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If r varies directly as s and inversely as the square of u, and r=2 when s=18 and u=2. find out r when u=3 and s=27

Sagot :

KAntoineDoixidn

✒️VARIATIONS

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[tex] \large\underline{\mathbb{PROBLEM}:} [/tex]

  • If r varies directly as s and inversely as the square of u, and r=2 when s=18 and u=2. find out r when u=3 and s=27

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[tex] \large\underline{\mathbb{ANSWER}:} [/tex]

[tex] \qquad \Large \:\: \rm{r = \frac{\,4\,}{3}} \\ [/tex]

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[tex] \large\underline{\mathbb{SOLUTION}:} [/tex]

» Create the equation of a combined variation in which k is the constant.

  • [tex] r = \frac{\,ks\,}{u^2} \\ [/tex]

» Find the constant of the variation.

  • [tex] 2 = \frac{\,k(18)\,}{2^2} \\ [/tex]

  • [tex] 2 = \frac{\,k(18)\,}{4} \\ [/tex]

  • [tex] 2 = \frac{\,k(9)\,}{2} \\ [/tex]

  • [tex] 2\cdot\frac{\,2\,}{9} = \frac{\,k(9)\,}{2} \cdot \frac{\,2\,}{9} \\ [/tex]

  • [tex] \frac{\,4\,}{9} = k \\ [/tex]

» The constant is 4/9. Find r when u is 3 and s is 27.

  • [tex] r = \frac{\,\frac49s\,}{u^2} \\ [/tex]

  • [tex] r = \frac{\,\frac49(27)\,}{3^2} \\ [/tex]

  • [tex] r = \frac{\,\frac{108}9\,}{9} \\ [/tex]

  • [tex] r = \frac{\,12\,}{9} \\ [/tex]

  • [tex] r = \frac{\,4\,}{3} \\ [/tex]

[tex] \therefore [/tex] The value of r is 4/3

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(ノ^_^)ノ

GreatNiclausidn

✒️[tex]\large{\mathcal{ANSWER}}[/tex]

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If r varies directly as s and inversely as the square of u, and r=2 when s=18 and u=2. find out r when u=3 and s=27.

[tex] \: \boxed{r = \frac{4}{3}} [/tex]

[tex]------------------[/tex]

Computation / Solution;

[tex]set \: r = m \frac{s}{u {}^{2} } [/tex]

r = 2 when s = 18 , u = 12

[tex]2 = m = \frac{18}{ {2}^{2} } [/tex]

[tex]2 = m = \frac{18}{4} [/tex]

[tex]18m = 8[/tex]

[tex]m = \frac{4}{9} [/tex]

[tex]r = \frac{4s}{9 {u}^{2} } [/tex]

when u = 3, s = 27

[tex]r = \frac{4 \times 27}{9 \times {3}^{2} } [/tex]

[tex]r = \frac{4 \times 27}{9 \times 3 \times 3} [/tex]

[tex]r = \frac{4}{3} [/tex]

So the answer is [tex]r = \frac{4}{3} [/tex]

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