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Semenov [28]
3 years ago
9

James built a small electric car and recorded the distance it traveled. The table below shows the distance traveled (n) during t

he first 4 seconds after starting (f). Elapsed Time (seconds) Distance Traveled (feet) 1 6.2 2 12.4 3 18.6 4 24.8 Which of the following equations represents the relationship between the distance traveled and the elapsed ti
Mathematics
1 answer:
Scrat [10]3 years ago
5 0
<span>Table

Elapsed Time (seconds) Distance Traveled (feet)

1                                         6.2

2                                        12.4

3                                        18.6

4                                         24.8

Explanation:

You can check that 6.2 / 1 = 12.4 / 2 = 18.6 / 3 = 24.8 / 4 = 6.2

So, the relationship between the distance traveled and the time elapsed is a constant:

distance traveled / time elapsed = 6.2

n / f = 6.2

=> n = 6.2 f

Answer: n = 6.2 f
</span>
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Determine if the lines r1(t) = &lt;3, 0, 2&gt; + t &lt;1, 2, −2&gt; and r2(s) = &lt;0, 1, −1&gt; + s &lt;4, 1, 1&gt; intersect,
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Answer:

Yes lines are intersecting, point of intersection is <4,2,0>.

Step-by-step explanation:

Given parametric equations of line are:

r_{1}(t) =  + t  \\ r_{1}(t) = \\ r_{1}(t) = ---(1)

r_{2}(s) =  + s \\ r_{2}(s) = \\ r_{2}(s) = ---(2)\\

If lines are intersecting then parametric coordinates of (1) are equal to (2)

3+t=4s---(A)\\2t=1+s---(B)\\2-2t=s-1---(C)\\

Considering A and B to find values of t and s

From A

t=4s-3---(D)

Putting in (B)

2(4s-3)=1+s

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s=1

Then

t=4-3

t=1

If lines are intersecting then these values of s and t must satisfy (C)

2-2(1)=1-1

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This shows lines are intersecting.

At this value of t, (1) becomes

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Putting s=1 in (2)

r_{2}(1)=4, 1+1,-1+1>\\=

Point of intersection is <4,2,0>.

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