Which equation describes this relationship? Remember to include k, the constant of variation. a varies jointly with b and c and inversely with d Choices: (A)a = kbc/d (B)a = kcd/b (C)a = kbcd (D)a = kc/bd

Direct Proportion Definition: Joint variation with b and c means a is directly proportional to the product of b and c, so we have a part of the equation as a = k * b * c.Inverse Proportion Definition: Inverse variation with d means a is inversely proportional to d, so we combine this with the direct proportion to get the full equation as a = k * b * c / d.Combining Proportions: Now we match our derived equation with the given choices to find the correct one.Matching with Choices: The equation a = k * b * c / d matches with choice (A) a = kbc/d.

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Which equation describes this relationship? Remember to include $k$ , the constant of variation. $\newline$ $a$ varies jointly with $b$ and $c$ and inversely with $d$ $\newline$ Choices: $\newline$ (A) $a = \frac{kbc}{d}$ $\newline$ (B) $a = \frac{kcd}{b}$ $\newline$ (C) $a = kbcd$ $\newline$ (D) $a = \frac{kc}{bd}$

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Algebra 2

Write joint and combined variation equations II

Full solution

Q. Which equation describes this relationship? Remember to include

k

, the constant of variation.

\newline

a

varies jointly with

b

and

c

and inversely with

d

\newline

Choices:

\newline

(A)

a = \frac{kbc}{d}

\newline

(B)

a = \frac{kcd}{b}

\newline

(C)

a = kbcd

\newline

(D)

a = \frac{kc}{bd}

Direct Proportion Definition: Joint variation with $b$ and $c$ means $a$ is directly proportional to the product of $b$ and $c$ , so we have a part of the equation as $a = k \times b \times c$ .
Inverse Proportion Definition: Inverse variation with $d$ means $a$ is inversely proportional to $d$ , so we combine this with the direct proportion to get the full equation as $a = k \times b \times c / d$ .
Combining Proportions: Now we match our derived equation with the given choices to find the correct one.
Matching with Choices: The equation $a = \frac{k \cdot b \cdot c}{d}$ matches with choice (A) $a = \frac{kbc}{d}$ .