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Express Cosx-3Sinx in form Rcos(x+a) and show that cosx-3sinx=4 has no solution MEI OCR June 2016 C4

Cosx-3sinx =R(CosxCosa-SinxSina) 1=Rcosa R^2=1^2+3^2 r=(10)^0.5=(approx)3.16 a=1.249 3.16Cos(x+1.249)=4 has no solution as 4<3.16 so as cos(theta) has maximum value of 1, there are no solutions

Answered by Jakub P. • Maths tutor

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Find CO-Ordinates of intersection of 2x+3y=12 and y=7-3x

Picture of Answer available on request

Answered by Jakub P. • Maths tutor

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Differentiate the function f(x) = (x^2 - 1)^3

Using the chain rule: f '(x) = (2x) (3) (x^2 - 1)^2 = 6x(x^2 - 1)^2

Answered by James B. • Maths tutor

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Let y = 4t/(t^2 + 5). Find dy/dt, writing your answer in it's simplest form, and find all values of t for which dy/dt = 0

We use the quotient rule to find dy/dt. Let u = 4t and v = (t^2 + 5). Then, u' = 4 and v' = 2t. Hence,

dy/dt = u'v - v'u / v²= 4(t^2 + 5) - 4t x 2t / (t^2 + 5)²= 20 - 4t

Answered by Jonathan H. • Maths tutor

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C4 June 2014 Q4: Water is flowing into a vase. When the depth of water is h cm, the volume of water V cm^3 is given by V=4πh(h+4). Water flows into the vase at a constant rate of 80π cm^3/s. Find the rate of change of the depth of water in cm/s, when h=6.

This question wants us to find: dh/dt. We are given: dV/dt=80π and V=4πh(h+4). The equation to use here is: dh/dt = dh/dV x dV/dt. We kn...

Answered by Suban K. • Maths tutor

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