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https://texercises.com/exercise/the-kings-crown/
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Exercise:
A king has a new crown made for him. For cost reasons the goldsmith uses a gold-silver mixture and processes VO metal. The finished crown rests on the king's head with mO. How much mass gold rgO and how much mass silver rsO did the smith use?

Solution:
If you mix up gold and silver their masses and volumes add up i.e. m m_ + m_ and VV_+V_. Substituting the volumes through mass and density one gets the following two s: tcbhighmathm m_ + m_ quad quad Vfracm_rho_+fracm_rho_ This system of s can be solved using the substitution method; In the first step you solve one it doesn't matter which one we use the first one because it looks easier for one unknown no matter which one: alm_ m-m_ Substitute what you got o the other : alVfracm_rho_+fracm-m_rho_ This can now be solved for the unknown m_; The rules of linear ondimensional algebra must be applied: V fracm_rho_+fracm-m_rho_ rho_rho_ V m_rho_ + rho_m-m_ rho_rho_ V m_rho_ + rho_m-rho_m_ rho_rho_ V - rho_m m_rho_-rho_ m_ fracrho_rho_ V - rho_mrho_-rho_ SolQtymgrgX*rsX*VX-rgX*mX/rsX-rgXkg SolQtymsmX-mgXkg m_ fracrho_rho_ V-rho_ mrho_-rho_ mg m_ m-m_ ms
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Exercise:
A king has a new crown made for him. For cost reasons the goldsmith uses a gold-silver mixture and processes VO metal. The finished crown rests on the king's head with mO. How much mass gold rgO and how much mass silver rsO did the smith use?

Solution:
If you mix up gold and silver their masses and volumes add up i.e. m m_ + m_ and VV_+V_. Substituting the volumes through mass and density one gets the following two s: tcbhighmathm m_ + m_ quad quad Vfracm_rho_+fracm_rho_ This system of s can be solved using the substitution method; In the first step you solve one it doesn't matter which one we use the first one because it looks easier for one unknown no matter which one: alm_ m-m_ Substitute what you got o the other : alVfracm_rho_+fracm-m_rho_ This can now be solved for the unknown m_; The rules of linear ondimensional algebra must be applied: V fracm_rho_+fracm-m_rho_ rho_rho_ V m_rho_ + rho_m-m_ rho_rho_ V m_rho_ + rho_m-rho_m_ rho_rho_ V - rho_m m_rho_-rho_ m_ fracrho_rho_ V - rho_mrho_-rho_ SolQtymgrgX*rsX*VX-rgX*mX/rsX-rgXkg SolQtymsmX-mgXkg m_ fracrho_rho_ V-rho_ mrho_-rho_ mg m_ m-m_ ms
Contained in these collections:
  1. 10 | 12
  2. Krone des Königs by TeXercises
    5 | 8


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Tags
crown, density, gold, king, mass, mechanics, physics, silver, volume
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(4, default)
Points
4 (default)
Language
ENG (English)
Type
Calculative / Quantity
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