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