At 1: 00pm, ship a is 30 miles due south of ship b and is sailing north at a rate of 15 mi/hr. if ship b is sailing

west at a rate of 10 mi/hr, find the time at which the distance d between the ships is minimal.

2:23 pm

Step-by-step explanation:

We can solve this considering a a right triangle

let t = travel time of both ships

therefore,

15t = distance traveled by ship A

however, it is traveling toward the point of reference, therefore we write it

(30-15t)

and

10t = distance traveled by ship B, away from the point of reference

Let d = distance between the ships at t time, (the hypotenuse of the right triangle)

and combine like terms

from this d to minimum we can find the axis of symmetry, where in

a=325 and b= -900

the t=-b/2a

t= 1.384 hours

now putting the value we get

solving this we get

d= 16.64 miles

therefore,

16.64 mi apart after 1.3846 hrs, minimum distance between the ships

now, 1.384 hours = 1+60(0.348) hour

= 1 hour and 23 minutes

so, the time at which the distance d between the ships is minimal = 1:00 pm + 1 hour and 23 minutes = 2:23 pm

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: