ElectricPavlov

The guy (hypotenuse)  and the tower and the ground form a RIGHT triangle.

Find the height of the tower    sin 32 = opp/hyp = height/guy

                                                  .5299 = height/45               height = 23.85 ft tall

Now use the 100 foot guy

sin (angle) = 23.85/100 = .2385      arcsin (.2385) = 13.8 ^o

I am not sure of this answer:

An ellipse is a graph of points where the sum of the distances from two foci is a constant....

this looks like the equation for two distances from two foci

first foci  would be 3 , -4        other is   -5, 8

distance between these points is      (3- -5)^2  +  (-4 - 8)^2 = d^2

                                                              64       + 144   = d^2                      d = sqrt 208      

First find the length of the hypotenuse using pythagorean theorem       c²  = a²+b²

^{then draw the triangle}

sin a  =  opposite / hypotenuse        where ' opposite'   is the side leg that is opposite angle A

Area of trapezoid is height x  average of two bases 

    38  *  (24+x)/2 = 581.4     Solve for 'x'   

line 1   re-arranged    y = -3/4 x -14/4       slope, m,  is   - 3/4     perpindicular slope = - 1/m  = 4/3

line 2     y = 4/3 x +b    put in point given

             7 = 4/3 (5) + b     resulting in b = 1/3

y = 4/3 x  + 1/3           m = 4/3    b = 1/3     you can add them....

Thanx for the correction , Geno!

I do not know why there is a limit.....  there is not one for registered users.   Just open an account.

Multiply both sides by  z+1 to get

(BUT there is another consideration.....see Geno's answer below)

Count over to x = 7     count up to where you intersect the red graph   this is   h(7)    and it equals 5

   now count over x = 5    and count to the red line     -1                    h h(7) = -1

B unit rate  =  40.5 m / 1.25 gal  = 32.4 m/g        B can go   32.4 miles on one gallon

R unit rate   =  27.2m/ (4/5gal) =   34 m/ gal       R cn go 34 miles on one gallon