If the number of steps moved down is represented by negative integers and the number of steps moved up by positive integers, represent his moves in part (i) and (ii) by completing the following:

(a) [tex]-3+2-\ldots=-8[/tex]

(b) [tex]4-2+\ldots=8[/tex]

In (a), the sum [tex]-8[/tex] represents going down by eight steps. What will the sum [tex]8[/tex] in (b) represent?



Answer :

Sure, let's tackle this step-by-step with a clear breakdown of what each part represents, based on the given information.

Given:
(a) [tex]\(-3 + 2 - \ldots = -8\)[/tex]
(b) [tex]\(4 - 2 + \ldots = 8\)[/tex]

First, let's interpret what part (a) tells us:
- Negative integers (e.g., -3) represent steps moved down.
- Positive integers (e.g., +2) represent steps moved up.
- The final result [tex]\(-8\)[/tex] indicates that overall, there was a descent of 8 steps.

Now, let's move on to part (b):
- Here we see the expression [tex]\(4 - 2 + \ldots\)[/tex].
- The final result [tex]\(8\)[/tex] indicates that there was a net increase of 8 steps.

Given the question asks about the sum [tex]\((b)\)[/tex] where the sum equals 8, we need to interpret this result:
- The positive net result of 8 in part (b) represents an overall ascent, moving up by eight steps.

Thus, the sum of [tex]\(8\)[/tex] in part (b) represents going up by eight steps. This means that despite moving a combination of up and down steps, the total net movement resulted in moving upward by 8 steps.

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