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Simplifying v(t) = 5t2 + -10t Multiply v * t tv = 5t2 + -10t Reorder the terms: tv = -10t + 5t2 Solving tv = -10t + 5t2 Solving for variable 't'. Reorder the terms: 10t + tv + -5t2 = -10t + 5t2 + 10t + -5t2 Reorder the terms: 10t + tv + -5t2 = -10t + 10t + 5t2 + -5t2 Combine like terms: -10t + 10t = 0 10t + tv + -5t2 = 0 + 5t2 + -5t2 10t + tv + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 10t + tv + -5t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(10 + v + -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 '(10 + v + -5t)' equal to zero and attempt to solve: Simplifying 10 + v + -5t = 0 Reorder the terms: 10 + -5t + v = 0 Solving 10 + -5t + v = 0 Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -5t + -10 + v = 0 + -10 Reorder the terms: 10 + -10 + -5t + v = 0 + -10 Combine like terms: 10 + -10 = 0 0 + -5t + v = 0 + -10 -5t + v = 0 + -10 Combine like terms: 0 + -10 = -10 -5t + v = -10 Add '-1v' to each side of the equation. -5t + v + -1v = -10 + -1v Combine like terms: v + -1v = 0 -5t + 0 = -10 + -1v -5t = -10 + -1v Divide each side by '-5'. t = 2 + 0.2v Simplifying t = 2 + 0.2vSolution
t = {0, 2 + 0.2v}
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