ElectricPavlov

Just use the calculator on this website!

If the slope is 25% then the road must RISE 25 feet for every 100 feet of horizontal distance

tan x = opposite/adjacent = rise/run = slope = 25/100 = .25

Arctan(.25) = x = 14 degrees

Subtract '1' from both sides of the equation to get:

-5x = 20     Now, divide by -5 to get 'x'

x = 20/(-5) = -4

Statics:   Since the object is hanging in equalibrium, all of the vertical forces have to balance(i.e. sum= o) and all of the horizontal forces have to balance.

Vertical forces:

32rope = tcos32

24rope=  t'tcos24

weight = -450          

SO they must balance:  tcos32 + t'cos24 - 450 =0

tcos32 +t'cos24 = 450    (FIRST equation)

Horizontal forces must cancel out too:   (the horizontal force in 32rope must equal horizontal force in 24rope)

32rope = t sin 32

24rope = t' sin 24       These forces are EQUAL (if they were not EQUAL something would MOVE)

tsin32 = t'sin24            we can solve this for t and substitute into the FIRST eqaution for VERTICAL forces to solve

t = t'  sin 24/sin32       (SECOND equation)

Substitute:  (t' sin24/sin32)  * cos32 + t'cos24 = 450

                   t' (.6509 + .9135) = 450       t' = 287.64 lbs   (tension in 24 degree rope)

SECOND equation  t = t' sin 24/sin32    t = 220.77  lbs   (tension in 34 degree rope)

Total temperature change = 16-(-33)= 49 degrees

Time change 2:00 to 9:00      7 hours                           

Average drop per hour     49/7 = 7 degrees/hr         

Assuming that births are evenly distributed throughout the year:

30 days in September

365 days in a year 

30/365 = 6/73

(72)(13/15)(5/6) = 72 (65/90) = 72(13/18)      (13/18) is how much is left as a fraction of the origianal 72   =  52$

Use the x^y function on the calculator and put the 'power' in parentheses

Example:

4 ^(2/3)     is   4 to the two thirds power......

That is the equation for a line....ANY point on that line will be a solution of the equation.

OK...I think I got ya.....the roof will have a LARGER area than  6 x 5 = 30 sq m

the 90 degree roof ridge will form a 45 degree angle with the vertical resulting in a 45-45-90 triangle

The TWO legs of the triangle will be equal and = 5/2   or 6/2  depending on exactly how the roof is positioned over the area of the floor

for the 5/2 orientation:

the hypotenuse will be     5/2^2 + 5/2^2 = hyp^2    Hyp = 3.54    EACH SIDE of the roof will be 3.54 x 6m = 21.21 sq m

    you will need a left and right side    so    2 x 21.21 = 42.42 sq m   for this orientation

NOW let's rotate tthe roof 90 degrees, then the legs of the triangle will be 6/2

6/2 ^2  + 6/2 ^2 = hyp^2   hyp = 4.24       the other side of the roof line will be  5 meters and we need two of these

          2  x  (4.24 x 5) = 42.42   (the same)

SO it does not matter the roof orientation, the minumum area of roof wil be   42.42 sq m