CPhill

Thanks, hectictar....I didn't even realize we had that.....LOL!!!!

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2. Adam ran across the field at a speed of 5 yards per second and walked back along the same path at a speed of 2 yards per second. For how many seconds did he run if the total round-trip time was three and a half minutes?

3 1/2 minutes  = 3 min 30 sec =   210 sec

Call the distance across the field D

And   Distance / Rate  = Time  ...so..

Time Running + Time Walking  = Total Time.

D / 5  +   D / 2   =  210

2D + 5D

________   =   210        multiply through by  10

    10

7D  =  2100    divide both sides by  7

D = 300 yards

So....the time walking  =  300/2 = 150 sec =  2 min 30 sec

And the time running = 300/5  = 60 sec =  1 minute

\( \frac{1-n}{n+1} + \frac{n-1}{1-n} = 1\)

(1-n)^2 + (n+ 1)(n - 1)

_________________     =      1                  multiply both sides by the fraction denominator

      (1 + n) (1 - n)

(1 - n)^2 + (n+ 1) (n - 1)    =  (1 + n) (1 - n)     simplify

1 - 2n + n^2 + n^2 - 1  =   1 - n^2

2n^2  - 2n = 1 - n^2

3n^2 - 2n - 1  = 0

(3n + 1) (n - 1) = 0

Set each factor to 0 and solve for n

3n +1 = 0                n - 1   = 0

3n = -1                    n = 1      (reject as this makes an original denominator = 0 )

n = -1/3

\(4 - \frac{3x + 1}{4} = x + \frac{3x + 14}{2}\)      get common denominators

16 -[3x + 1]             2x + 3x + 14

__________   =       ___________         

       4                          2

15 - 3x            5x  + 14

______    =   __________          cross-multiply

     4                       2

2 ( 15 - 3x)  =  4(5x + 14)     sinmplify

30 - 6x  =  20x  + 56         add 6x to both sides, subtract 56 from both sides

-26  =  26x       divide both sides by  26

-1 = x

The scale factor of the large cone to the smaller  is  12/3  = 4

The volume of the larger cone   =

(Volume of smaller cone) * (scale factor)^3  =

21  * (4)^3  =

21 * 64  =

1344 in^2

We know the y coordinate wil be 0....so...let the point be (x,0)

And we need to solve this

(0 - x)^2 + (4 - 0)^2   =  (-2 - x)^2 + (0-0)^2     simplify

x^2 + 4^2  = x^2 + 4x + 4

x^2 + 16  = x^2 + 4x + 4  

12 = 4x

3  = x

So  the point is (3,0)

Scale factor  for areas  = √[72/98]  = √72 / √98  = √[36 * 2 ] / √[ 49 * 2 ] =  [6√2] /[7√2]  = 6 /7

Ratio of volumes  = (scale factor)^3  =  (6/7)^3  = 216 / 343  = 216 : 343

The scale factor  =  ³√[27 / 64]  =  3 /4

The ratio of  the surface areas =  (scale factor)^2  = (3/4)^2  =  9 /16 = 9 : 16

20^(5/2) = √20^5  = √[ 20^4 * 20 ] = 20*20√20 =  400√[4*5]   = 2*400√5  =  800√5