CPhill

Notice, tertre, that  inscribed angle ACE  intercepts minor arc AE which measures  (3/7)  of the circumference of the circle  =  (3/7)(360° )

So.....the measure of    ACE  =  measure of α =  (1/2) of its  intercepted arc  =

(1/2)* (3/7) (360°)   =

(3 /14)(360°) 

So  7 times this  is  

(7)(3/14)(360°)   =

(3/2)(360°)  =   540°

Sorry, Julius...I don't know this one...!!!

Mmmm...let's see if I know this one.....

Let the width of the rectangle  = x

And let the height  =  -3x^2 + 4

So....the area, A  =  width * height   =  x (-3x^2 + 4) = -3x^3 + 4x

Take the derivative of A    and set to  0

A'   =  -9x^2  +  4

-9x^2 +  4  =  0

-9x^2  =   -4          divide both sides by -9

x^2  =  4/9             take the positive root

x = 2/3     =  width

And  the height is given  by:

 -3(2/3)^2  + 4   = 

-3(4/9) + 4

-4/3 + 4

8/3

So....the max area  is

(2/3)(8/3)  =   16/9   units^2

OK, Adam  !!!

Don't worry....you're not bothering me...LOL!!!

We should have t  instead of   x  in the function

If  we let  1990  =  year "0".....then we can consider 1992 as  year "2"

And so....10 years after this is year "12"

So   we want to find this

[ Consumption in year 12  - Consumption in year 2 ]

__________________________________________

                12   -  2

[  ( 6(12)^2 - 8√12 + 3)  - ( 6(2)^2 - 8√2 + 3 ) ]

____________________________________

                    10

[ (6(12)^2 - 8√12  - 6(2)^2  + 8√2 ]

___________________________

                 10

[ 864  - 8√12 + 8√2 - 24 ]

____________________ 

             10

[ 840  - 8√12 + 8√2 ]

________________   ≈     82.36 billions per year  ⇒  Answer "a"

           10

3)Let ABCDEFGH be a cube. Find angle ACH in degrees.

Without a loss of generalization, assume the cube has edges of length 1.....so....

Let  C  =  (0, 0 , 0)

Let A  =  ( -1, 1, 0)

Let H  =  ( -1, 0 , - 1)

l A l   =   √  [  (-1)^2  + 1^2  + 0^2]  =  √2

l H l   =  √ (-1)^2  + 0^2 + (-1)^2 ]  =  √2

And the dot product  of the vectors A and H  =    A (dot) H   =   (-1)(-1) + (1)(0) + (0)(-1)   =   1

So....  the angle of ACH  =  the angle between the vectors A and H  and is given by :

cos(ACH)  = A (dot) B                  1                    1

                    ________   =        _______  =      ____

                     l A l * l H l             √2 * √2               2

So

arccos  (1/2)    =  ACH  =    60°

The marginal profit is the additional profit made by producing one more unit

We can find this by taking the derivative of P(x)  =

P' (x)   =  .006x^2  + 100

So

P(50)  =  .006(50)^2  +  100     =  $115

I think there might be a slight typo here

What is the equation ??

OK.....we can calculate this as follows

[ Sales in 2006  - Sales in 2003 ]

__________________________

    2006  - 2003

[215000  -  128000]

________________

           3

$29000

Let the entire purchase amount be the number of bags he bought, B,  times the price per bag

So   B*8  =  the entire purchase price

From  this ...he subtracts  $10     and pays $30

So  we have this

B*8  -  10  =  30       add 10 to both sides

B*8  =  40        divide both sides by 8

B  = 5  bags