CPhill

Here's a graphical solution: https://www.desmos.com/calculator/f7c6wqsvxl

Note....as x grows larger and larger, the value of 7^x  is much greater than 5^x......so......this function approaches [  -inf  ]  as x grows sufficiently large

Thus......the limit does not exist

If we assume the real-value root, the answer  is -5  - a real number

If we assume the principal root the answer  is    5*cube root (-1)  - not a real number

Good work,  guest #1   ......!!!!

The key to this problem is to see that (1/3)(1-y)   is actually treated as a coefficient on "x" and then completing the square based on that coefficient

Look at the graph here, Solveit :  https://www.desmos.com/calculator/ogakicvciq

Note that, for every point (a,b)  on the graph y = 2/x² ,  the point (b, a) exists on the graph y = 2/y²

Thus, both graphs, with respect to each other,  are symmetric about the line y = x

48 x (7/8) x .55  = $23.10

 sqrt [(5) / (x + 3)]  = 4 / [x + sqrt(4)]        

 sqrt [ (5) / (x + 3)]  = 4/ [x + 2]           square both sides

5  / [x + 3]  =   16/ [x^2 + 4x + 4]         cross-multiply

5 [ x^2 + 4x + 4 ]  = 16[x + 3]     simplify

5x^2 + 20x + 20  = 16x + 48 

5x^2 + 4x -28  =  0     factor

[5x  + 14] [ x - 2]  = 0     

Setting each factor to O  we have that x = -14/5   or x = 2

However.....x = -14/5  produces a negative quantity on the right hand side of the original equation, and we can never get a negative out of the left hand side......so.......the two sides would have unequal signs, so x = -14/5  is not a soluition

So.......x = 2   is the only solution.....

................

80 / sin(40) =  about 124.458

We can use a proportion, here:

Let x be the main span length

15 ft/ 1cm  =  x ft / 284 centimeters      cross-multiply

284 * 15  = x   = 4260 ft

0=2x-10y+7     add 10y to both sides

10y = 2x - 7     divide both sides by  10

y = [2/10]x - 7/10

y = [1/5]x - 7/10    

And in the form, y = mx + b.......m is the slope....so........1/5 is the slope