# Discuss Rocmike3's answer to: Mathematics needs constants to the variables. Why?

Mathematics needs constants to the variables. Why?

Matrices and quadratics are only two of the umpteen ways we work multiple variables against each other, never the need for a constant value.  Here is a typical problem (simplified greatly).

We have four containers of unknown radionuclides, which means we have unknown half-life, radiation products, and rate of decay.  We work from sealed vials, because we must determine the contents before we open these ghastly things with the hands: unexcited radiation is not as dangerous as a "flash."  Even a well-designed glove box will not protect us from a flash.  So, suit up, put your hands in the gloves, and get busy.

The vials are depleted /92/U\238 and weigh 1 Kg, with an interior volume of 750 ML.  They present the interior contents with a radiation shield equivalent to nine feet of steel plate.

Vial 1 emits 22.4 R/H.  (Roentgens per hour) 3 hours later, it still emits 22.4 R/H.

Vial 2 emits 180 R/H.  3 hours later, it emits 90 R/H.

Vial 3 emits 27 R/H.  3 hours later, it emits 25 R/H.

Vial 4 emits 10 R/H.  3 hours later, it emits 9.75 R/H.

Note that we have four variables.  Because the constants all factor out, we now have a workable equation and can predict the radioactive decay.

Vial 1 emits 22.4 R/H.  3 hours later, it still emits 22.4 R/H.  We have a long-term half life.  We now weigh the vial.  34.25 KG.  What are the isotopes and percentages?

We compare its radioactive decay profile to 95/Am\243, 78%, 90/Th\235 19%, and 2/He\4 3%.

The variables now include their present rate of decay and the base refined element that has degenerated.  Without going through all the math, we find that the sample was 94/Pu\239, pulled out of a breeder reactor about 45 years ago.

Now, it is your turn.  Describe the contents of Vial 2.

http://en.wikipedia.org/wiki/Identity_matrix

http://en.wikipedia.org/wiki/Polynomials

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