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Prove that the sum of the squares of any two consecutive numbers always leaves a remainder of 1 when divided by 4.

(n)^2 + (n + 1)^2n2 + n2 + 2n + 12n2 + 2n + 12(n2+ n) + 12n(n+1) + 1Since the numbers are consecutive, either n or (n+1) are even and divisible by 2. There is already a factor of 2 so 2n(n+1) is a multipl...

Answered by Ana Maria O. • Maths tutor

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A particle P of mass 0.4 kg is moving under the action of a constant force F newtons. Initially the velocity of P is (6i – 27j) m s−1 and 4 s later the velocity of P is (−14i + 21j) m s−1 . Find, in terms of i and j, the acceleration of P.

On the whiteboard I would provide a brief drawing of the particle, and of all the information provided (force applied to P and its before and after velocity) as a visual aid for the student. I would ask/r...

Answered by Finn W. • Maths tutor

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Factorise 3x + 6

Hcf=3
3(x+2)

Answered by Rumsha A. • Maths tutor

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Complete the square of the following expression: 2x^2 -8x+21

2(x-2)^2 +13

Answered by Iliya F. • Maths tutor

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A point lies on a circles diameter such that the distance from the point to the edge of circle is 4 times the distance from the point to the centre. What is the circles area in cm^2 if the distance from the point to edge is 5cm?

first we know that the length given has a 4:1 ratio with the remaining length of the radius so 5/4 + 5 = 25/4 = radius, the formula for the area of a circle is A=pi*(r^2) so the area is 625/16*pi.

Answered by Luka R. • Maths tutor

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