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Simplifying H(t) = 5t2 + 100t Multiply H * t tH = 5t2 + 100t Reorder the terms: tH = 100t + 5t2 Solving tH = 100t + 5t2 Solving for variable 't'. Reorder the terms: -100t + tH + -5t2 = 100t + 5t2 + -100t + -5t2 Reorder the terms: -100t + tH + -5t2 = 100t + -100t + 5t2 + -5t2 Combine like terms: 100t + -100t = 0 -100t + tH + -5t2 = 0 + 5t2 + -5t2 -100t + tH + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 -100t + tH + -5t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-100 + H + -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 '(-100 + H + -5t)' equal to zero and attempt to solve: Simplifying -100 + H + -5t = 0 Solving -100 + H + -5t = 0 Move all terms containing t to the left, all other terms to the right. Add '100' to each side of the equation. -100 + H + 100 + -5t = 0 + 100 Reorder the terms: -100 + 100 + H + -5t = 0 + 100 Combine like terms: -100 + 100 = 0 0 + H + -5t = 0 + 100 H + -5t = 0 + 100 Combine like terms: 0 + 100 = 100 H + -5t = 100 Add '-1H' to each side of the equation. H + -1H + -5t = 100 + -1H Combine like terms: H + -1H = 0 0 + -5t = 100 + -1H -5t = 100 + -1H Divide each side by '-5'. t = -20 + 0.2H Simplifying t = -20 + 0.2HSolution
t = {0, -20 + 0.2H}
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