SOLUTION: A is proportional to t^2 A is proportional to r^3 t=47 when r=0.25 find r when t=345 and pls tell the relationship between t and r

Algebra ->  Proportions -> SOLUTION: A is proportional to t^2 A is proportional to r^3 t=47 when r=0.25 find r when t=345 and pls tell the relationship between t and r      Log On


   

Question 971794: A is proportional to t^2
A is proportional to r^3
t=47 when r=0.25
find r when t=345
and pls tell the relationship between t and r
Answer by anand429(138) About Me  (Show Source):
You can put this solution on YOUR website!
As per given proportionality conditions,
Let A+=+k%2A+t%5E2+%2A+r%5E3 where k is any proportionality factor
When r=0.25, t=47
i.e A+=+k%2A+47%5E2+%2A+%280.25%29%5E3
=> A%2Fk+=+47%5E2+%2A+%280.25%29%5E3 -(i)
So, when t=345, we have,
A%2Fk+=+345%5E2+%2A+r%5E3 -(ii)
From eqn. (i) and (ii),
r%5E3+=+47%5E2+%2A+%280.25%29%5E3+%2F+345%5E2 (Solve it)
And relatonship between t and r is given by initial condition
t%5E2+%2A+r%5E3+=+47%5E2+%2A+%280.25%29%5E3