What is the angle of depression between a woman in a hot air balloon that is 94 feet off the ground and her friend that is 200 feet from being directly underneath the balloon

The angle of depression between the woman and her friend is 64.83°

Step-by-step explanation:

The woman in the hot balloon is 94 feet above the ground

Her friend is about 200 feet away from directly being under the balloon.

We may wish to denote the angle of depression between the woman and her friend by "x"°

We can use one of the trigonometric ratios to determine the angle of depression between the woman and her friend:

Opposite/adjacent = tan x°

Where the opposite in this case is 200 feet.

The adjacent in this instance is 94 feet.

Therefore substituting accordingly, we will have:

200/94 = tan x

tan x = 2.128

x° = tan-1 2.128

x°= 64.83°

Therefore the angle of depression between the woman and her friend is 64.83°

when functions are first introduced, you will probably have some simplistic "functions" and relations to deal with, usually being just sets of points. these won't be terribly useful or interesting functions and relations, but your text wants you to get the idea of what the domain and range of a function are. small sets of points are generally the simplest sorts of relations, so your book starts with those.

step-by-step explanation:

state the domain and range of the following relation. is the relation a function?

{(2, –3), (4, 6), (3, –1), (6, 6), (2, 3)}

the above list of points, being a relationship between certain x's and certain y's, is a relation. the domain is all the x-values, and the range is all the y-values. to give the domain and the range, i just list the values without duplication:

domain: {2, 3, 4, 6}

range: {–3, –1, 3, 6}

(it is customary to list these values in numerical order, but it is not required. sets are called "unordered lists", so you can list the numbers in any order you feel like. just don't duplicate: technically, repetitions are okay in sets, but most instructors would count off for this.)

while the given set does indeed represent a relation (because x's and y's are being related to each other), the set they gave me contains two points with the same x-value: (2, –3) and (2, 3). since x = 2 gives me two possible destinations (that is, two possible y-values), then this relation is not a function.

note that all i had to do to check whether the relation was a function was to look for duplicate x-values. if you find any duplicate x-values, then the different y-values mean that you do not have a function. remember: for a relation to be a function, each x-value has to go to one, and only one, y-value.

state the domain and range of the following relation. is the relation a function?

{(–3, 5), (–2, 5), (–1, 5), (0, 5), (1, 5), (2, 5)}

i'll just list the x-values for the domain and the y-values for the range:

hello, there is a new name in town and that's the human spider!

answer: d.) the total number of protons and neutrons is 15

merry christmas!

~

your friendly neighborhood human spider! .