Y is inversely proportional to √x x is directly proportional to T3 Given that y = 8 when T = 25 find the exact value of T when y = 27

Question

Y is inversely proportional to √x

x is directly proportional to T³

Given that y = 8 when T = 25

find the exact value of T when y = 27

Answer 1

y=k/sqr(x)

x=KT^3

y=k/sqr(KT^3)= k/sqrK(sqrT^3)

8= k/sqrK(sqr(25)^3)

k/sqrK = 5(8)(sqt5)= 40sqr5

y= (40sqr5)/sqrT^3

sqrT^3= (40sqr5)/27

square both sides

T^3= (1600)(5)/27^2=8,000/729= (20/9)^3

take the cube root of both sides

T= 20/9 = 2 2/9 = 2.222...

T=20/9 when y=27

check the answer

x=K(20/9)^3= 8000K/729

27= k/sqrx = k/sqr(8000K/729)

=(k/K)/sqr(8000/729)=40sqr5/(20/9)(sqr(20/9)

=18sqr5/(2/3)sqr5=18(3/2)=27