SOLUTION: Let a be directly proportional to m and n^2​, and inversely proportional to y^3. If a=4 when m=9​, n=4​, and y=2​, find a when m=8​, n=3​, and y=5.

Algebra ->  Expressions-with-variables -> SOLUTION: Let a be directly proportional to m and n^2​, and inversely proportional to y^3. If a=4 when m=9​, n=4​, and y=2​, find a when m=8​, n=3​, and y=5.      Log On


   

Question 1155352: Let a be directly proportional to m and n^2​, and inversely proportional to y^3. If a=4 when m=9​, n=4​, and y=2​, find a when m=8​, n=3​, and y=5.
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
a=+km%2An%5E2%E2%80%8B and
a=k%2Fy%5E3
=> a=+k%28m%2An%5E2%2Fy%5E3%29
If a=4 when m=9%E2%80%8B, n=4%E2%80%8B, and y=2​, we have
a=+k%289%2A4%5E2%2F2%5E3%29
4=144k%2F8
32=144k
k=32%2F144
k=2%2F9

=>a=+%282%2F9%29%28m%2An%5E2%2Fy%5E3%29

find a when m=8%E2%80%8B, n=3%E2%80%8B, and y=5

+a=+%282%2F9%29%288%2A3%5E2%2F5%5E3%29
+a=+16%2F125
a=0.128

Answer by MathTherapy(10551) About Me  (Show Source):
You can put this solution on YOUR website!

Let a be directly proportional to m and n^2​, and inversely proportional to y^3. If a=4 when m=9​, n=4​, and y=2​, find a when m=8​, n=3​, and y=5.
matrix%281%2C3%2C+a%2C+%22=%22%2C+kmn%5E2%2Fy%5E3%29
matrix%281%2C3%2C+4%2C+%22=%22%2C+k%289%29%284%5E2%29%2F2%5E3%29 ------ Substituting matrix%284%2C3%2C+4%2C+for%2C+a%2C+9%2C+for%2C+m%2C+4%2C+for%2C+n%2C+2%2C+for%2C+y%29


matrix%281%2C3%2C+a%2C+%22=%22%2C+kmn%5E2%2Fy%5E3%29 
matrix%281%2C3%2C+a%2C+%22=%22%2C+%282%2F9%29%288%29%283%5E2%29%2F5%5E3%29 ------ Substituting matrix%284%2C3%2C+2%2F9%2C+for%2C+k%2C+8%2C+for%2C+m%2C+3%2C+for%2C+n%2C+5%2C+for%2C+y%29