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yrivers36
 4 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?
yrivers36
 4 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?

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raspberryjam
 4 years ago
Best ResponseYou've already chosen the best response.1Ok 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
 4 years ago
Best ResponseYou've already chosen the best response.0I think that I just figured out a. 340=[\sqrt{0.01}\]

Yrivers36
 4 years ago
Best ResponseYou've already chosen the best response.0divide the sqrt on both side and I got 3400

raspberryjam
 4 years ago
Best ResponseYou've already chosen the best response.1Yep so that gives you k.

Yrivers36
 4 years ago
Best ResponseYou've already chosen the best response.0for b I got R= 680 cubic feet per second

raspberryjam
 4 years ago
Best ResponseYou've already chosen the best response.1Okay so what does this tell you about the relationship between R and m?

Yrivers36
 4 years ago
Best ResponseYou've already chosen the best response.0the slope rised double

raspberryjam
 4 years ago
Best ResponseYou've already chosen the best response.1Yep so as m increases so does R right? This makes them proportional.
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