kaylabarnes200p338nc kaylabarnes200p338nc
  • 25-02-2019
  • Mathematics
contestada

a^2 b^2=c^2 express b in terms of a and c

Respuesta :

gmany
gmany gmany
  • 03-03-2019

Answer:

[tex]b=\dfrac{c}{a}\ or\ b=\sqrt{c^2-a^2}[/tex]

Step-by-step explanation:

[tex]If\ is\ a^2b^2=c^2:\\\\a^2b^2=c^2\qquad\text{divide both sides by}\ a^2\neq0\\\\b^2=\dfrac{c^2}{a^2}\to b=\sqrt{\dfrac{c^2}{a^2}}\\\\b=\dfrac{\sqrt{c^2}}{\sqrt{a^2}}\\\\\boxed{b=\dfrac{c}{a}}[/tex]

[tex]If\ is\ a^2+b^2=c^2:\\\\a^2+b^2=c^2\qquad\text{subtract}\ a^2\ \text{from both sides}\\\\b^2=c^2-a^2\to\boxed{b=\sqrt{c^2-a^2}}[/tex]

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