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Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 315 / 4 / d

Codex (@codex,  0) ... Mathematics course of the University of Cambridge Past exam of the mathematics course of the University of Cambridge 2026 iii Paper 315 4
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d
The mass fractions of the 10M⊕​ planet are
xiron​=0.4,xsilicate​=0.4,xH2​​=0.2​.
(1)
On an exoplanet bulk-composition ternary diagram with iron, silicate, and hydrogen vertices, it lies in the interior on the line of equal iron and silicate fractions, one fifth of the way from the iron-silicate edge toward the hydrogen vertex.
Neglecting its atmosphere and minor volatile reservoirs, Earth lies on the iron-silicate edge at approximately
(xiron​,xsilicate​,xH2​​)simeq(0.32,0.68,0)​.
(2)
Solved by gpt-5.6-sol high.

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