## yrivers36 Group Title Please explain how to set up and find answer. Thank you To protect cities from flooding during heavy rains, open channels are sometimes constructed to handle runoff. The rate R at which water flows through the channel is modeled by R=k sqrt m, where m= slope of the channel and k is a constant determined by the shape of the channel. a) suppose that a channel has a slope of m = 0.01 and a runoff rate of R=340 cubic feet per second. Find K. b) If the slope of the channel increases to m=0.04 what happens to R? 2 years ago 2 years ago

1. raspberryjam Group Title

Ok so to sum it up you have the equation: $R=k\sqrt{m}$ where R = rate at which water flows through the channel m = slope of the channel k = a constant a). In this part you are given m and R, so just plug them into the equation and solve for k. b). You can use the same k you found in part a to answer part b, but this time use .04 for m and solve for R. Compare this answer to the one in part a, what happened? Did R increase or decrease?

2. yrivers36 Group Title

I think that I just figured out a. 340=[\sqrt{0.01}\]

3. yrivers36 Group Title

divide the sqrt on both side and I got 3400

4. raspberryjam Group Title

Yep so that gives you k.

5. yrivers36 Group Title

for b I got R= 680 cubic feet per second

6. raspberryjam Group Title

Okay so what does this tell you about the relationship between R and m?

7. yrivers36 Group Title

the slope rised double

8. raspberryjam Group Title

Yep so as m increases so does R right? This makes them proportional.

9. yrivers36 Group Title

yes

10. yrivers36 Group Title

Thank u