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Simplifying y(t) = 5 + 10cos(30t) + 15cos(90t) Multiply y * t ty = 5 + 10cos(30t) + 15cos(90t) Remove parenthesis around (30t) ty = 5 + 10cos * 30t + 15cos(90t) Reorder the terms for easier multiplication: ty = 5 + 10 * 30cos * t + 15cos(90t) Multiply 10 * 30 ty = 5 + 300cos * t + 15cos(90t) Multiply cos * t ty = 5 + 300cost + 15cos(90t) Remove parenthesis around (90t) ty = 5 + 300cost + 15cos * 90t Reorder the terms for easier multiplication: ty = 5 + 300cost + 15 * 90cos * t Multiply 15 * 90 ty = 5 + 300cost + 1350cos * t Multiply cos * t ty = 5 + 300cost + 1350cost Combine like terms: 300cost + 1350cost = 1650cost ty = 5 + 1650cost Solving ty = 5 + 1650cost Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1650cost' to each side of the equation. -1650cost + ty = 5 + 1650cost + -1650cost Combine like terms: 1650cost + -1650cost = 0 -1650cost + ty = 5 + 0 -1650cost + ty = 5 Reorder the terms: -5 + -1650cost + ty = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -1650cost + ty = 0 The solution to this equation could not be determined.
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