yrivers36
  • yrivers36
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?
Mathematics
schrodinger
  • schrodinger
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raspberryjam
  • 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?
yrivers36
  • yrivers36
I think that I just figured out a. 340=[\sqrt{0.01}\]
yrivers36
  • yrivers36
divide the sqrt on both side and I got 3400

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raspberryjam
  • raspberryjam
Yep so that gives you k.
yrivers36
  • yrivers36
for b I got R= 680 cubic feet per second
raspberryjam
  • raspberryjam
Okay so what does this tell you about the relationship between R and m?
yrivers36
  • yrivers36
the slope rised double
raspberryjam
  • raspberryjam
Yep so as m increases so does R right? This makes them proportional.
yrivers36
  • yrivers36
yes
yrivers36
  • yrivers36
Thank u

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