Stratified sampling is a technique used in some instances to generate a 'fairer' sample than standard random sampling. Wherein a population is divided into subgroups called 'strata'. These strata are usually...
LS
Answered by Lewis S. • Maths tutor
6299 Views

Show, by counter-example, that the statement "If cos(a) = cos(b) then sin(a) = sin(b)" is false.

Let a=60 and b=300. Then cos(a)=cos(60)=0.5 and cos(b)=cos(300)=0.5, therefore cos(a)=cos(b). Then sin(a)=sin(60)=sqrt(3)/2 and sin(b)=sin(300)=-sqrt(3)/2, therefore sin(a)=sin(b) is incorrect. Therefore we ...
OG
Answered by Osian G. • Maths tutor
4966 Views

Differentiate y(x)=x^2 + 2x + 1, find the turning point and classify it as minimum or maximum.

dy/dx=2x + 2 Turning point is where dy/dx=0, so when x = -1 When x=-1, y=0. d^2y/dx^2=2 > 0 therefore minimum.
JF
Answered by John F. • Maths tutor
4616 Views