18652 questions

Explain the function of the human heart

Describe where the human heart is located - i.e. thoracic cavityDefine the function of the heart - to supply the body with blood, act as a pumpStructure of the heart - 4 chambers (2 ventricles, 2 atria), SAN, AVN, valves, vessels coming in and travelling outDescribe the pulmonary circulation and then the systemic circulationDescribe the electrical conduction of impulses through the heart muscle to achieve contractility
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Alexandra D.

Answered by Alexandra, Human Biology tutor with MyTutor

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How do I integrate (sin x)^6?

Letting z be the complex number cos x + i sin x, we will use the identities (zn + 1/zn) = 2 cos nx and (zn - 1/zn) = 2i sin nx. Both of these follow from De Moivre’s theorem and the odd and even properties of sine and cosine. To see this, notice that zn + 1/zn = cos nx + i sin nx + cos (-nx) + i sin (-nx) = cos nx + i sin nx + cos nx - i sin nx = 2 cos nx, and for the second identity, zn - 1/zn = cos nx + i sin nx - cos (-nx) - i sin (-nx) = cos nx + i sin nx - cos nx + i sin nx = 2i sin nx. We see that (2i sin x)6 = (z - 1/z)6 and    64 i6 sin6 x = z6 + 6(z)5(-1/z) + 15(z)4(-1/z)2 + 20(z)3(-1/z)3 + 15(z)2(-1/z)4 + 6(z)(-1/z)5 + (-1/z)6= z6 - 6z4 + 15z2 - 20 + 15/z2 - 6/z4 +1/z6from the binomial theorem. Now, the method we use is to pair up the terms into groups that look like the identities above. Here, we are pairing the first with the last, the second with the second last, and so on, to give 64 i6 sin6 x = (z6 + 1/z6) - 6(z4+1/z4) + 15(z2+1/z2) - 20. Using the identity for cosine, we obtain 64 i6 sin6x = 2cos 6x - 12cos 4x + 30 cos 2x - 20, so 64 (-1)3 sin6x = 2cos 6x - 12cos 4x + 30 cos 2x - 20 and we can then see that sin6x = -1/32 cos 6x + 3/16 cos 4x - 15/32 cos 2x + 5/16. Finally, we can integrate both sides with respect to x, as now we can use recognised integrals on the right. ∫ sin6x dx = ∫ -1/32 cos 6x + 3/16 cos 4x - 15/32 cos 2x + 5/16 dx   = ∫ -1/32 cos 6x dx + ∫ 3/16 cos 4x dx - ∫ 15/32 cos 2x dx + ∫ 5/16 dx which we can evaluate by using ∫ cos nx dx = 1/n sin nx + C, to give our final answer, ∫ sin6x dx = -1/192 sin 6x + 3/64 sin 4x - 15/64 sin 2x + 5/16 x + C
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Keenan D.

Answered by Keenan, Further Mathematics tutor with MyTutor

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Describe the differences in social deprivation in England and how this relates to health

Firstly, you would begin by defining what is meant by social deprivation. You would have to look at the Index of Multiple Deprivation and what factors that looks at - education, access to healthcare, infant mortality, average income, housing. You could then highlight the differences in England - e.g. the known North/South divide in terms of wealth and how this affects health by looking at figures from northern cities vs southern cities and also urban vs rural. You could also focus on one particular area such as the Kensington and Chelsea borough where there is extreme social disparities with the example of Grenfell Tower. All the social deprivation factors must lead back to how they impact health.
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Frances E.

Answered by Frances, Geography tutor with MyTutor

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When listening to a extract of music, what features should we be looking out for?

I would suggest always working out what the time signature is (how many beats in a bar), whether the music is slow or fast, what style the music is in and the general dynamics in the extract. I would then think about what instruments are playing and how they work together in the piece; are there soloists/is it tutti (playing all together)? We can then start to notice if there are any repeating motifs in the music, such as sequences and ostinatos.It is also beneficial to think about the form of the music, is it ABA? Are there any additional features such as ornaments (trills, turns etc), scalic passages, pitch bending, use of percussive sounds, large range of pitch, brass fanfare, crescendos, caesuras... These are all interesting things to consider when listening to a new extract of music.
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Izzy J.

