A train leaves Chicago for Los Angeles going a constant rate of 40 MPH. Two hours later, another train leaves Chicago for Los Angeles on the same track as the first going a constant rate of 60 MPH. 1. When will the 2nd train catch up to the first train?

2. How many miles will the trains have traveled when they meet?

1 . 4 hrs , 2 . total 400 miles because the first train had travelled 160 miles and 2nd one had travelled 240 miles

Step-by-step explanation:

in 1. use relative motion concept I. e. you sir on 1st train and put velo. of same mag. and in oppo. direction on the train on which you have sit and do the same with the velocity only with 2nd train means you stop the train on which you are sitting and put the velocity of the train on which you are sitting on 2nd train but in oppo. direction , so now the relative velocity comes out to be 20 mph and then apply formula time = Srel / Vrel and here we can find S rel by multiplying the velo. of 1st train by given time I. e. 2 hrs and in 2. multiply the time calculated by us by the velocity of both trains and by which you get the dist. travelled by both trains and then add them to get final answer.

the range of a function is the range of y-values for which it is defined, or exists. given that we are only looking at the y-values, we can already discount the first two answers as they deal with the domain of the function (range of x-values).

now, what we need to do is find the smallest and highest y-values for which the function is defined. if you'd like, you could take a ruler and start at the very bottom of the graph, find the lowest point, then move the ruler higher and higher until you reach the highest point. doing so either in your head or with an actual ruler, we can see that the lowest y-value is -5 and the highest y-value is -1.

the question now remains as to whether they are included in the range (fourth answer) or excluded (third answer). the key here is to recognise whether they are marked with an open or a closed circle. since both (-2, -5) and (2, -1) are marked with a closed circle, they are points that exist on the graph and are thus included in the range (note that if they were marked with an open circle like (4, -2) then that would signify that there is a break in the graph at that point).

thus, the fourth answer, (y | -5 ≤ y ≤ -1), is correct.

also note that usually it is good practice to scan your eye inbetween the highest and lowest point for any breaks in the graph - we do have one here at (4, -2), however -2 is still included in the range because there is another point that is included in the graph with the same y-value, ie. point (1, -2).

i hope that but if you require any further explanation don't hesitate to comment below.

$12. that is my answer.