The rate at which cars enter a parking lot is modeled by E(t)=30+5(t-2)(t-5)e^-0.2t. The rate at which cars leave the parking lot is modeled by the differentiable function L. Selected values of L(t) are given in the table below. Both E(t) and L(t) are measured in cars per hour, and time t is measured in hours after 5 AM. (t=0) Both functions are defined for 0≤t≤12. a) How many cars enter the parking lot from time t=0 to time t=12?
b) Use a trapezoidal sum with the four subintervals indicated by the data in the table to approximate ( ∫upper 12 lower 2 ) L(t)=dt. Using correct units, explain the meaning of ( ∫upper 12 lower 2 ) L(t)=dt in the context of this problem.
d) For 0≤t≤6, 5 dollars are collected from each car entering the parking lot. For 6≤t≤12, 8 dollars are collected from each car entering. How many dollars from time t=0 to t=12?

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.

arithmetic sequence

step-by-step explanation:

given that a sequence has terms as

19, 15, 11,

this is represented on a graph

the pattern indicates that the sequence is an arithmetic sequence with i term

a=19 and common difference d =-4

any general term

thus the sequence is reduced by 4 for each successive term starting from 1 and nth term is

24-5n.

first negative term would start after 5th term

5th term =24-25< 0

from 5th term onwards the sequence would be negative.

he sells x mount because thats eqivilqant to the maz and then divided into quarters

step-by-step explanation:

125 yards

step-by-step explanation:

i take 75 plus 50.