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Prove by induction the sum of n consecutive positive integers is of the form n(n+1)/2.

As proof by induction goes we always have to show that it works for the base case, which in this case is the very first positive integer:1. So we show that the sum of the first number(s) is equal to one w...

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If you have 20.82g of Lithium (Molar mass = 6.34gmol^-1), how many moles of Li is it?

number of moles = mass / molar massTherefore, n=20.82g/6.34gmol-1=3moles

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Answered by Sam H. Chemistry tutor
3009 Views

Define enthalpy of neutralisation and state standard conditions:

Enthalpy of Neutralisation: the energy change a system experiences when one mole of water is formed from the neutralisation of an acid with an alkali under standard conditions.Standard conditions: 298K, 1...

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Answered by Sam H. Chemistry tutor
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Increase 35 by 20%:

An increase by 20% is the same as multiplying by 1.2Therefore, 35 x 1.2 = 42

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Answered by Sam H. Maths tutor
4776 Views

Differentiate: f(x)=2(sin(2x))^2 with respect to x, and evaluate as a single trigonometric function.

f(x) = 2sin2(2x)Therefore, using the chain rule: f'(x)=2 x 2cos(2x) x 2sin(2x)(The 2 at the front arises from the constant 2, at the start of f(x), the 2cos(2x) comes from differentiating sin

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Answered by Sam H. Maths tutor
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