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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 know dV/dt, but still need to find dh/dV . For this, we can use the rec...
SK
Answered by Suban K. • Maths tutor
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How do you differentiate y=cox(x)/sin(x)?

Since we have to differentiate a fraction, we must use the quotient rule. The quotient rule: If y = u/v, dy/dx = (v du/dx - u dv/dx)/v 2 So we must work out each of the terms u, v, du/dx and dv/dx from the q...
RC
Answered by Raj C. • Maths tutor
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How do I solve simultaneous equations?

2x + y = 7 3x - y = 8 You cannot find x and y using only one equations, but using both you can! So first you have use algebra to make both equations = y. Try this for the first equation by rearranging it. Th...
SO
Answered by Stephanie O. • Maths tutor
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5Sin[x]-4=2Cos[2x]

x = 0.848,2.29
MM
Answered by Mostafa M. • Maths tutor
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Solve (11-w)/4 = 1 + w

So we start off with (11-w)/4 = 1+w First of all, we will multiply both sides by 4 to make the '/4' disappear. This gives us 11-w = 4+4w Then move all the w's to one side of the equation to leave us with 7 =...
JB
Answered by James B. • Maths tutor
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