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

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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.

true

step-by-step explanation:

answer: all of the odd numbers were opened

the first person was the one that was opening all of the lockers. since one is odd, this causes all of the odd number lockers to be opened in the end.