A puppy is tied to a leash in a back yard. His leash is 3 meters long, and he runs around in circles pulling the leash as far as it can go. What is the approximate distance the puppy runs in one lap?

A) between 13 and 14 meters
B) between 15 and 16 meters
C) between 17 and 18 meters
D) between 18 and 19 meters

The puppy runs a distance of D) 18 - 19 meters in one lap.

Step-by-step explanation:

Step 1; It is given that the leash measures 3 meters long. He runs pulling the leash as much as he can creating circles. Even though he keeps pulling, the leash will remain at a constant length of 3 meters. So we need to calculate the perimeter of the circle.

Step 2; The perimeter of any given circle is 2π times the radius. The radius of this circle is equal to 3 meters.

Perimeter of the circle = 2π × r = 2 × 3.1415 × 3 meters = 18.85 meters.

So the puppy runs a distance of 18.85 meters in a lap.

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:

i believe your answer is 99.7% of 7-year-old children are between 46.6 inches and 49.5 inches tall.