At time t = 0 hours, a tank contains 3000 litres of water.
Water leaks from the tank.
At the end of every hour, there is x% less water in the tank than at the start of the hour.
The volume of water, in litres, in the tank at time t hours is Vt.
Given that: Vt = KtV0
V2 = 2881.2
Work out the value of K and the value of X.
- Please, if you can, could you try and make this the most understandable as possible. Thank you.
Answers
Answer:
At t=0, Volume of Water = = 3,000 Litre
After t hours , the Volume of water in the tank =
As it is also given , At the end of every hour there is a x% less water in the tank then at the start of the hour
= Amount of water after an hour = 3,000 - = 3,000 - 30 x
= Amount of water after two hour =(3,000 - 30 x) - (3,000 - 30 x)×= (3,000 - 30 x)
Also,
⇒ = 288120
⇒300000 - 3000 x - 3000 x + 30 x² = 288120
⇒ 30 x ² - 6,000 x + 11880= 0
Dividing both sides by 30, we get
⇒ x² - 200 x + 396=0
Factorizing the quadratic expression
(x -198)(x-2) = 0
x = 198, x = 2
Read more on Brainly.com - https://brainly.com/question/11604092#readmoreWhich gives a value of x = 2 as a possible solution of this equation.
Also, V_{1} = k ^1 V_{0}
k = \frac{V_{1}}{V_{0}}
V_{1} = 3,000 - 30 \times 2 = 3,000 - 60= 2,940
k = \frac{2940}{3000}= 0. 999.......(non terminating repeating)
k= 0.999 (approx)
Answer:
At t=0, Volume of Water = = 3,000 Litre
After t hours , the Volume of water in the tank =
As it is also given , At the end of every hour there is a x% less water in the tank then at the start of the hour
= Amount of water after an hour = 3,000 - = 3,000 - 30 x
= Amount of water after two hour =(3,000 - 30 x) - (3,000 - 30 x)×= (3,000 - 30 x)
Also,
⇒ = 288120
⇒300000 - 3000 x - 3000 x + 30 x² = 288120
⇒ 30 x ² - 6,000 x + 11880= 0
Dividing both sides by 30, we get
⇒ x² - 200 x + 396=0
Factorizing the quadratic expression
(x -198)(x-2) = 0
x = 198, x = 2
Read more on Brainly.com - https://brainly.com/question/11604092#readmoreWhich gives a value of x = 2 as a possible solution of this equation.
Also, V_{1} = k ^1 V_{0}
k = \frac{V_{1}}{V_{0}}
V_{1} = 3,000 - 30 \times 2 = 3,000 - 60= 2,940
k = \frac{2940}{3000}= 0. 999.......(non terminating repeating)
k= 0.999 (approx)
Step-by-step explanation: