# What is the speed of an object that travels from #( 8 , 4, 1 ) # to #( 6 , 0, ,2 ) # over #2 s#?

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To find the speed of the object, we first need to calculate the distance traveled. Using the formula for distance in three-dimensional space, we have:

[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} ]

Substituting the given coordinates, we get:

[ \text{Distance} = \sqrt{(6 - 8)^2 + (0 - 4)^2 + (2 - 1)^2} = \sqrt{(-2)^2 + (-4)^2 + 1^2} = \sqrt{4 + 16 + 1} = \sqrt{21} ]

Now, to find the speed, we use the formula:

[ \text{Speed} = \frac{\text{Distance}}{\text{Time}} ]

Substituting the given time of 2 seconds, we have:

[ \text{Speed} = \frac{\sqrt{21}}{2} \approx 1.443 , \text{units per second} ]

So, the speed of the object is approximately 1.443 units 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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