The intensity of light, $\mathrm{I}$, in watts per meter-squared, is inversely proportional to the distance squared and given by the equation $I=\frac{13}{x^{2}}$, where $x$ is meters from the light source.
Where is the intensity at least 18.77 watts per meter-squared?
Round to two decimal places.
Answer
Final Answer: The intensity is at least 18.77 watts per meter-squared at a distance of approximately \(\boxed{0.83}\) meters from the light source.
Step 1 ：Given the intensity of light, \(I\), in watts per meter-squared, is inversely proportional to the distance squared and given by the equation \(I=\frac{13}{x^{2}}\), where \(x\) is meters from the light source.
Step 2 ：We are asked to find the distance from the light source where the intensity is at least 18.77 watts per meter-squared. This means we need to solve the equation \(I=\frac{13}{x^{2}}\) for \(x\) when \(I\) is 18.77.
Step 3 ：We can rearrange the equation to \(x=\sqrt{\frac{13}{I}}\) and substitute \(I\) with 18.77 to find \(x\).
Step 4 ：Substituting \(I\) with 18.77, we get \(x = \sqrt{\frac{13}{18.77}}\) which simplifies to \(x = 0.8322226659953956\).
Step 5 ：Rounding to two decimal places, we get \(x = 0.83\).
Step 6 ：Final Answer: The intensity is at least 18.77 watts per meter-squared at a distance of approximately \(\boxed{0.83}\) meters from the light source.
