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How can I derive an equation to find the sum of an arithmetic sequence?

This isn't a requirement of many courses but understanding and proving mathematics has order is what makes mathematics unique and enjoyable to many. Imagine the sum of a sequence with n terms, denoted S n , ...
RH
Answered by Rhys H. • Maths tutor
4987 Views

The speed of water moving through a turbine is 2.5 m/s. Show that the mass of water passing through an area of 500 metres squared in one second is about 1 x 10^6 kg (density of sea water = 1030 kg/m^3)

This is a past exam question from an A level paper for OCR Physics B.We know that in one second, a volume of water (V), travelling at 2.5 m/s is passing through an area of 500 metres squared in one second. T...
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Answered by Catherine H. • Physics tutor
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If (2/3)^n=〖(3/2)〗^2 what is the value of n

Reciprocal is when you interchange the numerator (the number on top in a fraction) with the denominator (the number at the bottom in a fraction). The numerator, is now the denominator and the denominator is ...
GW
Answered by Gift W. • Maths tutor
15919 Views

A quarter circle represents a piece of land. The length of the straight sides is 100 ft each. If the land is enclosed by a fence, what is closest to the length, in feet, of the fence?

Perimeter of a quarter circle = (2πr)/4 r = 100ft P = (2πr)/4 = (2×3.14×100)/4 = 157 Because we are calculating the length of the fence – as the fence goes around the land – for the two straight sides - the ...
GW
Answered by Gift W. • Maths tutor
7534 Views

Explain the process of allopatric speciation

A population of one species is separated by a physical barrier, e.g a geographical barrier such as the movement of tectonic plates. There will then be 2 isolated groups of the same species unable to interbre...
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Answered by Matthew S. • Biology tutor
9074 Views