Answer :
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.
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.
