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Water is flowing into a rightcircular cone at the rate r (volume of water per unit time). The cone has radius a, altitude b and the vertex or "tip" is pointing downwards. Find the rate at which the surface is rising when the depth of the water is y.

Always a good first step to a problem like this, is to draw a diagram, making sure to label any lengths. The unknown in this question, is the rate at which the surface of water, in the cone, is rising. Howev...
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Answered by Joss O. • Maths tutor
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Differentiate y=x^2+4x+12

y=x^2+4x+12dy/dx=2x+4
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Answered by Robert H. • Maths tutor
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Calculate (7-i*sqrt(6))*(13+i*sqrt(6))

We expand the parentheses to get to the equation: 7 13-13 i sqrt(6)+7 i sqrt(6)-i i sqrt(36) which after some further calculations equals to: 91-6 i sqrt(6)+sqrt(36) [We got +sqrt of 36 because i i*=sqrt(-1)...
Answered by • Maths tutor
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Why is the derivative of ln(x) equal to 1/x.

This fact can be deduced several ways, and I would encourage tutees to find other methods, (such as using implicit differentiation, or the chain rule.) However one of the simplest explanations is given below...
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Answered by Christopher V. • Maths tutor
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There are 40 counters in a bag. 13 are red, 20% are green and the rest are yellow. What proportion of counters are yellow?

20% green counters - means 1/5 of all counters are green. 1/5 of 40 = 40/5 = 8 counters are greenthe number of counters that are green + the number of counters that are red = 8 + 13 = 21the number of counter...
Answered by • Maths tutor
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