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Simplifying H(t) = 160t + -10t2 Multiply H * t tH = 160t + -10t2 Solving tH = 160t + -10t2 Solving for variable 't'. Reorder the terms: -160t + tH + 10t2 = 160t + -10t2 + -160t + 10t2 Reorder the terms: -160t + tH + 10t2 = 160t + -160t + -10t2 + 10t2 Combine like terms: 160t + -160t = 0 -160t + tH + 10t2 = 0 + -10t2 + 10t2 -160t + tH + 10t2 = -10t2 + 10t2 Combine like terms: -10t2 + 10t2 = 0 -160t + tH + 10t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-160 + H + 10t) = 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 '(-160 + H + 10t)' equal to zero and attempt to solve: Simplifying -160 + H + 10t = 0 Solving -160 + H + 10t = 0 Move all terms containing t to the left, all other terms to the right. Add '160' to each side of the equation. -160 + H + 160 + 10t = 0 + 160 Reorder the terms: -160 + 160 + H + 10t = 0 + 160 Combine like terms: -160 + 160 = 0 0 + H + 10t = 0 + 160 H + 10t = 0 + 160 Combine like terms: 0 + 160 = 160 H + 10t = 160 Add '-1H' to each side of the equation. H + -1H + 10t = 160 + -1H Combine like terms: H + -1H = 0 0 + 10t = 160 + -1H 10t = 160 + -1H Divide each side by '10'. t = 16 + -0.1H Simplifying t = 16 + -0.1HSolution
t = {0, 16 + -0.1H}
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