ElectricPavlov

You're told  'x' is in Q III     then   x/2 will be in Q II and be negative also

    using the identity       cos x/2  = +- sqrt   (   (1+(-2/3)) /2) = +- sqrt 1/6   =  +-  1/sqrt6  =  sqrt 6  / 6 

                                                                                                                     BUT it is   in Q II    - sqrt 6/6

The graph crosses y= -1   four times           4

Trig identity

cos (x/2)   = +-  sqrt  ( (1+cos x)/2 )       Plug and chug   ....

Here is a Venn diagram:

The LCM  of  40    50    and   60      is  600 minutes   which is    10 hours from 7:30.......

x  * .4   = amount OFF

x * . 6 = price after 40% off

x * .6  = price after 40% off

x * .6  * .5       +    x  *  .4   = 490 

.3 x     + .4x = 490          x = 700 dollars    original price      

You should plot all of the given points to more easily answer this question....

Sorry....all of your answers appear to me to be incorrect  

It LOOKS like the period is 32      at t= 4   value is 41,7    then it decreases and rises back up to 41.7   at  t = 36

       36-4 = 32 s

The min is 20    the max  is 41.7       (41.7-20)/2 = amplitude         Midline = 20 + amplitude

These values are garnered by looking at the data in the table....a graph of the data would be better...especially when they ask for phase shifts in similar questions....

x = nickels                          value  .05 x

d = dimes = (15-x)              value  .10 (15-x)      the values summed = 1.35

.05x        +    .10 (15-x )        =   1.35       solve for 'x' the # nickels        then dimes  =   15-x

1/x   +   1/(x-1)   =   1/2

x-1  +    x    = 1/2 (x )(x-1)

2x-1  =  1/2x^2  - 1/2 x

0 = 1/2 x^2 - 2.5x +1     Use quadratic formula to find

X= 4.56 HOURS        AND     3.56 HOURS     

Strong work CU !!         (at least we BOTH got the same answer !)