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Simplifying y(t) = -16t2 + 150t Multiply y * t ty = -16t2 + 150t Reorder the terms: ty = 150t + -16t2 Solving ty = 150t + -16t2 Solving for variable 't'. Reorder the terms: -150t + ty + 16t2 = 150t + -16t2 + -150t + 16t2 Reorder the terms: -150t + ty + 16t2 = 150t + -150t + -16t2 + 16t2 Combine like terms: 150t + -150t = 0 -150t + ty + 16t2 = 0 + -16t2 + 16t2 -150t + ty + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -150t + ty + 16t2 = 0 Factor out the Greatest Common Factor (GCF), 't'. t(-150 + y + 16t) = 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 '(-150 + y + 16t)' equal to zero and attempt to solve: Simplifying -150 + y + 16t = 0 Reorder the terms: -150 + 16t + y = 0 Solving -150 + 16t + y = 0 Move all terms containing t to the left, all other terms to the right. Add '150' to each side of the equation. -150 + 16t + 150 + y = 0 + 150 Reorder the terms: -150 + 150 + 16t + y = 0 + 150 Combine like terms: -150 + 150 = 0 0 + 16t + y = 0 + 150 16t + y = 0 + 150 Combine like terms: 0 + 150 = 150 16t + y = 150 Add '-1y' to each side of the equation. 16t + y + -1y = 150 + -1y Combine like terms: y + -1y = 0 16t + 0 = 150 + -1y 16t = 150 + -1y Divide each side by '16'. t = 9.375 + -0.0625y Simplifying t = 9.375 + -0.0625ySolution
t = {0, 9.375 + -0.0625y}
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