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Sagot :

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.