# Khan/khan-exercises

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 Direct and inverse variation
[["x", "y"], ["a", "b"], ["m", "n"]] randFromArray(VARIABLE_NAMES) { v1: "<code><var>V1</var></code>", v2: "<code><var>V2</var></code>", } rand(2) randRange(2, 9) MULTIPLIER_IS_FRACTIONAL ? MULTIPLIER_VALUE : "\\frac{1}{"+MULTIPLIER_VALUE+"}" MULTIPLIER_IS_FRACTIONAL ? "\\frac{1}{"+MULTIPLIER_VALUE+"}" : MULTIPLIER_VALUE
randFromArray([ $._("%(v1)s is directly proportional to %(v2)s", V1V2),$._("%(v1)s and %(v2)s vary directly", V1V2), $._("%(v1)s varies directly with %(v2)s", V1V2),$._("%(v1)s and %(v2)s are in direct variation", V1V2) ])

STATEMENT.

Which of these equations could represent the relationship between V1 and V2?

V1 = MULTIPLIER \cdot V2

STATEMENT if V1 = k \cdot V2 for some constant k

V1 = MULTIPLIER \cdot V2 fits this pattern, with k = MULTIPLIER.

• V1 \cdot V2 = MULTIPLIER
• V1 \cdot V2 = MULTIPLIER_INVERSE
• V1 = MULTIPLIER \cdot \frac{1}{V2}
• MULTIPLIER \cdot V1 = \frac{1}{V2}
• MULTIPLIER_INVERSE \cdot V1 = \frac{1}{V2}
• MULTIPLIER \cdot \frac{1}{V1} = V2
• MULTIPLIER_INVERSE \cdot \frac{1}{V1} = V2
• V1 + V2 = MULTIPLIER_INVERSE
• V1 = MULTIPLIER - V2

\frac{V1}{V2} = MULTIPLIER

STATEMENT if V1 = k \cdot V2 for some constant k

If you divide each side of this expression by V2, you get \dfrac{V1}{V2} = k for some constant k.

\dfrac{V1}{V2} = MULTIPLIER fits this pattern, with k = MULTIPLIER.

MULTIPLIER \cdot V1 = V2

STATEMENT if V1 = k \cdot V2 for some constant k

If you divide each side of this expression by k, you get \dfrac{1}{k} \cdot V1 = V2.

MULTIPLIER \cdot V1 = V2 fits this pattern, with k = MULTIPLIER_INVERSE.

randFromArray([ $._("%(v1)s is inversely proportional to %(v2)s", V1V2),$._("%(v1)s and %(v2)s vary inversely", V1V2), $._("%(v1)s varies inversely with %(v2)s", V1V2),$._("%(v1)s and %(v2)s are in inverse variation", V1V2) ])

STATEMENT.

Which of these equations could represent the relationship between V1 and V2?

V1 = MULTIPLIER \cdot \frac{1}{V2}

STATEMENT if V1 = k \cdot \dfrac{1}{V2} for some constant k

V1 = MULTIPLIER \cdot \dfrac{1}{V2} fits this pattern, with k = MULTIPLIER.

• \frac{V1}{V2} = MULTIPLIER
• \frac{V1}{V2} = MULTIPLIER_INVERSE
• V1 = MULTIPLIER \cdot V2
• V1 = MULTIPLIER_INVERSE \cdot V2
• MULTIPLIER \cdot V1 = V2
• MULTIPLIER_INVERSE \cdot V1 = V2
• MULTIPLIER \cdot \frac{1}{V1} = \frac{1}{V2}
• MULTIPLIER_INVERSE \cdot \frac{1}{V1} = \frac{1}{V2}
• V1 - V2 = MULTIPLIER_INVERSE
• V1 = MULTIPLIER + V2

V1 \cdot V2 = MULTIPLIER

STATEMENT if V1 = k \cdot \dfrac{1}{V2} for some constant k

If you multiply each side of this expression by V2, you get V1 \cdot V2 = k for some constant k.

V1 \cdot V2 = MULTIPLIER fits this pattern, with k = MULTIPLIER.

MULTIPLIER \cdot \dfrac{1}{V1} = V2

STATEMENT if V1 = k \cdot \dfrac{1}{V2} for some constant k

If you divide each side of this expression by k, you get \dfrac{V1}{k} = \dfrac{1}{V2}.

Then you can take the inverse of each side to get \dfrac{k}{V1} = V2.

MULTIPLIER \cdot \dfrac{1}{V1} = V2 fits this pattern, with k = MULTIPLIER.

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