To determine the length of the tire marks [tex]\(x\)[/tex] for a car traveling at 90 miles per hour using the equation [tex]\( s = 2 \sqrt{5x} \)[/tex], we can rearrange the equation to solve for [tex]\(x\)[/tex]. Here’s a step-by-step solution:
1. Write down the given equation and the known speed:
[tex]\[
s = 2 \sqrt{5x}
\][/tex]
Given speed, [tex]\( s = 90 \)[/tex] miles per hour.
2. Isolate the square root term by dividing both sides of the equation by 2:
[tex]\[
\frac{s}{2} = \sqrt{5x}
\][/tex]
Substitute [tex]\( s = 90 \)[/tex]:
[tex]\[
\frac{90}{2} = \sqrt{5x}
\][/tex]
Simplify:
[tex]\[
45 = \sqrt{5x}
\][/tex]
3. Square both sides of the equation to eliminate the square root:
[tex]\[
(45)^2 = (\sqrt{5x})^2
\][/tex]
[tex]\[
2025 = 5x
\][/tex]
4. Solve for [tex]\(x\)[/tex] by dividing both sides of the equation by 5:
[tex]\[
x = \frac{2025}{5}
\][/tex]
[tex]\[
x = 405
\][/tex]
Thus, the length of the tire marks would be [tex]\(405\)[/tex] feet.
This detailed, step-by-step solution shows that a car traveling at 90 miles per hour would leave tire marks that are 405 feet long.
