25992 questions

A is an array with N elements which suffers M operations: 0 a b- find the maximum value in [a,b] and 1 a b- the element on the position a becomes b. Answer each question '0' in the most efficient way.

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Victor S.

Answered by Victor, who tutored Computing A Level with MyTutor


Given a graph with n nodes and m edges, every edge has a passing cost that can be negative, find the minimum distance between node 1 and every other node

We will use the Bellman-Ford algorithm to compute the minimum distance between that start node and every other one, by passing through each edge for a maximum of n times and "relaxing the edge", where possible, to obtain the best path. Also, we will improve the algorithm by using only the nodes that helped us relax a path in the past, the other ones being redundant. This will be done by using a queue and the final algorithm will have an O(n*m) complexity but is much faster in practice.
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Victor S.

Answered by Victor, who tutored Computing A Level with MyTutor



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Nick M.

Answered by Nick, Maths A Level tutor with MyTutor


Outline Asch’s findings in relation to two variables affecting conformity. Briefly explain two limitations of Asch’s conformity research. [8 marks]

Read over what the question is asking you carefully and look at a number of marks the question is worth. This question is worth 8 marks. You can get 4 marks from the first part of the question ‘Outline Asch’s findings in relation to two variables affect conformity’, and the last 4 marks from the second half ‘Briefly explain two limitations of Asch’s conformity research’. In order to get full marks for part one, you need to not only show your knowledge about two variables found that can affect conformity, but also detail what Asch found out about those variables. It is not enough to only mention the variable. For example, if you were to mention group size as a variable that affects conformity, you would also need to point out that Asch found that group size acted as a variable to a point – conformity levels increased but only up to a group majority of 3 confederates, any larger and conformity levels plateaued or did not significantly increase. Remember, pick out two variables affecting conformity and what Asch found out about each variable. By doing this, you will get the first 4 marks. For the second part of this question, you need to show you understand two limitations of Asch’s study. You can get one mark from stating the limitation, and another mark for giving an explanation of the limitation. You’ll need to do this twice in order to get the full 4 marks for this section. For example, you could mention that one limitation of the study is that it was made up of males and has a gender bias, thus not representative of female behaviour. You could also pick out that the study is not representative of a larger population as the sample was that of young male college students, thus the behaviour of people from other educational backgrounds, ages, and gender are not taken into account in the final result. Finally, remember to use specific terminology where appropriate in order to get full marks, i.e. ‘sample’, ‘variables’, ‘confederates’, etc.
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Scott M.

Answered by Scott, who tutored Psychology A Level with MyTutor


How do you conjugate the 'passé composé' ?

The passé composé goes hand in hand with the présent de l'indicatif. It is formed by putting an auxiliary verb, être or avoir and a past participle together. The passé composé is used to describe an action that has occured in the past and that is done. Example: Hier j'ai chanté. Je suis sorti(e). In both of these examples, an auxiliary verb and a past participle have been put together. For the passé composé the auxiliary verb has to be conjugated at the present tense (j'ai-tu as-il/elle/on a-nous avons-vous avez...) In terms of past particples, some verbs follow relatively simple rules. For -er verbs, past participles end in -é, for -ir verbs they end in -i. Example: Chanter = chanté Dormir = dormi
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Camille B.

Answered by Camille, French GCSE tutor with MyTutor


To what extent do you agree with the view that the novel is a total condemnation of transgression? (Frankenstein by Mary Shelly)