Answered by Izzy, Music tutor with MyTutor

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Jodie works for a bookshop. She is paid £6.50 an hour plus 5% of the cost of each book she sells. On Saturday, Jodie worked for 3 hours and sold £220 worth of books. How much money did Jodie earn?

We can break down this question in to two parts.
Firstly we should work out how much Jodie earns for the hours that she worked. Since she worked 3 hours on Saturday to work out how much she was paid we have to multiply it by the hourly rate which is, £6.50. So, 3 x 6.50 = £19.50Secondly, we should work out how much she is paid in addition to this for the books she sells. To do this we have to work out 5% of £220. To work out 10%, we divide 220 by 10 which is £22. So, 5% is £22 divided by 2 which is £11.
So to work out the total we do, £19.50 + £11 = £30.50
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Fizzah A.

Answered by Fizzah, who has applied to tutor Maths with MyTutor

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Explore Shakespeare's presentation of blindness in King Lear. You must relate your discussion to relevant contextual factors and ideas from your critical reading.

There is literal and metaphorical blindness omnipresent in this play. Shakespeare presents patriarchs clinging onto power in the characters of Lear and Gloucester; their desperation ultimately resulting in self-deceit, since both men become unable to see those most loyal to them, banishing Cordelia and Edgar. This blindness is a moral one, the men are incapable of seeing reality, of seeing who is good and what is right: both are deluded and vulnerable. Jan Kott sees this vulnerability as "grotesque", particularly the scene of Gloucester's attempted leap from the stage, since the tragedy treads near to comedy since Gloucester is reduced to such a point of pity, as powerless as "flies to wanton boys". Before Gloucester leaps, he addresses the sky in exclamation, "o you mighty gods, this world I do renounce and in your sights shake patiently my great affliction off", a moment epitomising this 'grotesque' and pitiable melodrama, centred around Gloucester's blindness. Interestingly, Shakespeare writes the "sights" of the gods, their role as viewer and cruel spectator provides a painful and poignant contrast. However, in blindness, paradoxically, can profound truth be found for both Lear and Gloucester, a concept epitomised by Edgar's "reason in madness". As Lear is reduced to "unaccommodated man" in the storm, becoming aware of the "poor, bare, forked animal" which man actually is, having rejected Cordelia in blindness, being consumed by nothingness, Lear finally sees his failure of responsibility to his subjects (and family) as king. As this play was first performed on Boxing Day in 1606 in front of King James's court, the day when traditionally the rich give to the poor, perhaps Shakespeare was encouraging charitable giving and warning James about the dangers of selfish preoccupation with power. The question must therefore be posed, whether Shakespeare's presentation of blindness has a didactic function. The answer is neither black nor white, since the recognition Lear reaches of his own culpability in the storm is then punished by the death of Cordelia at the close of the play. It is the audience who then share Lear's blindness, the immoral and dark horrors of the final scene are unexpected and shocking, where there appears no redemption for Lear, and a bleak darkness which swallows the stage.
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Constance E.

Answered by Constance, English Literature tutor with MyTutor

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There are 25 CDs in a box. A shop orders 14 boxes. How many CDs did the shop order?

Here we have to find out the total number of CDs that the shop ordered. One box has 25 CDs and the shop has ordered 14 boxesSo, to work it out the total we have to multiply 14 by 25, this can be solved by long multiplication. This gives us 350.
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Fizzah A.

Answered by Fizzah, who has applied to tutor Maths with MyTutor

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if you have 2 moles of CaCl2 and you dissolve it in a solvent, how many moles of cl- will you have?

This question is to remind you that moles is just a fancy way of saying a certain number. This number is known as avogadro's constant and it is 6.02214086 × 1023. another way of thinking about this question is; a person has 2 legs, if there are 2 dozens people in a room, how many dozens of legs are there in the room? dozen is just a fancy way of saying 12, if we have 2 dozens people in the room, that's 24 people and each person has 2 legs so number of legs =24 x 2 OR 2 dozens x 2= 4 dozens.To answer the question, you will have 4 moles of Cl- because each CaCl2 has 2 Cl-.
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Babatunde O.

Answered by Babatunde, Chemistry tutor with MyTutor

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