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A Curve has parametric equation x=2sin(t), y= 1+cos(2t), -pi/2<=t<=pi/2. a) Find dy/dx when t=pi/3. b) Find the Cartesian equation for the curve in form y=f(x), -k<=x<=k. c) Find the range of f(x)

x=2sin(t), y=1+cos(2t) a) By chain rule, dy/dx = (dy/dt)/(dx/dt) dy/dt = -2sin(2t), dx/dt= 2cos(t) dy/dx= -sin(2t)/cos(t) dy/dx=-2sin(t)cos(t)/cos(t) dy/dx=-2sin(t) when t = pi/3, dy/dx= -sqrt(3) b) dy/dx = ...
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Answered by Max B. • Maths tutor
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Find the first and second derivatives of: y = 6 - 3x -4x^-3, and find the x coordinates of the line's turning points

dy/dx = -3 +12x^-4 d^2y/dx^2 = -48x^-5
MS
Answered by Matthew S. • Maths tutor
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Discuss the causes and associated health problems of atherosclerosis

Causes- Too much cholesterol in the blood. This can be as a result of high LDL and low HDL levels in the blood. or as it is more known as a high LDL:HDL ratio. LDL are not very good for you and a way to reme...
LK
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What is £23 increased by 4%?

There are two steps to solving this problem. First, we want to find out how much the increase itself is, so we want to calculate 4% of £23. Then, we want to add the result to the £23. That will give us the f...
GB
Answered by Giulia B. • Maths tutor
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What is natural selection?

Natural selection is when certain characteristic are 'selected' for. Each species have simiar characteristics but differences in genes means that their characteristics can vary for example individual birds o...
AM
Answered by Anna M. • Biology tutor
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