Alan

The distance between points (x1, y1) and (x2, y2) is given by sqrt( (x2-x1)² + (y2-y1)² ).

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Increase as a percentage calculated as follows:  100*(9.83 - 9.48)/9.48 → 3.69%

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Multiply by 10^-12 to convert from picometers to meters; so multiply your result by 10^-36 to convert from picometers cubed to meters cubed!

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Add the two equations term by term

2x + y - y = 5 + 9  or  2x = 14  so x = 7

Put this back into the first equation

7 + y = 5

Subtract 7 from both sides

y = 5 - 7   so  y = -2

"Find four numbers that form a geometric progression such that the second term is less than the first by 36 and the third term is greater than the fourth term by 324."

I'll leave you to calculate the values of each set of four!

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I've assumed that by 0.3 per month you meant exactly that.  If you meant 0.3% per month then you would have to divide the 0.3 by 100.

final population = initial population*(1 + yearly percentage/100)^number of years

a)final population = 25000*(1 + 1.2/100)^4

final amount = initial investment*(1 + monthly increase)^number of months

a) final amount = 700*(1 + 0.3)^5

refractive index of sapphire ≈ 1.77  so sin(i)/sin(45) = 1.77,   sin(i) = 1.77*sin(45)

relative refractive index between the two materials is sin(57)/sin(45) ≈ 1.186,    sin(57) = 1.186*sin(45)

refractive index of other material is   sin(i)/sin(57)  = 1.77*sin(45)/(1.186*sin(45))  ≈ 1.5

Likely material:  Glass.

Depends on the context.

It can mean the number 2.71828...

If it's in a computer program in the form, say, 5.2e4 it means "times ten to the power of" i.e. 5.2e4 is 5.2*10^4

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