You might read this question and instantly want to make a start on your exam piece. DON’T! Make sure to read the question fully, twice. It’s important to make sure you understand what’s being asked of you, especially in a carefully worded question such as this. You can lose marks if you misunderstand the question. After reading the question, break it down into key phrases. In this question, the phrases are ‘to what extent’, ‘do you agree with the view’, and ‘total condemnation of transgression’. This question is asking how much you agree with the opinion that Frankenstein disapproves or criticises ‘transgression’. You do not need to fully agree, you can state that you agree to a ‘certain existent’, or ‘to a small extent’ with the view. Remember, however you choose to argue in this essay, you need relevant examples from the text. Relevant examples show the marker that you understand and have engaged with the text. Moreover, a balanced essay – one which points out evidence both for and against the view – will display that you have considered the entirety of the novel and given the argument a lot of thought. When writing your argument, you should state what boundaries are being transgressed and how these are represented in the text. For example, Frankenstein’s monster represents the transgression of the boundaries between life and death because he is made of body parts from corpses. Then show how the transgression is depicted in the text. How is it represented in the text? How does the text show this? What techniques are used? Make sure to link all your points back to the main question. This demonstrates to the marker that you are considering and answering the question carefully. Finally, your conclusion needs to summarise your argument. Reiterate how much you agree with the state and the points you have made. Do not add points to the conclusion that you did not write about in the main body of your essay. This can look rushed and does not add to your essay. Keep in mind: break down the question into key words, have examples and evidence for your argument, and refer to the question.
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Scott M.

Answered by Scott, who tutored English Literature A Level with MyTutor


How do you simplify something of the form Acos(x) + Bsin(x) ?

This sort of question is quite common, and a *little* bit complicated, so the explanation is quite long! But it's a great one to understand. There are a few tricks you need to know to be able to do it. The first thing you need to know is what you can simplify it to. There are two similar formats you might be asked to simplify it into; these are Csin(x+e), or Ccos(x+f). The fact that you can simplify this sum into a single sinusoidal (sinusoidal = sine or cosine) function means that the new wave has the same shape as either of the original waves, but it will have been stretched and laterally translated (shifted sideways). The C represents the amplitude of the new wave (how high and low it stretches), and e or f represents the lateral translation (sideways offset from a normal sine or cosine wave). To explain the method for working out C and e or f, it is probably easiest to use an example! Let's start with: 3cos(x) - sin(x) and try and get to the new form Csin(x+e). This means A = 3, and B = -1 Let's start by equating our original expression with the target expression: 3cos(x) - sin(x) = Csin(x+e) The first trick is to expand the right hand side using the general rule sin(a+b) = sin(a)*cos(b) + cos(a)*sin(b) Remembering to multiply everything by C, we get: 3cos(x) - sin(x) = Csin(x)*cos(e) + Ccos(x)*sin(e) Before we do the second trick, I'm going to rearrange the equation above slightly: [3]*cos(x) + [-1]*sin(x) = [Csin(e)]*cos(x) + [Ccos(e)]*sin(x) The second, and strangest, trick involves realising that both sides of the equation are in the same format, that is [something]*cos(x) + [something]*sin(x) . We can actually equate both pairs of somethings because of this! This gives us two new equations: 3 = Csin(e) , and -1 = Ccos(e) What this trick has done is gotten rid of x from the equations and let only C and e, the two variables we want to find. Now we can use these two new equations like simultaneous equations to work out C and e. Wonderful! The easiest way to work out C and e now is to find a way to eliminate one of them from the equations. It doesn't matter which one you try to eliminate first, but normally I choose to eliminate e first. To do so, first square both of the simultaneous equations to give 9 = C2sin2(e) and 1 = C2cos2(e) . Then you can make use of a special trigonometric identity, which is sin2(x) + cos2(x) ≡ 1, by adding both equations together to give; 10 = C2[sin2(e) + cos2(e)], which gives 10 = C2. This means C = sqrt(10) . Almost there! Now we have to work out e. There are a few ways to do this, and unfortunately, all of them involve some pitfalls! I'll show you what I think is the easiest way to go about this. Returning to the two simultaneous equations, this time, divide the first (the one with the sin term) by the second (the one with the cos term), to give 3 / -1 = Csin(e) / Ccos(e), which gives -3 = tan(e) Now we can use the inverse tan function (tan-1 or arctan on your calculator) to solve for ee = tan-1(-3) Now this is where the possible pitfall appears. Your calculator will probably give the answer e = -1.25 (using the radians setting instead of degrees). However, one of the special things about inverse trig functions is that they actually have multiple solutions, and your calculator can only show one! The reason I chose this method is because working out the other possible solutions is quite easy for the inverse tan function, simply add or subtract multiples of pi (π) from -1.25. So, how do you know what the right solution is? There are always two possible solutions; your calculator output (-1.25) or that output plus pi (-1.25+π). First let's test -1.25. This would make our very final solution; 3cos(x) - sin(x) = sqrt(10)*sin(x-1.25) Is this correct? Let's see what happens at x=0, when cos(x)=1 and sin(x)=0; 3 - 0 = sqrt(10)*sin(-1.25) If you trying inputting sqrt(10)*sin(-1.25) into your calculator (in radians), you should get about -3, not +3, which means this solution is incorrect. So now we should go back and try e=-1.25+π, which makes our final solution; 3cos(x) - sin(x) = sqrt(10)*sin(x-1.25+π) If you apply the same test at x=0, you will find the right hand side does give +3, which shows this solution is correct. Which means... HOORAY! We're done! ----------------some extra notes---------------- If you want to convince yourself that it is possible to express the sum of a sine and cosine term as a single function, try plotting it on Wolfram Alpha (e.g. " plot y=3cos(x)-sin(x) ", you'll see it has the same shape! However, this only works when you have the same thing inside the sine and cosine brackets. For instance, if you had 3cos(x) - sin(2x), it wouldn't be possible. If you're asked for the simplified form Ccos(x+f), you'll need to know the expansion rule for cos, which is; cos(a+b) = cos(a)*cos(b) - sin(a)*sin(b) from which the same principle can be applied. A **very helpful shortcut** is to notice that the resultant amplitude (C) can always be easily worked out using the rule C2 = A2 + B2 ! It's good to use this as a double check once you've worked it out normally. ***It's also worth saying that, in an exam situation, even if you don't remember the little things like maybe needing to add pi to the bracket, you could still easily get most or even all of the marks! So don't panic if this seems very complicated, I'm just trying to make my explanation as thorough as possible!***
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Jack M.

