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The mass of the particles that a river can transport is proportional to the fifth power of the speed of the river. A certain river normally flows at
a speed of 4 miles per hour. What must its speed be in order to transport particles that are 12 times as massive as usual? Round your
answer to the nearest hundredth.

The Mass Of The Particles That A River Can Transport Is Proportional To The Fifth Power Of The Speed Of The River A Certain River Normally Flows At A Speed Of 4 class=

Sagot :

olayemiolakunle65

Answer:

6.58 miles per hour

Step-by-step explanation:

Let the mass and speed be represented by m and s respectively. So that,

m [tex]\alpha[/tex] [tex]s^{5}[/tex]

m = k[tex]s^{5}[/tex]

where k is the constant of proportionality.

For a certain river, speed = 4 miles per hour.

m = k [tex](4)^{5}[/tex]

m = 1024k ............ 1

In order to transport particles that are 12 times as massive as usual;

12m = k[tex]s^{5}[/tex]

m = [tex]\frac{ks^{5} }{12}[/tex] ............. 2

Thus,

[tex]\frac{ks^{5} }{12}[/tex] = 1024 k

[tex]s^{5}[/tex] = 12 x 1024

   = 12288

[tex]s^{5}[/tex] 12288

s = [tex]\sqrt[5]{12288}[/tex]

  = 6.5750

s = 6.58 miles per hour

Therefore, its speed must be approximately 6.58 miles per hour.

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