AUnVerifedTaxPayer

Observe that x2+3xy+y2−2x−2y+4​=(x+y−1)2+3(xy+4)​.

Thus, x⋆y=xy+4(x+y−1)2+3(xy+4)​​. Let an​=(((⋯((2007⋆2006)⋆2005)⋆⋯)⋆n).

Then we can write the recurrence relation an​=an−1​n+4(an−1​+n−1)2+3(an−1​n+4)​​.

Note that a1​=1. We can compute a2​,a3​,… using this recurrence relation. A

fter some computations, we find that a_2007 = 2008/2007.

P_1 P_2 + P_2 P_3 + P_3 P_4 + \dots + P_9 P_{10} + P_{10} P_1 is equal to 20.

The time difference between driving at 60 mph and 40 mph is 45 minutes, which is 3/4 of an hour. So, the equation for the time you spent driving is:

time = (rate * time_difference) / (rate - new_rate)

Plugging in the known values, we get:

time = (40 mph * 3/4 hours) / (40 mph - 25 mph)

time = 7.5 hours

Since the rate is in miles per hour and the time is in hours, the distance traveled is simply the product of the two:

distance = rate * time

distance = 40 mph * 7.5 hours

distance = 300 miles

Therefore, you drove 300 miles to the beach.

The expression simplifies to 6 - 3*3^(1/3).