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Simplifying S(t) = -16t2 + 30t Multiply S * t tS = -16t2 + 30t Reorder the terms: tS = 30t + -16t2 Solving tS = 30t + -16t2 Solving for variable 't'. Reorder the terms: -30t + tS + 16t2 = 30t + -16t2 + -30t + 16t2 Reorder the terms: -30t + tS + 16t2 = 30t + -30t + -16t2 + 16t2 Combine like terms: 30t + -30t = 0 -30t + tS + 16t2 = 0 + -16t2 + 16t2 -30t + tS + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -30t + tS + 16t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-30 + S + 16t) = 0Subproblem 1
Set the factor 't' equal to zero and attempt to solve: Simplifying t = 0 Solving t = 0 Move all terms containing t to the left, all other terms to the right. Simplifying t = 0Subproblem 2
Set the factor '(-30 + S + 16t)' equal to zero and attempt to solve: Simplifying -30 + S + 16t = 0 Solving -30 + S + 16t = 0 Move all terms containing t to the left, all other terms to the right. Add '30' to each side of the equation. -30 + S + 30 + 16t = 0 + 30 Reorder the terms: -30 + 30 + S + 16t = 0 + 30 Combine like terms: -30 + 30 = 0 0 + S + 16t = 0 + 30 S + 16t = 0 + 30 Combine like terms: 0 + 30 = 30 S + 16t = 30 Add '-1S' to each side of the equation. S + -1S + 16t = 30 + -1S Combine like terms: S + -1S = 0 0 + 16t = 30 + -1S 16t = 30 + -1S Divide each side by '16'. t = 1.875 + -0.0625S Simplifying t = 1.875 + -0.0625SSolution
t = {0, 1.875 + -0.0625S}
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