Question

A quantity Q is obtained by adding three quantities.
The first is a constant, the second varies directly as the
square root of y and the third varies directly as the cube
root of y. When y = 1, Q = 90, when y 64, Q 450
and when y = 729, Q 1270. Find the constant.
​

Answer 1

when Y=1, Q=90  

90= C + A. sq rt 1 + B.cu rt190  

= C+ A + B ......................1)  

when Y=64 sq rt Y= 8, cu rt Y= 4; Q=450  

=> 450= C + 8A + 4B.........................................  

y=729, Q=1270; sq rt Y 27, cu rt Y= 9  

=> 1270 = C + 27A + 9B.........................................  

solve the 3 equations for C, A & B.. by elimination