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Which equation describes this relationship? Remember to include kk, the constant of variation.\newlineaa varies jointly with bb and cc and inversely with dd\newlineChoices:\newline(A) a=kbcda = \frac{kbc}{d}\newline(B) a=kcdba = \frac{kcd}{b}\newline(C) a=kbcda = kbcd\newline(D) a=kcbda = \frac{kc}{bd}

Full solution

Q. Which equation describes this relationship? Remember to include kk, the constant of variation.\newlineaa varies jointly with bb and cc and inversely with dd\newlineChoices:\newline(A) a=kbcda = \frac{kbc}{d}\newline(B) a=kcdba = \frac{kcd}{b}\newline(C) a=kbcda = kbcd\newline(D) a=kcbda = \frac{kc}{bd}
  1. Direct Proportion Definition: Joint variation with bb and cc means aa is directly proportional to the product of bb and cc, so we have a part of the equation as a=k×b×ca = k \times b \times c.
  2. Inverse Proportion Definition: Inverse variation with dd means aa is inversely proportional to dd, so we combine this with the direct proportion to get the full equation as a=k×b×c/da = k \times b \times c / d.
  3. Combining Proportions: Now we match our derived equation with the given choices to find the correct one.
  4. Matching with Choices: The equation a=kbcda = \frac{k \cdot b \cdot c}{d} matches with choice (A) a=kbcda = \frac{kbc}{d}.

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