Given:
The table of values.
v and x are in direct proportion.
To find:
The formula connecting v and x.
Solution:
(a)
v and x are in direct proportion.
[tex]v\propto x[/tex]
[tex]v=kx[/tex] ...(i)
Where, k is the constant of proportionality.
Putting v=13.6 and x=32.64, we get
[tex]13.6=k(32.64)[/tex]
[tex]\dfrac{13.6}{32.64}=k[/tex]
[tex]\dfrac{5}{12}=k[/tex]
Putting the value of k in (i), we get
[tex]v=\dfrac{5}{12}x[/tex]
Therefore, the required formula that connecting v and x is [tex]v=\dfrac{5}{12}x[/tex].
(b)
Putting v=n and x=8.16, we get
[tex]n=\dfrac{5}{12}(8.16)[/tex]
[tex]n=3.4[/tex]
Therefore, the value of n is 3.4.
