ElectricPavlov

Like Hecticar started, factor out 6 from the first two terms

6 (j^2 - j)     - 12      'complete the square' for j

6 (j-1/2)²   - 6/4 - 12

6 (j-1/2)² - 13 1/2

Without calculus:

  this is a dome shaped parabola (due to the -1 coefficient of t²)

    maximum value will occur at the vertex  t value of  - b/2a = - 18 / (2*-1)  = t=9

       this is th maximum t     

             since this is a function of 't' you will need to sub in this value of t into the equation to calulate the maximum value of the function             

    -9^2 + 18(9) - 4 = 77

Thanx for the kind words, SmartMathMan !   You're welcome !       ~ EP

cos x = + 2/3       cosine is positive in Q I   and Q IV    .... or from 0 -90   and   270 = 360^o

discriminant will have to be POSITIVE to have 2 real roots

b^2 - 4ac > 0

m^2 - 4(2)(18) >0

m^2 > 144

m > 12 

m < -12                  you can write it in interval notation......right?

multiply second equatin by -2 

  it becomes  -8x+4y = -2                  the same equation as the first.....both of these are equations of the same line: Infinite Solutions

is that sqrt8    * x

  or   sqrt (8x)

      0r sqrt (8x+9)  ?

x coordinate will be midway betwen -1 and 4      @ 1.5

y                                                         9 and 8           8.5

Solve for x and y

Multiply first eqaution by - 2 to get

  -11x -15y = -1860      add to second equation to get

x = 60    which is the number of smaller containers         only answer  that matches this is D

Square both sides of the equation to get

9 (x+2) = x+4

9x+18 = x+4

8x = 4-18                   I think you can finish !