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Simplifying S(t) = -5t2 + 80t Multiply S * t tS = -5t2 + 80t Reorder the terms: tS = 80t + -5t2 Solving tS = 80t + -5t2 Solving for variable 't'. Reorder the terms: -80t + tS + 5t2 = 80t + -5t2 + -80t + 5t2 Reorder the terms: -80t + tS + 5t2 = 80t + -80t + -5t2 + 5t2 Combine like terms: 80t + -80t = 0 -80t + tS + 5t2 = 0 + -5t2 + 5t2 -80t + tS + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -80t + tS + 5t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-80 + S + 5t) = 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 '(-80 + S + 5t)' equal to zero and attempt to solve: Simplifying -80 + S + 5t = 0 Solving -80 + S + 5t = 0 Move all terms containing t to the left, all other terms to the right. Add '80' to each side of the equation. -80 + S + 80 + 5t = 0 + 80 Reorder the terms: -80 + 80 + S + 5t = 0 + 80 Combine like terms: -80 + 80 = 0 0 + S + 5t = 0 + 80 S + 5t = 0 + 80 Combine like terms: 0 + 80 = 80 S + 5t = 80 Add '-1S' to each side of the equation. S + -1S + 5t = 80 + -1S Combine like terms: S + -1S = 0 0 + 5t = 80 + -1S 5t = 80 + -1S Divide each side by '5'. t = 16 + -0.2S Simplifying t = 16 + -0.2SSolution
t = {0, 16 + -0.2S}
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