Answered by Jack, Maths A Level tutor with MyTutor


Comment on how Handel uses the following elements in And the glory of the Lord: Melody, Harmony & tonality, Dynamics, Texture, Mood

In typical Baroque fashion, Handel creates a decoratve melody by using trills and grace notes. He also uses devices effectively to create an interesting melody. For example he employs melismatic writing, which means he uses more than one note per syllable- for example the long drawn-out phrases on the second syllable of 'revealed.' The arcing melody on this syllable also functions as a recurring motif which is satisfying for the listener as it creates a sense of familiarity, as we hear a similar tune applied to different words in later phrases. The tonality is major throughout the movement, creating a joyous feel, appropriate for the thanksgiving sentiment. Any modulaions in the piece are to the dominant key, stabilising the tonality in the tonic A major key throughout. As expected the movement features many perfect cadences, but curiously it ends with a plagal one. This gives particularly resounding sense of finality, as 'Amens' often use this cadence. The diatonic harmony, free of chromaticism, also suits the thanksgiving nature of the movement.  Terraced dynamics are used throughout the movement, with sudden changes in dynamics to create contrast. This is common in Baroque music. The piece starts of quietly with a orchestral introduction and ends with a dramatic rest and then a loud cadence. There are several examples of canonic imitation in the movement, as phrases are passed around and different time and pitch intervals. However this polyphonic activity is balanced with homophonic moments, to create emphatic phrases of praise- the final phrase is a good example of this, with the final three words of the phrase, 'The mouth of the Lord hath spoken it'. This homophony adds to sense of finality the plagal cadence gives us. 
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William R.

Answered by William, Music GCSE tutor with MyTutor

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