SOLUTION: y varies jointly as a and b, and inversely as the square root of c. If y=135 when a=3, b=9, and c=4; then find y when a=12, b=7, and c=9. thank you!

Algebra ->  Linear-equations -> SOLUTION: y varies jointly as a and b, and inversely as the square root of c. If y=135 when a=3, b=9, and c=4; then find y when a=12, b=7, and c=9. thank you!      Log On


   

Question 1113128: y varies jointly as a and b, and inversely as the square root of c. If y=135 when a=3, b=9, and c=4; then find y when a=12, b=7, and c=9.
thank you!
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
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y varies jointly as a and b, and inversely as the square root of c.
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y=abk%2Fsqrt%28c%29
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k=y%2Asqrt%28c%29%2F%28ab%29

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If y=135 when a=3, b=9, and c=4; then fi......
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Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Let +k%5Ba%5D+, +k%5Bb%5D+, and +k%5Bc%5D+
= constants of proportionality
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(1) +y+=+k%5Ba%5D%2Aa+
(2) +y+=+k%5Bb%5D%2Ab+
(3) +y+=+k%5Bc%5D%2A%28+1%2Fsqrt%28c%29+%29+
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(1) +135+=+k%5Ba%5D%2A3+
(1) +k%5Ba%5D+=+45+
and
(2) +135+=+k%5Bb%5D%2A9+
(2) +k%5Bb%5D+=+15+
and
(3) +135+=+k%5Bc%5D%2A%28+1%2Fsqrt%284%29+%29+
(3) +k%5Bc%5D+=+135%2Asqrt%284%29+
(3) +k%5Bc%5D+=+135%2A2+
(3) +k%5Bc%5D+=+270+
=======================
+a+=+12+
(1) +y+=+k%5Ba%5D%2A12+
(1) +y+=+45%2A12+
(1) +y+=+540+
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+b+=+7+
(2) +y+=+k%5Bb%5D%2A7+
(2) +y+=+15%2A7+
(2) +y+=+105+
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+c+=+7+
(3) +y+=+k%5Bc%5D%2A%28+1%2Fsqrt%28c%29+%29+
(3) +y+=+270%2A%28+1%2Fsqrt%289%29+%29+
(3) +y+=+270%2F3+
(3) +y+=+90+