Describe where the function has a vertical asymptote and how you found your answer. remember that an asymptote is represented by an equation of a line and not just a single value.

x=-4 is a vertical asymptote

Step-by-step explanation:

A vertical asymptote of the graph of a rational function f(x) is a line x=a, such that one of of these statements is fulfilled

Our function is

To find the candidate values of a, we set the denominator to zero

Factoring

Which gives us two possible vertical asymptotes: x=-4 or x=-5

We now must confirm if one of the two conditions are true for each value of a

The numerator can be factored as

So our limit is

Simplifying:

We can see x=-4 is a vertical asymptote

Checking with x=-5, and using the simplified limit:

The limit exists and is 3, so x=-5 is NOT a vertical asymptote

The only vertical asymptote of the function is x=4

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,