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The curve C has the equation: y=3x^2*(x+2)^6 Find dy/dx

To find dy/dx, we must use a combination of the Product Rule and the Chain Rule. If we let 3x^2=u and (x+2)^6=v, the Product Rule tells us that (uv)' = uv'+vu' u'=6x, but to find v' we need to use the Chain ...
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Answered by Sam H. • Maths tutor
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How to solve a quadratic equation?

There are several ways to solve a quadratic equation. 1.Quadratic formula ax 2 + bx + c = 0, where a can't equal 0 but b and c can.x = (-b± (b 2 - 4ac)) / 2a2. completing the square(x + b/2) 2 + c3. factoris...
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Answered by Alvaro M. • Maths tutor
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How can I understand eigenvalues and eigenvectors?

A matrix is a linear transformation between vector spaces. Often we want to think about linear maps from an n -dimensional vector space to itself. When the vector space that we're mapping to and from is the ...
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Answered by James W. • Maths tutor
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66 people went on a day trip and each took part in one activity: skating, bowling or painting. 43 were female. 4 out of the 10 that went skating were male. 20 people did painting. 10 males went bowling. How many females did painting?

This question is worth 4 marks and requires us to work with the information we are given. To set this up clearly, I would suggest drawing out a table with the three activities listed down the side and male a...
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Answered by Abby G. • Maths tutor
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If I throw a ball vertically upwards with a velocity of 15 m/s and we assume the gravitational acceleration is 10 m/s^2. Draw the distance-time, and velocity-time graphs, how long is the ball in the air before it returns to the point I threw it from?

We will need a SUVAT equations, so first fill in what information we have:S = 0 (the point where the ball returns to the start)U = +15 m/sV = -15 m/s (from graph)A = -10 m/s (important that this is the oppos...
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Answered by Barnaby F. • Maths tutor
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