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Simplifying H(t) = 48t + -8t2 Multiply H * t tH = 48t + -8t2 Solving tH = 48t + -8t2 Solving for variable 't'. Reorder the terms: -48t + tH + 8t2 = 48t + -8t2 + -48t + 8t2 Reorder the terms: -48t + tH + 8t2 = 48t + -48t + -8t2 + 8t2 Combine like terms: 48t + -48t = 0 -48t + tH + 8t2 = 0 + -8t2 + 8t2 -48t + tH + 8t2 = -8t2 + 8t2 Combine like terms: -8t2 + 8t2 = 0 -48t + tH + 8t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-48 + H + 8t) = 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 '(-48 + H + 8t)' equal to zero and attempt to solve: Simplifying -48 + H + 8t = 0 Solving -48 + H + 8t = 0 Move all terms containing t to the left, all other terms to the right. Add '48' to each side of the equation. -48 + H + 48 + 8t = 0 + 48 Reorder the terms: -48 + 48 + H + 8t = 0 + 48 Combine like terms: -48 + 48 = 0 0 + H + 8t = 0 + 48 H + 8t = 0 + 48 Combine like terms: 0 + 48 = 48 H + 8t = 48 Add '-1H' to each side of the equation. H + -1H + 8t = 48 + -1H Combine like terms: H + -1H = 0 0 + 8t = 48 + -1H 8t = 48 + -1H Divide each side by '8'. t = 6 + -0.125H Simplifying t = 6 + -0.125HSolution
t = {0, 6 + -0.125H}
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