Solve this Direct and Inverse Variation

P varies directly as Q² and inversely as root R. When Q=8 and R=25,P=16. Find P when Q=5 and R=9.

simple

P ¤ Q²  
     √R

STEP 1: Applying the constant K in the variation formula above

When we apply K in the above would have
P=K x Q²
      √R

STEP 2: Substituting with the given values
16=K x 8²
       √25  
16=K x 64
        5
 
STEP 3: Cross multiplying the value
when you cross multiply we would have
16 x 5 = k x 64
80=64k  

STEP 4: Dividing both sides by 64
80  = 64k
64 =   64  
k=1.25  

STEP 5: Finding P in the given question
In order to find P, we will still use the formula above in step one.  
P= k x 5²
      √9
P=1.25 x 5²
       √9
P=1.25 x 25
         3
P=10.417 answer

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