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Prove by induction that 1^2 + 2^2 + 3^2 + . . . + n^2 = (1/6)n(n+1)(2n+1)

Base case - First let us consider the base case where n=1. Then the left hand side of the equation becomes 1 and the right hand side is (1/6) 1 2*3=6/6=1. Thus LHS=RHS and we are done. Induction hypothesis -...
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The velocity of a car at time, ts^-1, during the first 20 s of its journey, is given by v = kt + 0.03t^2, where k is a constant. When t = 20 the acceleration of the car is 1.3ms^-2, what is the value of k?

Our task is to find out the value of k, which we can determine from the equations for velocity or acceleration if we know 2 of the 3 variables in either equation. We are given the value of acceleration at t(...
LM
Answered by Lascelle M. • Maths tutor
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What is the difference between classical and operant conditioning?

Classical conditioning and classical conditioning are both forms of learning. Classical conditioning is the pairing of a stimulus with an involuntary response, whereas operant conditioning is the association...
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Answered by Steph V. • Psychology tutor
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Explain why Jeremy Bentham's Hedonic Calculus seeks to determine a moral cause of action

The moral framework within which the Hedonic Calculus operates is Act Utilitarianism, which establishes the greatest good for the greatest number of people as the proper goal of a moral framework, arguing th...
Answered by • Philosophy tutor
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'Loss and suffering are familiar conditions with human experience.'

In Chaucer's 'The Merchant's Tale' and Webster's 'The Duchess of Malfi' the writer's contemporary societies are reflected in the society portrayed, with both consisting of a feudal system governed by Richard...
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