If two lines are perpendicular describe the relationship between their slopes

1 answer:

7 0

Perpendicular lines have slopes that are negative reciprocals. example: line a has a slope of 2/3, line b has a slope if -3/2 if they are perpendicular.

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The Atlantic Salmon swim upstream at a steady rate of 2 miles every 3 minutes. Fill in the table to describe the relationship. R

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The distance traveled by the Salmon is proportional to the duration spent

swimming.

A table of the distance traveled by the Atlantic Salmon is presented as follows;

$\begin{tabular}{|c|c|c}\underline{Time in minutes}&\underline{Miles Traveled at 2/3 miles per minute } \\1&2/3 \\2&4/3\\3&2\\4&8/3\\5&10/3\\6&4\end{array}$

Reasons:

The given parameter are;

The steady rate at which Atlantic Salmon swims = 2 miles in 3 minutes

Distance the Salmon swims, d ∝ Time taken, t

Therefore;

d = s·t

Where;

s = The constant of proportionality = The speed

Which gives;

$\displaystyle s = \mathbf{\frac{Distance, \, d}{Time, \, t}}$

The speed with which the Atlantic Salmon swims per minute is therefore;

$\displaystyle The \ speed = \mathbf{\frac{2 \ miles}{3 \ minutes}} = \frac{2}{3} \ miles /minute$

The distance travelled, <em>d</em>, is given as follows;

$\displaystyle d = \mathbf{\frac{2}{3} \times t}$

A table showing the distance travelled by the fish with time is presented as follows;

$\begin{tabular}{|c|c|c|}\underline{Time, t, in minutes}&\underline{t \times d}&\underline{Miles Traveled, d, at 2/3 miles per minute } \\1&1 \times 2/3 = 2/3&2/3 \\2&2 \times 2/3 = 4/3&4/3\\3&3 \times 2/3 = 2&2\\4&4 \times 2/3 = 8/3&8/3\\5&5 \times 2/3 = 10/3&10/3\\6&6 \times 2/3 = 4&4\end{array}$