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Simplifying H(t) = -12t2 + 480t Multiply H * t tH = -12t2 + 480t Reorder the terms: tH = 480t + -12t2 Solving tH = 480t + -12t2 Solving for variable 't'. Reorder the terms: -480t + tH + 12t2 = 480t + -12t2 + -480t + 12t2 Reorder the terms: -480t + tH + 12t2 = 480t + -480t + -12t2 + 12t2 Combine like terms: 480t + -480t = 0 -480t + tH + 12t2 = 0 + -12t2 + 12t2 -480t + tH + 12t2 = -12t2 + 12t2 Combine like terms: -12t2 + 12t2 = 0 -480t + tH + 12t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-480 + H + 12t) = 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 '(-480 + H + 12t)' equal to zero and attempt to solve: Simplifying -480 + H + 12t = 0 Solving -480 + H + 12t = 0 Move all terms containing t to the left, all other terms to the right. Add '480' to each side of the equation. -480 + H + 480 + 12t = 0 + 480 Reorder the terms: -480 + 480 + H + 12t = 0 + 480 Combine like terms: -480 + 480 = 0 0 + H + 12t = 0 + 480 H + 12t = 0 + 480 Combine like terms: 0 + 480 = 480 H + 12t = 480 Add '-1H' to each side of the equation. H + -1H + 12t = 480 + -1H Combine like terms: H + -1H = 0 0 + 12t = 480 + -1H 12t = 480 + -1H Divide each side by '12'. t = 40 + -0.08333333333H Simplifying t = 40 + -0.08333333333HSolution
t = {0, 40 + -0.08333333333H}
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