CPhill

We can use the cosine inverse to find "theta"

cos^-1 (22/38) = theta = about 54.62°

This evaluates to "pi"

Since this an irrational number, it is never precisely "accurate".....however....we can make it as "accurate" as we want to a specified number of digits......

4b+1/4=5/12     multiply each term by the common denominator of 4 and 12, i.e., 12

48b + 3 = 5      subtract 3 from both sides

48b = 2          divide both sides by 48

b = 2/48  =  1/24

502.65  = pi (r)^2 * 8   divide both sides by 8pi

502.65 / [8pi]  = r^2     take the square root of both sides

r ≈ 4.472 in

Hey, ND.....good to see you!!!

Here's my take on this one......

If the Celestial North Pole traces out a complete orbit every 26,000 years, it must move through 360°  during that time....so.....in one year it must move:

(1/26000) * 360°   =  (9/650)°  = about  0.01384615° =

about    0.8307 ' 50"  [roughly]

C = 2.00P + 7.50

1. 4x/3-5=11    add 5 to both sides

4x/3  = 16       multiply both sides by 3

4x  = 48         divide both sides by 4

x = 12

 2. 2/5(3x+4)=6       multiply both sides by the reciprocal of 2/5   = 5/2

3x + 4   = 6(5/2)    simplify

3x + 4  = 30/2

3x + 4  = 15       subtract 4 from both sides

3x  = 11             divide both sides by 3

x = 11/3

3. 2(3x+4)=4x+12     distribute the 2 on the left side

6x + 8  = 4x + 12    subtract 4x, 8 from both sides

2x  = 4                  divide both sides by 2

x = 2

Thanks, rarinstraw......this could also be :

[3x+2] / 5=7          if so.....multiply both sides by 5

3x + 2  = 35        subtract 2 from both sides

3x  = 33               divide both sides by 3

x = 11

This is a linear model....note that everytime x changes by 1, y changes by 4......and the slope of a line = change in y / change in  x   =  4 / 1   = 4

And using the point (1,6), we have

y - 6  = 4(x - 1)   simplify

y - 6  = 4x  - 4    add 6 to both sides

y = 4x + 2

I assume that you mean that angle Y  = 90°...if so, we have

cosZ  = 28/35     = 4/5      take the inverse cos

cos^-1 (4/5)  = Z  = about 36.87°