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Thanx, Chris..... and goodnight !    ~ EP  

Daniel has to cover 1/3 mile at the difference in speeds (5 m/hr) to catch up

1/3 m / 5 m/hr  = 1/15 hr = 4 minutes

v =  22      c  = 6

So   we   have  that

-16t^2  +  22t   +  6  = 10       

-16 t^2  + 22t  - 4  =  0           multiply through by  - 1

16t^2  - 22t   +  4   =  0        divide through   by 2

8t^2  - 11t  + 2 =  0

Using the quadratic formula

t  =    11  ± sqrt ( 11^2  - 4 * 8 * 2)                11  ± sqrt (57)

       ________________________   =       _____________

                   2 * 8                                               16

It  first reaches  10  ft      at     [  11  - sqrt (57)  ]  / 16   ≈  .216 sec

Conversion  factor  from mph  to ft - per - sec  =

mph  *  88 /  60

45 mph   =   45 *  88  / 60  =  66ft/s

50 mph  = 50 * 88  / 60   = 220/3  ft/ s

1/3  mile  =  5280 ft / 3  =   1760 ft  = the distance  that Daniel  must close to  catch Frank

The  difference  in their rates = Daniel's  effective closing rate   =  ( 220/3  - 66 ) ft/s

So....the time  (in seconds) to catch Frank  is

Distance  to close /  eff. closing rate

(1760)  /( 220/3  - 66)   =  240  sec  =   4 min

I mean is it good or bad to have a high score in emotional stability ?    

Of course.  Consider the inverse:  Would it be good to have a high score in emotional instability? 

25th term   =  9th term +  d (25  - 9)  =   -6 + (5/4) ( 16)   = -6  + 20  =   14

If an arc of 60° on circle A  has the same length as an arc of 45° on circle B, what is the ratio of the area of circle A to the area of circle B?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Circle M radius       R_(M) = 1                     |       Circle N radius   R_(N) = [(L_(A) * 8)/pi] / 2 = 4/3

                                                                 |

Arc length   L_(M) = 2rpi = 1.047197551     |        Arc length  L_(N) = L_(M)

                                                                  |

Circle M  area          A = 3.141592654      |       Circle N area      A = (4/3)²pi = 5.585053606

The ratio of the area of a circle M to the area of a circle N is:          A / B = 9 / 16

V_pyramid  =    area  of  base  *  height  /   3

Area of base =  sqrt  (3)  / 4  *   14^2   =  49sqrt (3)

Volume =   49 sqrt (3)  * 30   /  3  =      490 sqrt (3)   units^3   ≈  848.7  units^3

Excellent,  EP   !!!

Rectangular prism base =    4 x 4 x 9   m³

  triangular prism top  =   1/2 b * h   * l   =     1/2 *4 * 3 * 9   m³

    Compute and add reds together for final answer.... 

Welll        y/z  * z/w   = y/w = 2/3 * 5/8 =   10/24 = y/w = 40/96

  and     x/y * y/z = x/z = 3/4 * 2/3 = 6/12

        then x/z * z/w = x/w   =    6/12 * 5/8 = 30/96 = x/w  

 and  w/w = 1 = 96/96

sooooo    (  x+ y+w)  / w   =   ( 40 + 30 + 96) / 96 = ........

CPhill!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!                          I     NEEED   your help plsssss

1 is 4a+15b
2 is 5x-4
3 is 2x-22
4 is 8x-21
5 is 25x + 55
6 is 55x - 17

   4 minutes costs 2 dollars   or 50 cents per hour minute 

Typo      Focus = (0, 1/4)

Post    4 x 60 = 240 in^2

 PLUS sign    8x8   +  1/2 8 * 5 = 84

= 324 in ²

S₁     3 7 11 15 19 23 27 31 35 39 43 47 51

S₂     1 6 11 16 21 26      31      36 41 46 51

makes a new series     11   31   51      a = 11   d = 20

S = (n/2) × (2a + (n−1)d)

 S₂₀ = 20/2 ( 2(11)+19(20))

        = 10 (22+ 380) = 10(402) = 4020

From 2 minutes to 6 minutes  (4 minutes) is an increase of 2 dollars charge

   4 minutes costs 2 dollars   or 50 cents per hour

at 2 minutes the rental charge would be 1 dollar meanning it costs 9 initially

10.25   - 9 initial leaves   1.25      at 50 cents a minute this woud get you   2 1/2 minutes      (what a bargain! )

Northwest is 315^o

^{Start at oigin 0,0    find components of north and west for each}

A    2 hours          2 * 10.5 * sin 315  =14.85  W

                             2 * 10.5 * cos 315 = 14.85 N

B  2 hours             28 sin 280 = 27.57 W

                              28 cos 280 = 4.86 N     

Ship A is   |14.85 - 4.86| = 9.99   N-S   km

  and          |14.85 - 27.57|   = 12.72   W-E   km       of ship B         Pythag theorem    sqrt (12.72^2 + 9.99^2) = 16.17 km  apart

(I hope I did that correctly! )

Correct! Nice job! Good explanation! I like your method!

5 4 3

5 4 2

5 3 3

5 4 4  

5 5 4

5 5 3

5 5 2

5 5 1 

5 5 5        nine?

Ok. Thank you for telling me Melody. 

                  2x^3      - 5x^2    +   x       - 2

x  +  7    [  2x^4   +   9x^3     -  34x^2    +   5x    -   14   ]

                 2x^4  +   14x^3

                ____________________________________

                              - 5x^3    -  34x^2

                             - 5x^3    -   35 x^2

                           ________________________

                                               x^2    +    5x

                                               x^2    +    7x

                                               ___________________

                                                          -2x        -14

                                                          -2x       - 14

                                                       ____________

Let  A  be the  arc length

A   =  R1  ( pi/3)    →     A / (pi/3)   =  R1

A  =   R2  ( pi/4)   →     A / (pi  / 4) =  R2

R1  / R2   =   [A / ( pi/3) ]  /  [ A /(pi/4) ]  =   [ 3/pi ]  / [ 4/pi ]  =   3  /  4

Ratio of areas =  (3/4)^2   = 9/16

Don't worry about it.  We were both in the wrong.  

Just remember to respond positively to people when they try to help you.

If they are wrong take the time to find their error or at least post an explanation of why they are wrong. (the correct answer)

Even if it is just as simple as :

"Thanks, but I think your answer might be wrong because when I put your answer in the box the response said 'wrong' "

Although, a proper explanation, if you have one, would be a lot better.