CPhill

Let the volume be

V =  x^2*h      where x is the side of the base and h is the height    (1)

And.....using the total cost for the surface area....we know that

Total cost for top/ bottom + Total cost for sides =  15

2x^2(3) + 4xh(1.5) =  15

15 - 6x^2  = 6xh

[ 15 - 6x^2] / [6x]  = h      (2)

Put (2)  into (1)  and we have that

V = x^2 [ 15 - 6x^2] / [ 6x]

V =  x [ 15 - 6x^2] / 6

V =  (1/6) (15x - 6x^3 )       take the derivative and set to 0

(1/6) (15 - 18x^2) = 0

18x^2 =  15

x^2  =  15/18    =  5/6

x = √[5/6]  

So.....the volume of the box is :    (1/6)√[5/6] (15 -6 (5/6) )  = (1/6)√[5/6] (10) =  (5/3)√[5/6] ft^3    

LOL!!!.....not possible.....!!!!

1. When 310 is divided by a two-digit positive integer K, the remainder is 37. What is the sum of all possible values of K?

310 - 37 =  273

273 = 3  * 7 * 13

310 / 39 =  7(39) + 37

310 / 91 = 3(91) + 37

Sum of all possible K's  =   39 + 91  =  130

1. AD is parallel to  BC

    AB is parallel to  DC                                                 Definition of a parallelogram

2. Extend segment CB in the direction of B to E                        A line connects any two poins

3. Angle ABE = Angle DAB             A transversal cutting parallel lines form equal alternative ineterior angles

4. Angle CBE = 180                       Definition of a straight angle                           

5. m Angle CBA + m Angle ABE = m Angle CBE         Angle addition postulate

6.   m Angle CBA + m Angle ABE = 180                   Substitution    

7.  Angle CBA is spplemental to angle  ABE       Definition of supplemental angles

8. Angle DAB is supplemental to angle CBA       Substitution

9. Angle BCD = Angle DAB        Opposite angles in a parallelogram are congruent

10. Angle  BCD is supplemental to Angle CBA      Substitution

Here's (b)

We can use the Pythagorean Theorem for  3 dimensions

The distance is given by : √[ 3^2 + 4^2 + 12^2 ]  = √ [ 25 + 144 ]  = √169  =  13 inches

Rate * Time = Distance

The total distance they travel = 1880 km .....so......we have this equation

220T  + 250T = 1880     simplify

470 T  =  1880     divide both sides by  470

T = 4  hours

So

Lian travels   250 * 4   =  1000 km

1)  The minimum is the lowest y value on the graph ⇒  y =1

2)  The max is the highest y value on the graph ⇒  y = - 2

The period is 10  units

Correct, AT....!!!!

Notice that

l 0 l  =  - 0   =  0

Now....suppose that x is negative

So

l x  l  =  - x

For instance ..... suppose that x = - 3   .....we have......

l  -3 l =  - (-3)  =  3