ElectricPavlov

Hey proyaop.....

    You misread Tiggsy's answer ....   '99 squared'       not 99      so    18 works   the result is 9801 =99²

4(x + 7)(12 - x)    expand to:

-4x^2 + 20x + 336           max will occur at   x  =  - b/2a   =  -20 /(2(-4)) = 2.5

sub in that value in the equation  to find the max is   361

Well  for the first log_1/5  portion,     x has to be > 0     there are no logs of negative numbers...or    log of  zero    so the   domain goes from    0 < x < +inf

   the corresponding  RANGE can go from - inf   ( for very, very small x)  to + inf for very, very large x  values

      the base of the logs is irrelavent

Then for the SECOND log portion   log₆    again you cannot have negative numbers or zero    ....this means that 'x' has to be => 1 for the first log fxn (remember no negative numbers!)

    then the range will change from log₆(1) = 0   to  + infinity

so   in summary    domain      1<=x <= + inf

                              range        0 <= y <=+ inf

See the previous two examples for methodology.....

here is a start

-2 ( x^2 + 5x)    - 83             now complete the square.......

x^2 - 8x + 66           'complete the square

(x - 4)^2   - 16 + 66

(x-4)²  + 50         <========== you can finish

6 ( x^2 - 1/3 x )  - 3        now 'complete the square

6 (x - 1/6)²   -1/6 -3

6 ( x-1/6)² - 3 1/6     <========= You can finish

Sub in x = 0     will show   c = 0

now sub in x = 1    to get   a+b = 2

  now sub in x = 2  to get   4a + 2b = 9             Solve red equations to get    a = 2.5      b = -.5

2.5 x²  - .5 x  + 0 = 0      now sub in x = 3   to find your answer

Here is a Venn Diagram of this scenario.....just add the numbers....

The value of y varies inversely as x^2 and when x = 24, y = 15

this means    y = k/x^2       where k is proportionality constant

                       or    y x^2  = k        now when x = 24    y = 15

                              15 (24^2)  = 8640

now when y = 13            13 (x^2) = 8640    solve for 'x'  value(s)

Look at the zeroes of the quadratic ....this is where y = profit = zero

   using quadratic formula   x = 19.677   or  - 1.677     (see graph below)

     so the need to produce at least 20  to mak a profit ( a positive 'y' value)