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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 simply ...
JA
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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 BD = BA + AB = (3a - b) + (a - 9b) = 4a - 10b BC = 1/2 BD. Using basic vector rules, we know that if vectors are multiples, then they are parallel. Since BC and B...
JA
Answered by Jonathan A. • Maths tutor
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How can you use roots of in Arabic to form different words?

Arabic is a very formulaic language, and you can use this to your advantage! Arabic words are derived from basic root words, usually comprising of three letters. Let's use the example of كتب ., which is a ve...
SH
Answered by Sam H. • Arabic 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: 11/36 Find pi: Multipl...
FC
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, ie ...
VI
Answered by Victoria I. • Maths tutor
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