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The general solution is theta = pi/4 + 2*pi*k.

d + f = 6.

-9cos (x)  =  4

cos (x)  =  -4/9

Take  the  arccos

arccos (-4/9) = x     =  2.031       and      2pi - 2.031  = 4.252

Yeah, you and I had the same idea! :)

I think we need to use modular arithmetic. This is how far I got \(n^2 - n = n(n - 1)\equiv 0\mod{10000}\).

I just realized that my "n" needs to be capitalized but whatever... :)

This  is  = the number  of ordered sets  formed  by  taking  3 objects  from 4  =

P(4,3)  =   24  sets

FV = PV x [1 + R]^N

FV =10,000 x 1.10^4

FV =10,000 x  1.4641

FV =$14,641.00

then don't comment an answer if you don't know what it is...

um... what. So Alice can have 3 choices, bob has 2, and carol has 1. That means its 6 ways..... so it's not just 3...

From  6 - 7   =  40 miles

From 7 - 8   =   20 miles

From 8 - 10  =  60 miles

From 10 - 11  = 40 miles

Avg  speed  =  Distance traveled  / Time  traveled =   [ 40 + 20 + 60 + 40 ]  / 5  = [ 160 ] / 5  =

32  mph

Not sure if this helps, but graphing may work. Try setting up circle inequalities?

{1, 2, 3} | {1, 2, 4} | {1, 3, 2} | {1, 3, 4} | {1, 4, 2} | {1, 4, 3} | {2, 1, 3} | {2, 1, 4} | {2, 3, 1} | {2, 3, 4} | {2, 4, 1} | {2, 4, 3} | {3, 1, 2} | {3, 1, 4} | {3, 2, 1} | {3, 2, 4} | {3, 4, 1} | {3, 4, 2} | {4, 1, 2} | {4, 1, 3} | {4, 2, 1} | {4, 2, 3} | {4, 3, 1} | {4, 3, 2} (total: 24)

Average speed = total distance traveled/total time it took.

The trip took 5 hours in total and they travelled 160 miles, giving you an average speed of 160/5 = 32 mph.

Voldemort has a savings account containing $\$10000$. Interest accumulates so that every five years, the amount of money in that account grows to 11/10  of its amount at the beginning of the five years. How much money is in that account after twenty years, given that no money is put into or taken out of the account?

We  have  4 compounding  periods  in a 20 year period.....so...

10000  (11/10)^4  =   $14,641