What is the solution of x^y=y^x and y=2x?

x=0, y=0

x=2, y=4

Step-by-step explanation:

x = 2, y = 4.

Step-by-step explanation:

x^y = y^x

Substitute y = 2x in the above:

x^2x = (2x)^x

x^2x = 2*x * x^x      Divide both sides by x^x:

x^2x / x^x = 2*x

x^(2x-x) = 2^x

x^x = 2^x

So x = 2.

and y = 2x = 4.

We can also make x = 0 and y = 0  but

I'm not sure if  this result is valid because 0^0 is undefined.

Looking further into this there seems to be different opinions on this with some mathematicians say 0^0 = 1, so x=0, y = 0 may be acceptable.

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.

54 km / hours

step-by-step explanation:

we need to convert seconds to hours

60 seconds = 1 minutes

60 minutes = 1hour

15 m         60 second   60 minutes

  * *         = 54000 meters/ hour

second     1 minute             1 hour

now we need to convert meters to km

1000 m = 1 km

54000 m       1 km

*   = 54 km / hours

hour               1000m