Answer:
Therefore the tank will be half empty after 10.10 days.
Therefore there will be 2735.53 liters water in the tank after 4 days.
Step-by-step explanation:
Given that,the square root of the volume of remaining water in the tank is proportional to the rate of water leakage.
Let V be volume of water at any instant time t.
![\therefore \frac{dV}{dt} \propto \sqrt V](https://tex.z-dn.net/?f=%5Ctherefore%20%5Cfrac%7BdV%7D%7Bdt%7D%20%5Cpropto%20%20%5Csqrt%20V)
where k is constant of proportionality.
![\Rightarrow \frac{dV}{\sqrt V}= k \ dt](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cfrac%7BdV%7D%7B%5Csqrt%20V%7D%3D%20k%20%5C%20dt)
Integrating both sides
![\Rightarrow \int \frac{dV}{\sqrt V}= \int k \ dt](https://tex.z-dn.net/?f=%5CRightarrow%20%5Cint%20%5Cfrac%7BdV%7D%7B%5Csqrt%20V%7D%3D%20%5Cint%20k%20%5C%20dt)
[ C is integrating constant]
At t=0, the volume of water is 350 liters
![2\sqrt{350}=k.0+C](https://tex.z-dn.net/?f=2%5Csqrt%7B350%7D%3Dk.0%2BC)
![\Rightarrow C=2\sqrt{350}](https://tex.z-dn.net/?f=%5CRightarrow%20C%3D2%5Csqrt%7B350%7D)
The equation becomes
![\Rightarrow 2\sqrt V=kt+2\sqrt{350}](https://tex.z-dn.net/?f=%5CRightarrow%202%5Csqrt%20V%3Dkt%2B2%5Csqrt%7B350%7D)
Again at t=1, the volume of water is(350-20)liters=330 liters
![2\sqrt {330}=k.1+2\sqrt{350}](https://tex.z-dn.net/?f=2%5Csqrt%20%7B330%7D%3Dk.1%2B2%5Csqrt%7B350%7D)
![\Rightarrow k=2\sqrt {330}-2\sqrt{350}](https://tex.z-dn.net/?f=%5CRightarrow%20k%3D2%5Csqrt%20%7B330%7D-2%5Csqrt%7B350%7D)
The equation becomes
![2\sqrt V=2(\sqrt{330}-\sqrt{350} ) t+2\sqrt{350}](https://tex.z-dn.net/?f=2%5Csqrt%20V%3D2%28%5Csqrt%7B330%7D-%5Csqrt%7B350%7D%20%29%20t%2B2%5Csqrt%7B350%7D)
![\Rightarrow \sqrt V=(\sqrt{330}-\sqrt{350} ) t+\sqrt{350}](https://tex.z-dn.net/?f=%5CRightarrow%20%5Csqrt%20V%3D%28%5Csqrt%7B330%7D-%5Csqrt%7B350%7D%20%29%20t%2B%5Csqrt%7B350%7D)
Now when the tank is half empty,then V= (350÷2) liters = 175 liters
![\sqrt {175}=(\sqrt{330}-\sqrt{350} ) t+\sqrt{350}](https://tex.z-dn.net/?f=%5Csqrt%20%7B175%7D%3D%28%5Csqrt%7B330%7D-%5Csqrt%7B350%7D%20%29%20t%2B%5Csqrt%7B350%7D)
![\Rightarrow (\sqrt{330}-\sqrt{350} ) t=\sqrt{175}-\sqrt{350}](https://tex.z-dn.net/?f=%5CRightarrow%20%28%5Csqrt%7B330%7D-%5Csqrt%7B350%7D%20%29%20t%3D%5Csqrt%7B175%7D-%5Csqrt%7B350%7D)
![\Rightarrow t=\frac{\sqrt{175}-\sqrt{350}}{ (\sqrt{330}-\sqrt{350} )}](https://tex.z-dn.net/?f=%5CRightarrow%20t%3D%5Cfrac%7B%5Csqrt%7B175%7D-%5Csqrt%7B350%7D%7D%7B%20%28%5Csqrt%7B330%7D-%5Csqrt%7B350%7D%20%29%7D)
days
Therefore the tank will be half empty after 10.10 days.
After 4 days,
![\sqrt V=(\sqrt{330}-\sqrt{350} ) (4)+\sqrt{350}](https://tex.z-dn.net/?f=%5Csqrt%20V%3D%28%5Csqrt%7B330%7D-%5Csqrt%7B350%7D%20%29%20%284%29%2B%5Csqrt%7B350%7D)
![\Rightarrow \sqrt V= 16.54](https://tex.z-dn.net/?f=%5CRightarrow%20%5Csqrt%20V%3D%2016.54)
liters
Therefore there will be 2735.53 liters water in the tank after 4 days.
Answer:
angle M
horizontally in a positive
vertically in a positive
25
Vertical angles are congruent/equal :
Answer:
No.
Step-by-step explanation:
It is not possible to make a triangle that has the angles measuring 60 degrees, 30 degrees and 45 degrees because the angles of a triangle have to add up to 180 degrees. 30+45+60=135
Therefore, these angles would not measure up to 180 degrees. It is not possible to make a triangle that has these angles. These angles measure up to 135 degrees not 180 degrees.
Answer:
1. 1023
2. 8
3. The 7th Term
Step-by-step explanation: