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Answer :
To find the time [tex]\( t \)[/tex] in seconds it will take a stone to drop a distance [tex]\( s \)[/tex] of 181 feet, we will use the provided formula:
[tex]\[ t = 0.25 \times s^{\frac{1}{2}} \][/tex]
Here, [tex]\( s \)[/tex] is the distance in feet, which is 181 feet in this case.
Step-by-step Solution:
1. Substitute the value of [tex]\( s \)[/tex]:
Start by replacing [tex]\( s \)[/tex] with 181 in the formula:
[tex]\[ t = 0.25 \times (181)^{\frac{1}{2}} \][/tex]
2. Calculate the square root of [tex]\( s \)[/tex]:
Find the square root of 181:
[tex]\[ \sqrt{181} \approx 13.452 \][/tex]
3. Multiply by 0.25:
Next, multiply the square root result by 0.25:
[tex]\[ t = 0.25 \times 13.452 \][/tex]
4. Calculate the product:
Multiplying gives:
[tex]\[ t \approx 3.363 \][/tex]
5. Round the result:
Finally, round the result to the nearest tenth of a second:
[tex]\[ t \approx 3.4 \][/tex]
So, the time it will take the stone to drop a distance of 181 feet is approximately 3.4 seconds.
[tex]\[ t = 0.25 \times s^{\frac{1}{2}} \][/tex]
Here, [tex]\( s \)[/tex] is the distance in feet, which is 181 feet in this case.
Step-by-step Solution:
1. Substitute the value of [tex]\( s \)[/tex]:
Start by replacing [tex]\( s \)[/tex] with 181 in the formula:
[tex]\[ t = 0.25 \times (181)^{\frac{1}{2}} \][/tex]
2. Calculate the square root of [tex]\( s \)[/tex]:
Find the square root of 181:
[tex]\[ \sqrt{181} \approx 13.452 \][/tex]
3. Multiply by 0.25:
Next, multiply the square root result by 0.25:
[tex]\[ t = 0.25 \times 13.452 \][/tex]
4. Calculate the product:
Multiplying gives:
[tex]\[ t \approx 3.363 \][/tex]
5. Round the result:
Finally, round the result to the nearest tenth of a second:
[tex]\[ t \approx 3.4 \][/tex]
So, the time it will take the stone to drop a distance of 181 feet is approximately 3.4 seconds.
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