Atank holds 5000 gallons of water, which drains from the bottom of the tank in half an hour. the values in the table show the volume v of water remaining in the tank (in gallon) after t minutes. a) if p is the point (15,1275) on the graph of v, find the slopes of hte secant lines pq when q is the point on the graph with the following values.(5, 3410) -427/2(10, 2210) -187(20, 550) -145(25, 145) -113(30, 0) -85b) estimate the slope of hte tangent line at p by averaging the slopes of two adjacent secant lines. (round your answer to one decimal places).

The secant line joins two points on the curve of a graph.

Point P is given as:

(a) The slopes of the secant lines PQ

The points are given as:

The slope (m) is calculated using:

So, we have:

For Q = (5,3410), the slope of the secant line is:

For Q = (10, 2210), the slope of the secant line is:

For Q = (20, 550), the slope of the secant line is:

For Q = (25, 145), the slope of the secant line is:

For Q = (30, 0), the slope of the secant line is:

(b) The slope of the tangent by average

The closest secant lines to tangent P are

This is so, because point P (15, 1275) is between the above points.

The slopes of secant lines at are:

The average slope (m) is:

Hence, the average slope is -166

Read more about slopes of secant and tangent lines at:

link

Step-by-step explanation:

A) the slope values you have put in your problem statement are correct. As you know, they are computed from ...

  (change in gallons)/(change in time)

where the reference point for changes is P. Using the first listed point Q as an example, the secant slope is ...

  (3410 -1275)/(5 -15) = 2135/-10 = -213.5 . . . . gallons per minute

__

B) The average of the secant slopes for points Q adjacent to P is ...

  (-187 +(-145))/2 = -332/2 = -166 . . . . gallons per minute

The tangent slope at point P is estimated at -166 gpm.

your answer   is c

step-by-step explanation:

a.) list the factors of 40.

1/2/4/5/8/10/20/40

b.) list the factors of 40 that represent the number of cans that could be on each shelf.

5

c.) how many different arrangements of cans are possible?

just one because if you put more on one shelf you will go way over 40 and the cabinet will probably break.

d.) what are the possible arrangements of the cans?

put 5 cans on each self to reach 40 cans in total.

e.) which arrangement uses all the shelves?

5 because you can put 5 cans on each shelf, and since there are 8 shelfs you are equally going to get 40 cans.