Mathermatics?

Question

Stram A runs down a slope that drops 3 meters in elevation for every 10 meters in horizontal distance. Stream B runs down a slope that drops 5 meters in elevation for evey 20 meter in horizontal distane. Compare the gradients of the two streams.

Answer 1

The rise/drop of stream 1 for every 10 meters is 3 so its slope will be:

-3/10 = -0.3

The second stream's inclination drops for every 20 minute. Let us make it 10 so that it will be similar to stream 1:

5/20 = x/10
20x = 50
x = 50/20
x = 2.5

Therefore the second stream's inclination will drop 2.5 meters for every 10 meter horizontal distance. This means that its slope will be:

-2.5 / 10 = -0.25

If you compare the both gradients or slopes you will notice that stream a with the slope of -0.3 has a more inclination towards the vertical axis of the Cartesian Coordinate System than does the second stream with the slope of -0.25.


Good luck.

Answer 2

Stream A
m = 3 / 10 = 6 / 20
Stream B
m = 5 / 20
Gradient of stream A is greater

Answer 3

Gradient = Slope = vertical change / horizontal change.

The first gradient is -3/10
The second gradient is -5/20

Since -3/10 = -6/20, then the first stream is dropping farther (in fact -6/20th of a meter) for every meter of horizontal distance.

The first gradient is steeper.

Answer 4

3/10 ? 5/20

use LCD to make the comparison.

6/20 ? 5/20

therefore, 6/20 > 5/20. Stream A has a bigger gradient.

note: gradient = slope.

Answer 5

A 3/10=0.3; α=arctan 0.3=16.7º

B 5/20=1/4=0.25; ß=arctan 0.25=14.0º

A has a steeper gradient.

Answer 6

A
rise = -3
run = 10
slope = -3/10 = -0.3

B
rise = -5
run = 20
slope = -5/20 = - 1/4 = -0.25

Answer 7

Mathermatics?? Are you from Boston, Mass?