Question

If f(x) varies directly with x and f(x)= 64 when x=29 , find the value of f(x) when x=8.Round you final answer to the nearest whole number.

Answer 1

18

Explanation

Direct variation describes a simple relationship between two variables, it can be defined by the expression

$\begin{gathered} f(x)=kx \\ \text{where} \\ f(x)=\text{ y, } \\ \text{and k is a constant} \end{gathered}$

Step 1

find the k value,

set the equation and solve for k

so

let

f(x)=64 when x=29

so

$\begin{gathered} f(x)=kx \\ \text{replace} \\ 64=k\cdot29 \\ to\text{ solve for k, divide both sides by 29} \\ \frac{64}{29}=\frac{k\cdot29}{29} \\ \frac{64}{29}=k \end{gathered}$

Step 2

now, set the equation:

with k=64/29 , the function would be

$\begin{gathered} f(x)=kx \\ f(x)=\frac{64}{29}x \end{gathered}$

finally, to check the f(x) when x= 8, just replace and calculate

$\begin{gathered} f(x)=\frac{64}{29}x \\ f(8)=\frac{64}{29}\cdot8 \\ f(8)=\frac{512}{29} \\ f(8)=17.655 \\ \text{rounded} \\ f(8)=18 \end{gathered}$

threfore, the answer is

18

I hope this helps you