ElectricPavlov

x(x + 6) > 16 - 7x + 24  simplify 

x^2 + 6x > 40 - 7x 

x^2 +13x -40 > 0 

(x-10)(x-4) > 0      shows the intervals    - inf to 4    4 to 10    and  10 to + inf 

Subbing in values in these intervals will show that only the  4  thru 10 interval is not a solution   and 4 and 10 are not solutions

(-inf, 4)  U  ( 10, + inf) 

The answer I get is 36 cm ...... It took a while for me to figure a way to get the answer.....there is likely an easier way but here is my (long -hopefully-correct) solution:

See image :

Use arc tan to find the 63.435 angles then find the 53.13 angle     ( 63.435+63.435 + 53.13 = 180 ° ) 

           then use sin and cos functions for angle 53.13 °  to find the coordinates of T

              then use the coordinates of B and T to find the equation of the line BP to be   y = - 3/4 x + 30 

                   the equation of the Quarter circle is    x^2 + y^2 = 900    or    y = sqrt(900-x^2) 

                         equate this to the line equation and solve for the 'x' coordinate of  point P     then use the line equation and this value of the 'x' coordinate  to find the value of the 'y' coordinate for point P

           Now you have the coordiantes of the two endpoints of the chord line 

                        B    and   P  ====>    then finish by using the distance formula to find  BP = 36 cm 

There really must be an easier way !!!    Whew !   

Expand the far left side, then multiply the second term by   (3x-4)/3x-4)   and multiply the entire equation by  ( 3x-4)^2 

  and simplify the mess to get 

          80x^2- 96-128 = 0        Quadrtaic formula then shows x = 2 as the largest x 

This diagram seems incorrect.....    How can  0, 0   be between   -3,2   and  -2,1 ?     The x coordinates make no sense to me ...

Anyway...using the numbers given:

     all of the radii are the same length ...so the distance^2 from P to B is equal to the distance^2 from P to O

        then using the distance formula :

(x- -3)^2 + (y-2)^2   =  ( x-0)^2 + (y - 0)^2 

x^2 + 6x + 9     +    y^2 -4y +4 = x ^2 + y^2 

6x - 4y + 13 = 0   

Similarly , the distance^2 between P and A   is the same as distance ^2 from P to O 

resulting in  4x - 2y + 5 = 0 

Solving these two simultaneous equations results in   x = 3/2    y = 11/2    for the center of the circle   ( kinda nonsensical)  . 

If you do a search , you will find this question ( or one with slightly different numers) has already been posted and answered....  

Will rows    50 m/min * 45 min = 2250 meters    before Grace even starts

     so now there is only   2800 - 2250 = 550 meters between them 

       their closing speed when they are rowing toward each other is 30 + 50 = 80 m / min

           at this rate they will meet in    550 m / 80 m/min = 6.875 minutes after Grace starts       2:45 + 6.875 min = 2:51  and  52.5 seconds 

                                                                                                                         which is about 2:52 PM 

15 m X 60 m =   900 m ^2           <====== area of the wall 

now convert to ft^2 

900 m^2   / ( .3048 m/ft  * .3048 m/ft )  = 9687.5 ft^2 

Now find the paint required .....

  9687.5 ft^2 / 400 ft^2 / gal = 24.22 gallons   ... you will need to buy 25 gallons    

d = distance       s = plane speed       w = wind speed = 70

d/s  = 1.667 hr      ( distance/rate = time.....   this is for one way)     this shows   s = d/1.667

with and without the wind 

d/(s+w)  + d/(s-w) = 3.833 hr       re-arrange

d(s+w) + d(s-w) = 3.833 (s^2 - w^2)       now sub in some values 

d ( s+70) + d(s-70) 

2 ds   = 3.833 s^2 - 18781.7                 Sub in the definition for s (from above)

2d ( d/1.667) = 3.833 d^2/ 2.778 - 18781.7     Continue to simplify and solve for  'd' 

1.38 d^2  - 2d^2/1.667 - 18781.7 = 0  

.1802 d^2 - 18781.7 = 0 

d = 323 miles 

Very similar Q to help you complete this one:

Sorry... that should be 

4 ( x- 2.25)^2   - 20 .25 + p           SO   p would need to be  + 20.25         Sorry for my error !