Let f: a to b be a surjective map of sets prove that the relation a if and only if f(a) = f(b) is an equivalence relation whose equivalence classes are the fibers of f

Step-by-step explanation:

Denote this equivalence relation by (i.e, if and only if ), is clear that is an equivalence relation since is. Now, by definition we have that .

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,