Mathematics, 18.08.2019 12:30 Angelanova69134

Adiesel train left abuja and traveled toward johannesburg. a freight train left one hour later traveling 15 km/h faster in an effort to catch up it. after five hours the freight train finally caught up. what was the diesel train's average speed?

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Here is the solution:

Start with the fact that both trains have made the same distance= 's'.

In physics distance is a multiplication of speed of your train = 'v' and period of time in which it was moving= 'T' (this is only true when the speed doesn't change during movement, or we talk about avarage speed like in your task).
Then:
$s= v_{D} * T_{D}$
"D" symbol refers do diesel train

Freight train moves with 15[km/h] greater speed and it travels 1 [h] shorter then:
$s = v_{F} * T_{F} = (v_{D}+15)*(T_{D}-1)$

As the distance made by both train is the same you can compare the right parts of both equations:
$v_{D} * T_{D}=v_{F} * T_{F} = (v_{D}+15)*(T_{D}-1)$

Diesel train moved 6 hours and freight train 5 hours then:
$v_{D} * 6=(v_{D}+15)*5$
$6*v_{D}=5*v_{D}+75$
$6*v_{D}-5*v_{D}=75$
$v_{D}=75$

Here is your The average diesel train speed is 75 km/h

Answer from: Quest

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:

Answer from: Quest

multiple all that

step-by-step explanation:

27×17

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