7. water flows from a tank at a rate of 1500 litres per minute. the tank has a volume of 480 000 l.\na) fill…

7. water flows from a tank at a rate of 1500 litres per minute. the tank has a volume of 480 000 l.\na) fill in the following table showing how much water is left in 30 - minute intervals.\n|time elapsed (minutes)|volume of water remaining (l)|\n|0|\n|30|\n|60|\n|90|\n|120|\n|150|\nb) draw a graph of the data.\nc) calculate the slope. what does it represent?\nd) when will the tank be empty?

7. water flows from a tank at a rate of 1500 litres per minute. the tank has a volume of 480 000 l.\na) fill in the following table showing how much water is left in 30 - minute intervals.\n|time elapsed (minutes)|volume of water remaining (l)|\n|0|\n|30|\n|60|\n|90|\n|120|\n|150|\nb) draw a graph of the data.\nc) calculate the slope. what does it represent?\nd) when will the tank be empty?

Answer

Explanation:

Step1: Calculate water - loss formula

The rate of water flow is 1500 litres per minute. The initial volume of water in the tank is (V_0 = 480000) L. The volume of water remaining (V) after (t) minutes is given by the formula (V=V_0 - 1500t).

Step2: Fill the table for part a

  • When (t = 0), (V=480000-1500\times0 = 480000) L.
  • When (t = 30), (V=480000-1500\times30=480000 - 45000=435000) L.
  • When (t = 60), (V=480000-1500\times60=480000 - 90000 = 390000) L.
  • When (t = 90), (V=480000-1500\times90=480000 - 135000=345000) L.
  • When (t = 120), (V=480000-1500\times120=480000 - 180000 = 300000) L.
  • When (t = 150), (V=480000-1500\times150=480000 - 225000=255000) L. | Time elapsed (minutes) | Volume of water remaining (L) | | ---- | ---- | | 0 | 480000 | | 30 | 435000 | | 60 | 390000 | | 90 | 345000 | | 120 | 300000 | | 150 | 255000 |

Step3: For part b (graph - description)

The graph has the time elapsed (in minutes) on the x - axis and the volume of water remaining (in litres) on the y - axis. Plot the points ((0,480000)), ((30,435000)), ((60,390000)), ((90,345000)), ((120,300000)), ((150,255000)) and connect them with a straight - line.

Step4: Calculate the slope for part c

The slope (m) of a line in the form (y = mx + b) (here (V=- 1500t + 480000)) is (-1500). The slope represents the rate at which the volume of water in the tank is decreasing. It is the rate of water flow out of the tank, which is 1500 litres per minute. The negative sign indicates that the volume of water is decreasing over time.

Step5: Calculate empty - time for part d

Set (V = 0) in the equation (V=480000-1500t). Then (0 = 480000-1500t). Solving for (t): [ \begin{align*} 1500t&=480000\ t&=\frac{480000}{1500}=320 \end{align*} ] The tank will be empty after 320 minutes.

Answer:

a) See the filled - in table above. b) Plot the points ((0,480000)), ((30,435000)), ((60,390000)), ((90,345000)), ((120,300000)), ((150,255000)) and connect them with a straight - line (x - axis: time elapsed in minutes, y - axis: volume of water remaining in litres). c) The slope is (- 1500). It represents the rate at which water is flowing out of the tank (1500 litres per minute, with the negative sign indicating a decrease in volume over time). d) 320 minutes.