Find a formula for s in terms of t if s is proportional to the square root of t, and s = 115 when t = 48. Round the value for the proportionality constant to three decimal places. Note that "s =" is already provided. Do not include this in your submitted response to this question.

Find a formula for s in terms of t if s is proportional to the square root of t, and s = 115 when t = 48. Round the value for the proportionality constant to three decimal places. Note that "s =" is already provided. Do not include this in your submitted response to this question.

Question
Equations and inequalities
asked 2021-01-27
Find a formula for s in terms of t if s is proportional to the square root of t, and s = 115 when t = 48. Round the value for the proportionality constant to three decimal places. Note that "s =" is already provided. Do not include this in your submitted response to this question.

Answers (1)

2021-01-28
Given that s is propotional to the square root of t, we write: \(\displaystyle{s}={k}\sqrt{{t}}\)
Solve for k using s=115 and t=48: \(\displaystyle{115}={k}\sqrt{{48}}\)
\(\displaystyle\frac{{115}}{\sqrt{{48}}}={k}\sqrt{{48}}\)
To three decimal places, k~ 16.599ZSK
So the formula is: \(\displaystyle{s}={16.599}\sqrt{{t}}\)
0

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