A train traveling at a speed of s miles per hour applies its brakes before a buffer stop. Assuming d≥0 and s≥0, the distance, d, in yards from the train to the buffer stop once the train comes to rest is:d=0.5(−s2−1.2s+184)Which of the following equivalent expressions for d 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?Choose 1 answer:(A) −0.5s2−0.6s+92.3(B) −0.5(s−13)(s+14.2)(C) −0.5(s+0.6)2+92.48(D) (6.5−0.5s)(s+14.2)
Q. A train traveling at a speed of s miles per hour applies its brakes before a buffer stop. Assuming d≥0 and s≥0, the distance, d, in yards from the train to the buffer stop once the train comes to rest is:d=0.5(−s2−1.2s+184)Which of the following equivalent expressions for d 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?Choose 1 answer:(A) −0.5s2−0.6s+92.3(B) −0.5(s−13)(s+14.2)(C) −0.5(s+0.6)2+92.48(D) (6.5−0.5s)(s+14.2)
Given Equation: We are given the original equation for the distance d in yards: d=0.5(−s2−1.2s+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 d equals 0.
Analysis of Option (A): Let's analyze option (A):−0.5s2−0.6s+92.3This is not equivalent to the original equation because the coefficients and constants do not match the original ones when simplified.
Analysis of Option (B): Let's analyze option (B):−0.5(s−13)(s+14.2)If we expand this, we get:−0.5(s2+14.2s−13s−182.6)Simplifying further gives us:−0.5s2+0.5(13s−14.2s)−0.5×182.6−0.5s2−0.5(1.2s)+91.3This simplifies to:−0.5s2−0.6s+91.3This is also not equivalent to the original equation because the constant term does not match.
Analysis of Option (C): Let's analyze option (C):−0.5(s+0.6)2+92.48Expanding this gives us:−0.5(s2+1.2s+0.36)+92.48Simplifying further gives us:−0.5s2−0.6s−0.18+92.48This simplifies to:−0.5s2−0.6s+92.3This is equivalent to option (A) and is still not equivalent to the original equation.
Analysis of Option (D): Let's analyze option (D): (6.5−0.5s)(s+14.2) Expanding this gives us: 6.5s+92.3−0.5s2−7.1s Simplifying further gives us: −0.5s2−0.6s+92.3 This is equivalent to option (A) and option (C), and is still not equivalent to the original equation.
Conclusion: None of the options A, B, C, or D 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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