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Prove n^3-n is multiple of 6 for all n

factoring gives form n(n+1)(n-1) from here it should be realised that if n is not a multiple of 3 then n-1 is or n+1 is as multiples of 3 go up in 3s. Hence one of the values either n,n-1 or n+1 must be mult...
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Answered by Adithya N. • Maths tutor
7509 Views

A rectangle has the side lengths root6m and root3m, what is the area of the rectangle in its simplest form.

This question explores surds. To find the area of a rectangle we must multiply its two sides together. When multiplying surds we follow the rule that roota x roota = rootaxa, therefore in this case by multip...
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Answered by Hanah K. • Maths tutor
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why is it that When there is a small droplet on a phone the pixels of the screen can be seen

Given that the drop is small enough it produces a semi sphere on screen of liquid due to surface tension. This acts like a powerful convex lens for the light coming from pixels on the phone screen hence allo...
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Answered by Adithya N. • Physics tutor
2017 Views

Why do the boiling points of the hydrogen halides increase as you go down the group from HCl to HI?

That's a fantastic question. Here, we must consider two types of intermolecular forces as these are the attractive forces that affect the boiling point of a substance: van der Waals and permanent dipole perm...
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Answered by Amarpal S. • Chemistry tutor
18713 Views

How do blood vessels control body temperature?

Blood vessels control body temperature both, when the temperature gets too high as well as when it gets too low, since heat is carried in the blood stream. When the core body temperature gets too high, the b...
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Answered by Emily W. • Biology tutor
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