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3 years ago

8

The position of an open-water swimmer is shown in the graph. The shortest route to the shoreline is one that is perpendicular to

the shoreline. Write an equation that represents this path.

1 answer:

Stolb23 [73]3 years ago

6 0

Answer:

Step-by-step explanation:

To define the perpendicular line we need to first know the slope of the reference line graphed.

m=(y2-y1)/(x2-x1) we have points (0,5) and (2,1)

m=(1-5)/(2-0)

m=-4/2

m=-2

For lines to be perpendicular their slopes must satisfy

m1m2=-1, we have a line with a slope of -2 so

-2m=-1

m=1/2, so our perpendicular line is so far

y=x/2+b, it must have point (3,2) so we can solve for b

2=3/2+b

b=1/2, so the swimmer will travel along the line

y=x/2+1/2

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Either $\displaystyle \frac{-1522}{\sqrt{41}}$ (approximately $-238$ ) or $\displaystyle \frac{1522}{\sqrt{41}}$ (approximately $238$ .)

Step-by-step explanation:

Let $a$ denote the first term of this geometric series, and let $r$ denote the common ratio of this geometric series.

The first five terms of this series would be:

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Second equation:

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Similarly, rewrite and simplify the second equation:

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Therefore, the second equation becomes:

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