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At what point do the curves r₁(t) = (t, 2- t, 24 + t²) and r₂(s) = (6 - s, s - 4, s²) intersect?

User John Sibly
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1 Answer

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Final answer:

The curves r₁(t) = (t, 2- t, 24 + t²) and r₂(s) = (6 - s, s - 4, s²) intersect when their coordinates are equal. By setting up equations and solving them, we can find the values of t and s where the curves intersect.

Step-by-step explanation:

The curves r₁(t) = (t, 2- t, 24 + t²) and r₂(s) = (6 - s, s - 4, s²) intersect when their coordinates are equal. Therefore, we can set up the following equations:

t = 6 - s

2 - t = s - 4

24 + t² = s²

Simplifying and rearranging these equations, we get:

t + s = 6

t + s = 6

t² - s² = -24

Solving these equations, we find the values of t and s where the curves intersect.

User Jason Youk
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9.6k points
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