a tank 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 th
Question
2 Answer

1. User Answers sqdancefan
Answer:
 secant slopes: 213.5, 187, 145, 113, 85
 tangent slope: 166
Stepbystep 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.

2. User Answers MrRoyal
The secant line joins two points on the curve of a graph.
 The slopes of secant lines PQ are: 213.5, 187, 145, 113.5, 85
 The average slope of the tangent line is 166
Point P is given as:
[tex]P = (15,1275)[/tex]
(a) The slopes of the secant lines PQ
The points are given as:
[tex]Q = \{(5,3410),(10, 2210),(20, 550) ,(25, 145),(30, 0) \}[/tex]
The slope (m) is calculated using:
[tex]m = \frac{y_2  y_1}{x_2  x_1}[/tex]
So, we have:
For Q = (5,3410), the slope of the secant line is:
[tex]m_1 = \frac{1275  3410}{15  5}[/tex]
[tex]m_1 = \frac{2135}{10}[/tex]
[tex]m_1 = 213.5[/tex]
For Q = (10, 2210), the slope of the secant line is:
[tex]m_2 = \frac{1275  2210}{15  10}[/tex]
[tex]m_2 = \frac{935}{5}[/tex]
[tex]m_2 = 187[/tex]
For Q = (20, 550), the slope of the secant line is:
[tex]m_3 = \frac{1275  550}{15  20}[/tex]
[tex]m_3 = \frac{725}{5}[/tex]
[tex]m_3 = 145[/tex]
For Q = (25, 145), the slope of the secant line is:
[tex]m_4 = \frac{1275  140}{15  25}[/tex]
[tex]m_4 = \frac{1135}{10}[/tex]
[tex]m_4 = 113.5[/tex]
For Q = (30, 0), the slope of the secant line is:
[tex]m_5 = \frac{1275  0}{15  30}[/tex]
[tex]m_5 = \frac{1275}{15}[/tex]
[tex]m_5 = 85[/tex]
(b) The slope of the tangent by average
The closest secant lines to tangent P are
[tex]Q = \{(10, 2210),(20, 550)\}[/tex]
This is so, because point P (15, 1275) is between the above points.
The slopes of secant lines at [tex]Q = \{(10, 2210),(20, 550)\}[/tex] are:
[tex]m_2 = 187[/tex]
[tex]m_3 = 145[/tex]
The average slope (m) is:
[tex]m = \frac{m_2 + m_3}{2}[/tex]
[tex]m = \frac{187  145}{2}[/tex]
[tex]m = \frac{332}{2}[/tex]
[tex]m = 166[/tex]
Hence, the average slope is 166
Read more about slopes of secant and tangent lines at:
https://brainly.com/question/20356370