ElectricPavlov

y = mx +b    is slope intercept form    m = slope    b = y intercept     put in the values you are given for m and b and you are done !

Trig identity:

tan²(x)=    ( 1-cos(2x) )  / ( 1+cos(2x) ) ​

x+y = 51

x-y = 25     add the two equations

2x = 76

x = 38              Now you should be able to find 'y'

Distance east =   250 +  115 cos (-25)

   distance south = 115 sin (-25)                             (in this situation the - signs are really not needed)

Then Use Pyrthagorean theorem to find the

          RESULTANTdistance =   sqrt (  (250 +115 cos25)^2     +      (115 sin 25)^2  )

Have you graphed both of the lines to see the figure ?   try that first....

Here is the graph:

https://www.desmos.com/calculator/htrxqzjmw5

What !?     You only have    wavelength and frequency.....       f = c/lambda      f*lambda = C    or    f * (wavelength) = Speed of light

Amplitude can be anything....depends on the power put into the wave

Aww.....c'mon.....you're kidding me, right?  

(18 + c )t  =4     18t + ct = 4

(18-c) t = 2        18t - ct  = 2     add together

                          36t = 6       t  =  6/36   = 1/6 hr

(18 + c) ( 1/6) = 4

   3 + 1/6  c = 4

                c= 6 m/hr

The equation of the line is y = 2x - 4     or    0 = 2x - y - 4

      everything in the yellow area (including the line itself)

          would be less than  this line

                    2x - y - 4 >=0            a,b and c are integers and have no common factor  greater than 1 

Here is a graph:

https://www.desmos.com/calculator/cq8gtx2vek

Assuming it is a circular shaped button

area of circle = pi r^2

50.24 = pi r^2

sqrt (50.24/pi) = r