geno3141

Hint:  Use Pick's Theorem.

Since there are 5 factors and the product is 1/32, find the fiftth root of 1/32, which is 1/2.

Solve:  cos( pi / n )  =  0.50

--->   pi / n  =  cos^-1(0.50)

--->        pi  =  n · cos^-1(0.50)

--->        n  =  pi / cos^-1(0.50)

--->        n  =  3

Each of the other factors have a value of -0.50.

- sqrt( -29 )  =  -i·sqrt(29)

The volume of a cube can be found by:  V  =  s³   --->   512  =  s³   --->   s  =  8

The surface area of one side is  8 x 8  =  64 square inches.

If you want to know the surface area of three sides, you will need to multiply this answer by 3.

There are two asymptotes, one at x = 1 and the other at x = 5.

Therefore, the denominator must include these two factors:  (x - 1)(x - 5).

Since only one choice has this, it must be the one that you choose.

The floor:  9 feet by 12 feet is the same as 108 inches by 144 inches.

The area will be 108 inches x 144 inches  =  15,552 square inches.

Each tile is 4 inches by 6 inches which is an area of 4 inches x 6 inches  =  24 square inches.

Dividing 15,552 square inches by 24 square inches gives an answer of 648 tiles.

h  =    x

b₁ =   x

b₂ = 2x

Area  =  ½·h·(b₁ + b₂)   --->   Area  =  ½·x·(x + 2x)    --->   Area  =  ½·x·(3x) 

                                     --->   Area  =  (3/2)·x²

Let             x  =  liters of the 10% solution.

Then  30 - x  =  liters of the 30% solution

(percentage) · (amount)  +  (percentage) · (amount)  =  (final percentage) · (final amount)

             0.10 · x               +               0.30 · (30 - x)     =                        0.25 · 30 

                                                  0.10x + 9.00 - 0.30x  =  7.50         

                                                               9.00 - 0.20x  =  7.50

                                                                       - 0.20x  =  -1.50

                                                                                x  =  7.5     liters of the 10% solution

                                                                        30 - x  =  22.5    liters of the 30% solution

Try this:  (x - 1) / [ (x + 1)·(x - 2) ]  <= 0

There are 2! = 2 ways to arrange the 2 refuseniks.

There are 4! = 24 ways to arrange the other 4.

Multiplying these together, we get 48 ways.

There are 10 different places to put the refuseniks:  (X = refusenik; - = other)

          X-X---          -X-X--          --X-X-          ---X-X

          X--X--          -X--X-          --X--X

          X---X-          -X---X

          X----X

10 x 48  =  480 ways.