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Integrate the function x(2x+5)^0.5

integrate using substitution: (I = the symbol for integration)let u = 2x + 5 therefore x = (u - 5)/2 du/dx = 2 which means that du = 2dx ---> dx = 1/2 duThis means that the integral now = I((u - 5)/2 x...

Answered by Danielle P. • Maths tutor

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differentiate y=(3x)/(x^2+6)

using the quotent ruledy/dx= (3(x^2+6)-3x(2x))/(x^2+6)^2dy/dx=3(x^2+6-2x^2)/(x^2+6)^2dy/dx=(18-3x^2)/(x^2+6)^2

Answered by Michael S. • Maths tutor

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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 u...

Answered by Sam H. • 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 f...

Answered by James W. • 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 op...

Answered by Barnaby F. • Maths tutor

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