Respuesta :

For this case we have a direct variation of the form:

[tex]f (x) = kx[/tex]

Where "k" is the constant of proportionality. To find it, we use the following data:

[tex]f (x) = 40\ and\ x = 8[/tex]

Substituting:

[tex]40 = k * 8[/tex]

Clearing the value of k:

[tex]k = \frac {40} {8}\\k = 5[/tex]

Thus, the direct variation is given by:

[tex]f (x) = 5x[/tex]

For[tex]x = 2[/tex] we have:

[tex]f (2) = 5 * 2\\f (2) = 10[/tex]

Answer:

The value of the direct variation for [tex]x = 2[/tex]is: [tex]f (2) = 10[/tex]


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