# What is the speed of an object that travels from #( 7,-8,1) # to #( -1,4,-6 ) # over #2 s#?

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To find the speed of an object traveling from one point to another, you first need to calculate the displacement vector between the two points. Then, divide the magnitude of the displacement vector by the time taken to travel between the points.

Given the coordinates of the initial point (7, -8, 1) and the final point (-1, 4, -6), we can calculate the displacement vector:

Δx = -1 - 7 = -8 Δy = 4 - (-8) = 12 Δz = -6 - 1 = -7

The displacement vector is (-8, 12, -7).

Next, find the magnitude of the displacement vector:

|Δr| = √((-8)^2 + 12^2 + (-7)^2) ≈ √(64 + 144 + 49) ≈ √257 ≈ 16.03

Given that the object traveled over 2 seconds, the speed can be calculated as:

Speed = |Δr| / time ≈ 16.03 / 2 ≈ 8.02 m/s

So, the speed of the object is approximately 8.02 meters per second.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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