Question
Solve the equation for the indicated variable. (Leave \( \pm \) in the answer as needec \( h=s t^{2} \) for \( t \)
Ask by Howell Higgins. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( t = \pm \sqrt{\frac{h}{s}} \)
Solution
Starting with the equation
h = s·t²
we want to solve for t.
Step 1. Divide both sides by s (assuming s ≠ 0):
t² = h/s
Step 2. Take the square root of both sides, remembering to include the ± symbol:
t = ±√(h/s)
Thus, the solution for t is:
t = ±√(h/s)
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Simplify this solution Extra Insights
To solve the equation \( h = s t^2 \) for \( t \), start by isolating \( t^2 \). Divide both sides of the equation by \( s \): \[ \frac{h}{s} = t^2 \] Next, take the square root of both sides to solve for \( t\): \[ t = \pm \sqrt{\frac{h}{s}} \] So the solution for \( t \) in terms of \( h \) and \( s \) is: \[ t = \pm \sqrt{\frac{h}{s}} \]
