I dont get this. can you explain

Mathematics

1 answer:

Nikolay [14]3 years ago

3 0

The rightmost column is the product shown in the middle column. From top-to-bottom, those numbers will be 83.1, 831 (given), 8310.

The middle column is a re-write of the first column and is equal to the third column. You can figure the numbers there from either direction. In the center row, you need 8.31 × ___ = 831. It should not be difficult for you to figure out the number in the blank is 100. (It is also the power of 10 between 10 in the first row and 1000 in the third row.)

The divisor in the first column is the inverse of the multiplier in the second column. 0.1 = 1/10, 0.01 = 1/100, and in the third row, 0.001 = 1/1000. The missing number in the first column is 0.001.

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The four missing numbers are 83.1, 100, 0.001, 8310. (top to bottom, left to right)

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Find the distance between the points.<br> (r, s) and (0, 0)

zhenek [66]

Answer: $\sqrt{r^2+s^2$

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Reason:

Plot the points (0,0) and (r,s). You can place (r,s) anywhere you want.

Connect the two points mentioned and form a right triangle such that the segment from (0,0) to (r,s) is the hypotenuse of said right triangle.

The horizontal leg has a length of r-0 = r units, while the vertical leg will be 's' units.

Check out the diagram below.

We then apply the pythagorean theorem to say $r^2+s^2 = h^2$ where h is the hypotenuse. Solving for h gets us $h = \sqrt{r^2+s^2}$ . We only focus on the positive square root since a negative hypotenuse makes no sense.

Since we made the hypotenuse the segment with endpoints (r,s) and (0,0), this means the hypotenuse length and the distance are the same thing.

Therefore, the distance from (r,s) to (0,0) is $\sqrt{r^2+s^2}$

As an alternative, you can use the distance formula to get the same answer. The distance formula is effectively the pythagorean theorem phrased a different way.