CPhill

Thanks, hectictar  !!!!

1.

2x^2  -  4x   +   16  = 0      divide through by 2

x^2  -  2x  +   8   =  0      complete the square on  x

x^2 -  2x   +  1    =  - 8  +  1

(x - 1)^2  =   - 7

x  - 1   =   ±√-7

x  =   ± i√7    +  1

The second answer is correct

2. 

Here are the answers that go into each box 

x^4  +  2x^2y^2  + y^4

x^4  +  4x^2y^2

x^2 (x^2 + 4y^2)

2: Find constants A and B such that

          (x+7)/(x^2-x-2) = A/(x-2) + B/(x+1)

We can use partial fractions here

(x +7)  / [ ( x -2) (x + 1) ]   =    [ A (x + 1)  + B(x - 2) ] / [ ( x - 2) (x+1)]

And we can solve this

x + 7  =  A(x + 1)  + B(x - 2)   simplify

x + 7  = Ax + A  +  Bx  - 2B     

x + 7  =  (A + B)x  + ( A - 2B)      equate coefficients

A + B  =  1

A - 2B  = 7          subtract the second equation from the first

3B  = -6

B = -2

So   A  + (-2)  =    1       ⇒  A  =  3

So    { A, B}  =  { 3, -2}

The maximum number of turning points in any polynomial of degree N  is N - 1

We can find this thusly

Post Image Vertex = [Pre-Image Vertex - DilationCenter]*Scale Factor + Dilation Center

So we have

(7,2)  =   [ (-5, -2)   - (-2, -2) ] * Scale Factor  +   (-2, -2)

(7,2)   =  [ (-3, 0 )] * Scale Factor  +  (-2,-2)

(7,2)  - ( -2, -2)  =  (-3, 0) * Scale Factor

( 9, 0)  = (-3, 0) * Scale Factor 

9 / -3   =  Scale Factor

-3  = Scale Factor

a)    Distance along the floor, D, is given by

tan (10) =  60  / D      multiply both sides by D

D * tan (10)  =  60     divide both sides by tan (10)

D  =  60 / tan(10)  ≈  340 cm

b) Ramp Length, R

sin (10)  =  60 / R

R  =  60 / sin (10)  ≈  345.5  cm

Note that the tangent of an angle  is the opposite / adjacent

So.....consider the flagpole height the opposite side and the distance to the flagpole , D, is the adjacent side

So....

tan x  =   10  / D           multiply both sides by D

D *  tan x  =  10          divide both sides by tan x

D  = 10  / tan x

Does that make sense ??

1  =  sin  (5pi/4 -  d)

arcsin 1  =   arcsin  [ sin (5pi/4  - d) ]

pi/2   =  5pi/4  -  d

d  = 5pi/4  - pi/2

 d  = 5pi/4  - 2pi/4

d = 3pi/4  + n* 2pi       where n is an integer

1  =  sin [ 2 (pi -d)]

arcsin 1  =  arcsin  [sin [2(pi - d ) ]

pi/2   = 2 (pi - d)        divide both sides by 2

pi/4   = pi - d

d = pi  - pi/4

d  = 3pi/4  +  n * 2 pi      where n is an integer

J and S are facing each other on opposite sides of a 10 m flagpole. From j pov the top of the pole is at an angle of elevation of 50 degree. From S pov is 35 degree. How far apart are j and S?

Note that, from J's point of view

tan (50)  = 10 / D1       where D1 is the distance J is from the pole

And from S's point of view

tan (35)  =  10 / D2        where D2  is the distance S is from the pole

So.....rearranging both......their distance apart is given by :

D1   +  D2  =

10/tan(50)   +  10/tan(35)    ≈  22.67 m

 D) 

5,4

12,13

3,14)