Alan

You can use the cosine rule here.  First though, you must find the angle that is less than 90°.  This will be 180°-100° = 80°. 

If the length of the shorter diagonal is "a" then, a, 6 and 10 are the lengths of the sides of a triangle in which the angle opposite side "a" is 80°. 

Use a² = 6² + 10² -2*6*10*cos(80°)

I'll leave you to find "a" from this.

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You have a mix of at least two questions (or parts thereof) here!  I suggest you clarify exactly what question you want to be answered.

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Example:  "larger than" is a transitive property.

If A is larger than B and B is larger than C then A is larger than C.

Example of non-transitive property: "mother of" 

If A is mother of B and B is mother of C then A is not mother of C.

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This is a well-known problem, known as the Collatz conjecture (http://en.wikipedia.org/wiki/Collatz_conjecture) and the answer is still unknown.  It has been tested by computer up to many millions and no exception has yet been found.  It refers to the natural numbers (1, 2, 3, ...etc.) only.

Example

x = 3 odd so 3x+1 = 10

x = 10 is even so x/2 = 5

x = 5 is odd so 3x+1 = 16

x = 16 is even so x/2 = 8

x = 8 is even so x/2 = 4

x = 4 is even so x/2 = 2

x = 2 is even so x/2 = 1

1 is odd so 3x+1 = 4

and clearly the cycle 4, 2, 1 now repeats forever!

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It depends on the angle bwteen them.  If they are in line then the magnitude of the resultant is just 20 + 40.  However, if they are at right angles then the magnitude of their sum is √(20² + 40²).  For a general angle between them use the cosine rule.

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1cm = 10^-2m

1nm = 10^-9m

so there are 10^-2/10^-9 nm/cm = 10⁷ nm/cm

Hence there are (10⁷)² or 10¹⁴ square nm in a square cm.

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Multiply them by 100.  e.g. 2/5 is 100*2/5 = 200/5 = 40%

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CO₂ has 44 g/mole (Atomic weight of carbon atom = 12, that of oxygen atom = 16)

Avogadro's number is 6.0221415*10²³ molecules/mole

so there are (13.2/44)*6.0221415*10²³ molecules in 13.2 g of CO₂ 

$${\frac{{\mathtt{13.2}}}{{\mathtt{44}}}}{\mathtt{\,\times\,}}{\mathtt{6.022\: \!141\: \!5}}{\mathtt{\,\times\,}}{{\mathtt{10}}}^{{\mathtt{23}}} = {\mathtt{180\,664\,245\,000\,000\,000\,000\,000}}$$

or 1.80664245*10²³ in total.

In each of these molecules there are two oxygen atoms, so double this.

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