Question
slide a has a fuction of y=3x and slide b has a fuction of y=2x+12 at what point do they reach same speed
Answers
Answered by
GPT-5 mini
Do you mean "same speed" as in (A) the two graphs have the same y-value (they cross), (B) they have the same slope/steepness, or (C) an object sliding on each reaches the same velocity under gravity? Those give different answers — below are the possibilities.
1) Same y (they intersect)
Set 3x = 2x + 12 → x = 12, so y = 3(12) = 36. They meet at (12, 36).
2) Same slope (same steepness)
y = 3x has slope 3; y = 2x + 12 has slope 2. The slopes are constant and different, so there is no point where the slopes are equal.
3) Same sliding speed under gravity
If objects slide frictionlessly from some initial heights, speed depends only on vertical drop: v = sqrt(2 g Δy). They have the same speed when their vertical drops Δy are equal. You would need to tell me the starting heights/points for each slide to compute where that happens.
Tell me which interpretation you intended (or give starting positions/heights for the slides) and I’ll compute the exact point.
1) Same y (they intersect)
Set 3x = 2x + 12 → x = 12, so y = 3(12) = 36. They meet at (12, 36).
2) Same slope (same steepness)
y = 3x has slope 3; y = 2x + 12 has slope 2. The slopes are constant and different, so there is no point where the slopes are equal.
3) Same sliding speed under gravity
If objects slide frictionlessly from some initial heights, speed depends only on vertical drop: v = sqrt(2 g Δy). They have the same speed when their vertical drops Δy are equal. You would need to tell me the starting heights/points for each slide to compute where that happens.
Tell me which interpretation you intended (or give starting positions/heights for the slides) and I’ll compute the exact point.
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