## yrivers36 3 years ago 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?

1. raspberryjam

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

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

3. yrivers36

divide the sqrt on both side and I got 3400

4. raspberryjam

Yep so that gives you k.

5. yrivers36

for b I got R= 680 cubic feet per second

6. raspberryjam

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

7. yrivers36

the slope rised double

8. raspberryjam

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

9. yrivers36

yes

10. yrivers36

Thank u