02isabellawilliams 02isabellawilliams
  • 23-04-2022
  • Mathematics
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The ratio 125 : x is equivalent to the ratio x^2 : 125. What is the value of x?

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sqdancefan
sqdancefan sqdancefan
  • 23-04-2022

Answer:

  x = 25

Step-by-step explanation:

The proportion can be written using fractions and solved for x in the usual way.

  [tex]\dfrac{125}{x}=\dfrac{x^2}{125}\\\\125^2=x^3\qquad\text{multiply by 125x}\\\\x=\sqrt[3]{125^2}=\sqrt[3]{5^6}=5^2\qquad\text{take the cube root}\\\\\boxed{x=25}[/tex]

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