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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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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. Resolving down the plane : ma = m g sin30 - 0.2 R = m g sin30 - ...
MB
Answered by Matthew B. • Maths tutor
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Evaluate f'(1) for the function f(x) = (x^2 + 2)^5

First, we must differentiate the function. To do this we must let the contents of the bracket be equal to 'u'. We now can produce two equations, one by subbing in 'u' into the function f(x) to give us u^5. T...
TU
Answered by Tahrim U. • Maths tutor
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You have a five-litres jug, a three-litres jug, and unlimited supply of water. How would you come up with exactly four litres of water (with no measuring cup)?

You fill the 5-litres jug, and pour it into the 3-litres jug until it's full (now you have 2 litres in the 5-litres jug). Then, you pour out the 3-litres jug completely. Now, you pour the 2 litres from the 5...
DG
Answered by Diana G. • Maths tutor
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Prove that the square of an odd integer is odd.

Let n be an odd integer. This means that n is 1 more than an even integer. By definition, even integers are multiples of 2 so all even integers can be written in the form 2m where m is an integer. Therefore,...
MO
Answered by Mary O. • Maths tutor
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