Alan

Taking the smallest amount as unity we have the ratios as:

1250/312.5 : 937.5/312.5 : 312.5/312.5   or  4:3:1

To get the area multiply NinjaDevo's value of a by 8.

Yes, it took me a while though (and I could still be wrong!).

1% of 4800 is just one-hundredth of 4800, or 48

This means that 6% is 6 times as big or 6*48 = 288

Add to this 2/3 of 48 = 32 to get 288 + 32 = 320 in all.

Replace V by 120 to match the original question.

Hi Melody.  The n in (2n+1) is just an integer.

For a square root there are two solutions, so n takes on two values, say 0 and 1, and 2n+1 becomes 1 and 3.  

These give two values of -1 when plugged in to e^i(2n+1)pi. The two square roots of -1 are then found by taking the square root of these (e^i(2n+1)pi)^1/2 = e^i(2n+1)pi/2. When n = 0, e^i(2n+1)pi/2= e^ipi/2 = i, and when n = 1, e^i(2n+1)pi/2= e^i3pi/2 = -i.  Hence we have two values (i and -i) for the square root of -1, one for each value of n.

Similarly, we need three values of n (0, 1 and 2) for finding the three cube roots of -1, and four values for the four fourth roots etc.

Melody asked: Do I need to commit this to memory?

Probably best to remember it in terms of polar representation of complex numbers:

etc.  

120 ml solution contains 60 grams water.

40 ml solution is one-third of 120 ml, so it would contain one-third the mass of water, namely 20 grams.

If 20 grams is 1 mole, then 16 grams is 16/20 of a mole, or 4/5 of a mole (or 0.8 mol).

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