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Differentiate y=3xe^{3x^2}+2x

We differentiate y with respect to x:Firstly, we apply the Chain rule in the fist part of the RHS. Remembering the chain rule is uv -> u'v+uv', so d(3xe^{3x^2})/dx=3e^{3x^2}+18x^{2}e^{3x^2}now, we sim...

Answered by John A Alejandro B. • Maths tutor

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Using the diagram and your knowledge of vectors, show that BCD is a straight line

BC = BA - CA = (3a - b) - (a + 4b) = 2a - 5b ...

Answered by Jonathan A. • Maths tutor

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Given a spinner divided in 3 sections numbered 1, 2 and 3, and that the arc of section 2 is double that of section one (~57.6 cm), calculate pi to 2 decimal places. The radius of the spinner is 30cm and the angle sub-intended by section 3 is 30 degrees.

Use angle of section 3 to get ratios of arcs:Realise either one of the arcs 1 or 2 will do.Calculate 360-30 / 3 to get 110 degrees for section 1.Calculate ratio of arcs for section 1: 11/...

Answered by Filipe C. • Maths tutor

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Find the equation of the line L passing through (0, 3) and (5, 7). What would the gradient of a line perpendicular to this line be? What about a line parallel to it?

Since L is a straight line between two points, it has the form y=mx+c, where m is the gradient. To find m we use that it is the difference in y values of the points divided by the difference in x values, ...

Answered by Victoria I. • Maths tutor

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A particle of mass 0.5 kg is moving down a rough slope (with coefficient of friction = 0.2) inclined at 30 degrees to the horizontal. Find the acceleration of the particle. Use g = 9.8 ms^-2.

Resolving perpendicular to the plane: R - mg cos30 = 0. Therefore, R = m g cos30, where R is the reaction force perpendicular to the plane. Res...

Answered by Matthew B. • Maths tutor

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