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The rectangular hyperbola H has parametric equations: x = 4t, y = 4/t where t is not = 0. The points P and Q on this hyperbola have parameters t = 1/4 and t = 2 respectively. The line l passes through the origin O and is perpendicular to the line PQ.

This question asks us to find the cartesian equation of l. First we must find the points P and Q. To do this we substitute t with 1/4 to find P and substitute t with 2 to find Q.Doing this we get the coordin...
LB
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A curve has parametric equations x= 2sin(t) , y= cos(2t) + 2sin(t) for -1/2 π≤t≤ 1/2π , show that dy/dx = - 2sin(t)+ 1

A parametric equation is where both x and y are expressed separately, in terms of a parameter (t). In order to differentiate them we must use the chain rule, which here would be dy/dx= dy/dt ÷ dx/dt. The dif...
KL
Answered by Katie L. • Maths tutor
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What are the different hypothesised methods of DNA replication.

There are 3 types: conservative, semi conservative and dispersive.conservative entails the original DNA strand remaining intact with a whole newly synthesised DNA strand being formedsemi conservative entails...
RF
Answered by Ronan F. • Biology tutor
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Work out the angle between the two tangents of the curve y = sin(x) at y = 0 and y = 1

First we take the derivative of the function, this gives us dy/dx = cos(x) Now we work out the different x values for y = 0 and y = 1. sin(x) = 0 => x = 0, sin(x) = 1 => x = pi/2 (90 degrees) We then s...
KJ
Answered by Kieran J. • Maths tutor
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Explain how a fall in interest rates would affect aggregate demand (5 marks)

Aggregate Demand is equal to Consumption + Investment + Government Spending + (Exports - Imports). When interest rates fall, saving becomes less profitable, as consumers will receive a smaller additional pay...
RS
Answered by Rajiv S. • Economics tutor
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