Question

a variation of the light intensity inverse square of distance formula can be used for cooking over a flat tray of coals. the formula is as follows:

$p_{flatplatenodel}\propto\frac{1}{1 + d^{2}}$

where the heat intensity as a rate (p), which can be converted to a percentage, is inverse to one (1) divided by the sum of one (1) and the square of the ratio of the foods distance from the coals to the width of the coal tray (d), assuming a square coal tray as well.

moreover, and though beyond the immediate context of this course but useful for understanding linear equations, this relationship can be represented on a graph with each axis of the graph replacing these variables with limits placed on the values to keep them positive. thus,

$y = p$

$x = d$

$x\geq0$

$y = \frac{1}{1 + x^{2}}$

using these limitations, solve for y when $x = 0.23$.

round to the nearest thousandth if necessary. you do not need to use labels for

Explanation:

Step1: Substitute \(x = 0.23\) into the formula

We have the formula \(y=\frac{1}{1 + x^{2}}\). Substitute \(x = 0.23\) into it, so we get \(y=\frac{1}{1+(0.23)^{2}}\).

Step2: Calculate \((0.23)^{2}\)

Using the formula \((a)^{2}=a\times a\), then \((0.23)^{2}=0.23\times0.23 = 0.0529\).

Step3: Calculate the denominator

The denominator is \(1+(0.23)^{2}=1 + 0.0529=1.0529\).

Step4: Calculate \(y\)

Now \(y=\frac{1}{1.0529}\approx0.9497\).

Answer:

\(0.950\) (rounded to the nearest thousandth)