SOLUTION: a is directly proportional to b and inversely proportional to the square of c. if a=7 when b=9 and c=6, find a when b=4 and c=8

Algebra ->  Proportions -> SOLUTION: a is directly proportional to b and inversely proportional to the square of c. if a=7 when b=9 and c=6, find a when b=4 and c=8      Log On


   

Question 582421: a is directly proportional to b and inversely proportional to the square of c. if a=7 when b=9 and c=6, find a when b=4 and c=8
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
a is directly proportional to b and inversely proportional to the square of c. if a=7 when b=9 and c=6, find a when b=4 and c=8

First_quantity_mentioned =  

a = k·b%2Fc%5E2

Substitute the information from the situation when all the variables 
are given:

7 = k·9%2F6%5E2

Solve for k:

7 = k·9%2F36

7 = k·1%2F4

Multiply both sides by 4

28 = k

Substitute the value of k in the equation:

a = k·b%2Fc%5E2

a = 28·b%2Fc%5E2

Substitute the information from the other situation when all 
the variables BUT ONE are given:
 
a = 28·b%2Fc%5E2

a = 28·4%2F8%5E2

Solve for the missing variable, which in this case is "a":

a = 28·4%2F84

a = 28·1%2F16

a = 28%2F16

a = 7%2F4

a = 1%263%2F4 or

a = 1.75

Edwin