Alan

Yet another approach is simply to use Pythagoras to find the length of each side, then use the cosine rule to find the angles:

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197 grams of gold corresponds to 6.022810^23 atoms

0.4 grams of gold corresponds to 6.022*10^23*0.4/197 atoms  ≈ 1.2*10^21 atoms

Like so:  \(0.0004 \rightarrow 4\times 10^{-4}\)

Data on planet 9 according to Wikipedia (https://en.wikipedia.org/wiki/Planet_Nine):

The force of gravity between two objects is given by G*M1*M2/r^2  where G is gravitational constant, M1 and M2 are the masses and r is the disance between them.

Use Pythagoras theorem to get the distances between each successive point (in squares), then add them together and multiply the result by 60 to get the total distance in meters.

So, the distance between (0,0) and (-7,6) is sqrt((-7-0)^2 + (6-0)^2) = sqrt(49 + 36) = sqrt(85) ≈ 9.219

The distanve between (-7, 6) and (-2, 14) is sqrt((-2--7)^2 + (14-6)^2) = sqrt(5^2 + 8^2) = sqrt(25+64) = sqrt(89) ≈ 9.434

etc.  Can you take it from here?

See http://web2.0calc.com/questions/help-please_18539#r6

(4 + i)^2 → 4^2 +2*4*i + i^2 → 16 + 8i -1 → 15 + 8i

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A rational number can be expressed as a ratio of two whole numbers (i.e. as a fraction).  An irrational number cannot.

Divide 1063 by 105 to get the map distance in cm.

No you can't cancel the 3x's out!

(x²+3x-4)/(3x-7) can be written as (x+4)(x-1)/(3x-7)