ElectricPavlov

I think the problem is lies with finding the term 6.85dn or 6852300dn

6.8523  kn   dn      when dn is in mm

    when you convert to m   and N

       this just equals    6.8523 N  dn  

I am referring to your first equation.....it starts as 6.85 kn   which is   6852.3 N   not    6852300 N

Wait....now I see you converted dn to m   from mm which would make it   6852300.....

    looking some more....

Wait...again.....when you converted dn to m  you MULTIPLIED by 1000.....you should DIVIDE by 1000

Then I get   - 6.8523 d^2 + 464868 d + 5.28  = 0     resulting in dn = 67841.2

Pretty good....except you marked amplitude incorrectly on your drawing....it should be 1/2 of the wave height.

How do you go from 6.85 dn   to   6852300 dn

    shouldn't it be    6852.3 dn ?

cosine function

cos x

amplitude (which is 1/2 the total height of the wave) =5

5 cos x

period 2 pi

5 cos x

shifted left  pi/4

5 cos (x + pi/4)

shifted UP 4

5 cos (x+pi/4) +4

The midline of 10 rules out all of the choices except the last two.....

   normal period of sin fxn is 2 pi      if you divide 'x' by pi/2 you stretch the wave out by a factor of 2 /pi     2 pi *  2/pi =4

           so the last one is the correct one

1024    512    256    128    64

oops ....misread the Q !  

Nice work , Chris !   

6370 km  is any of the following:

637.0 x 10^1

63.70 x 10^2

6.370 x 10^3  km    (NOT kilos)      the positive exponent tells how far to move the decimal point to the right.

sqrt ((x+3)^2)  = 7    square both sides

(x+3)^2  = 49            

x+3    = +-7

x = 4   or  -10