Question

Determine the value of f, rounded to the nearest hundredth.f=

Answer 1

The value of
`\( f \)`, rounded to the nearest hundredth, is approximately 0.35.

To determine the value of
`\( f \)` in the stopping distance formula provided in the image, we have the quadratic formula for stopping distance \( d \) as a function of velocity
`\( v \)`:

`\[ d(v) = (2.15v^2)/(64.4f) \]`

We're given three pairs of
`\( v \)` and
`\( d \)` values in the table. We can substitute one pair into the equation to solve for
`\( f \)`. It's typically best to use all the data points to find the most accurate value for
`\( f \)`, but since we only need to determine
`\( f \)` to the nearest hundredth, we can use any one of the data points provided.

Let's use the pair
`\( v = 20 \)` and
`\( d = 38 \)` to find
`\( f \)`:

`\[ 38 = (2.15 \cdot 20^2)/(64.4f) \]`

Now, let's solve for
`\( f \)`.

The value of
`\( f \)`, rounded to the nearest hundredth, is approximately 0.35.

Answer 2

Okay, here we have this:

Considering the provided information, we are going to calculate the value of f, so we obtain the following:

We'll replace in the function with one of the provided points, so we have:

`\begin{gathered} d(v)=(2.15v^2)/(64.4f) \\ 38=(2.15\left(20\right)^2)/(64.4f) \\ 38=(860)/(64.4f) \\ 38\cdot\: 64.4f=(860)/(64.4f)\cdot\: 64.4f \\ 2447.2f=860 \\ (24472f)/(24472)=(8600)/(24472) \\ f=(1075)/(3059) \\ f\approx0.35 \end{gathered}`

Finally we obtain that f is approximately 0.35.