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A train traveling at a speed of ss miles per hour applies its brakes before a buffer stop. Assuming d0d \geq 0 and s0s \geq 0, the distance, dd, in yards from the train to the buffer stop once the train comes to rest is:\newlined=0.5(s21.2s+184)d=0.5(-s^{2}-1.2s+184)\newlineWhich of the following equivalent expressions for dd contains the traveling speed of the train, as a constant or coefficient, for which the train rests right at the buffer stop after applying its brakes?\newlineChoose 11 answer:\newline(A) 0.5s20.6s+92.3-0.5s^{2}-0.6s+92.3\newline(B) 0.5(s13)(s+14.2)-0.5(s-13)(s+14.2)\newline(C) 0.5(s+0.6)2+92.48-0.5(s+0.6)^{2}+92.48\newline(D) (6.50.5s)(s+14.2)(6.5-0.5s)(s+14.2)

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Q. A train traveling at a speed of ss miles per hour applies its brakes before a buffer stop. Assuming d0d \geq 0 and s0s \geq 0, the distance, dd, in yards from the train to the buffer stop once the train comes to rest is:\newlined=0.5(s21.2s+184)d=0.5(-s^{2}-1.2s+184)\newlineWhich of the following equivalent expressions for dd contains the traveling speed of the train, as a constant or coefficient, for which the train rests right at the buffer stop after applying its brakes?\newlineChoose 11 answer:\newline(A) 0.5s20.6s+92.3-0.5s^{2}-0.6s+92.3\newline(B) 0.5(s13)(s+14.2)-0.5(s-13)(s+14.2)\newline(C) 0.5(s+0.6)2+92.48-0.5(s+0.6)^{2}+92.48\newline(D) (6.50.5s)(s+14.2)(6.5-0.5s)(s+14.2)
  1. Given Equation: We are given the original equation for the distance dd in yards: d=0.5(s21.2s+184)d = 0.5(-s^2 - 1.2s + 184) We need to find an equivalent expression that represents the condition where the train rests right at the buffer stop after applying its brakes. This means we are looking for an expression where dd equals 00.
  2. Analysis of Option (A): Let's analyze option (A):\newline0.5s20.6s+92.3-0.5s^2 - 0.6s + 92.3\newlineThis is not equivalent to the original equation because the coefficients and constants do not match the original ones when simplified.
  3. Analysis of Option (B): Let's analyze option (B):\newline0.5(s13)(s+14.2)-0.5(s - 13)(s + 14.2)\newlineIf we expand this, we get:\newline0.5(s2+14.2s13s182.6)-0.5(s^2 + 14.2s - 13s - 182.6)\newlineSimplifying further gives us:\newline0.5s2+0.5(13s14.2s)0.5×182.6-0.5s^2 + 0.5(13s - 14.2s) - 0.5 \times 182.6\newline0.5s20.5(1.2s)+91.3-0.5s^2 - 0.5(1.2s) + 91.3\newlineThis simplifies to:\newline0.5s20.6s+91.3-0.5s^2 - 0.6s + 91.3\newlineThis is also not equivalent to the original equation because the constant term does not match.
  4. Analysis of Option (C): Let's analyze option (C):\newline0.5(s+0.6)2+92.48-0.5(s + 0.6)^2 + 92.48\newlineExpanding this gives us:\newline0.5(s2+1.2s+0.36)+92.48-0.5(s^2 + 1.2s + 0.36) + 92.48\newlineSimplifying further gives us:\newline0.5s20.6s0.18+92.48-0.5s^2 - 0.6s - 0.18 + 92.48\newlineThis simplifies to:\newline0.5s20.6s+92.3-0.5s^2 - 0.6s + 92.3\newlineThis is equivalent to option (A) and is still not equivalent to the original equation.
  5. Analysis of Option (D): Let's analyze option (D):
    (6.50.5s)(s+14.2)(6.5 - 0.5s)(s + 14.2)
    Expanding this gives us:
    6.5s+92.30.5s27.1s6.5s + 92.3 - 0.5s^2 - 7.1s
    Simplifying further gives us:
    0.5s20.6s+92.3-0.5s^2 - 0.6s + 92.3
    This is equivalent to option (A) and option (C), and is still not equivalent to the original equation.
  6. Conclusion: None of the options AA, BB, CC, or DD are equivalent to the original equation. There seems to be a mistake in the problem statement or the options provided, as none of them match the original equation exactly.

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