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.

6.58 miles per hour

Step-by-step explanation:

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

m

m = k

where k is the constant of proportionality.

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

m = k

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

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

12m = k

m = ............. 2

Thus,

= 1024 k

= 12 x 1024

   = 12288

12288

s =

  = 6.5750

s = 6.58 miles per hour

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

i think it would be 43 movies that would have to be watched.

step-by-step explanation:

think about it. for the second plan, every month is 8 dollars. 8 x 12= 96. so thats the number for the second plan. now for the first plan, its annual meaning you have to pay 10 dollars every year. so now you have to get an equivalent amount of 86 since 96-10=86. 86 divided by 2 since every movie costs 2$ then you would have to watch 43 movies a year to get the same as the second plan. i really hoped this . have a wonderful day as well!