Question

1. Suppose that F(x) varies directly with x and f(x) = 160 when x = 5.

What is F(x) when x = 0.5?

Answer 1

$\boxed{f(x=0.5)=16}$

Explanation:

In this exercise, we have a function $f(x)$ that varies directly with x. Direct variation is a case of variation expresses as the following form:

$f(x)=kx \\ \\ For \ a \ non-constant \ zero$

This indicates that $f(x)$ incrases as x increases. Moreover, this is a line with slope $k$ and passes through the origin. So finding $k$:

$f(x)=kx \\ \\ Isolating \ k: \\ \\ k=\frac{f(5)}{5} \\ \\ k=\frac{160}{5}=32$

So:

$f(x)=32x$

Finally, when x = 0.5, then

$f(x=0.5)=32(0.5) \\ \\ \boxed{f(x=0.5)=16}$

Learn more:

System of equations: https://brainly.com/question/13799715

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