Answer:
If an equality divide or multiply by a negative number, then the sing of inequality changes. Therefore the first step is distributive property. The solution of the given inequality is x<-0.2. In both sides,addition or subtraction should be done.
Step-by-step explanation:
Where is Tenisha's system?
y = 2x - 1
Lets see something:
y = 2x - 1
y = f(x)
If we want to do translations in vertical we just have to add an constant, where postive moves it upward and negatives, downward
y = f(x) + c
y = f(x) - 1
y = 2x - 1 - 1
y = 2x - 2
Now let's see this translation to the right
If we want to translate it in horizontal we just have to add a constant inside the function, where positive moves it to the left, and negative to the right
y = f(x) - 1
y = f(x - 3) - 1
y = 2.(x - 3) - 1 - 1
y = 2x - 6 - 2
y = 2x - 8
Answer:
Step-by-step explanation:
rate of leaking water = 9500 cm³/min
height of tank, H = 6 m = 600 cm
diameter of tank, = 4 m
radius of tank, R = 2 m = 200 cm
dh/dt = 20 cm/min
at any time, h = 2 m Let at that time radius of the tank is r.
According to the diagram
R / H = r / h
200 / 600 = r / h
r = h/3
The volume of tank is given by
![V = \frac{1}{3}\pi\times r^{2}h](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B3%7D%5Cpi%5Ctimes%20r%5E%7B2%7Dh)
![V = \frac{1}{27}\pi\times h^{3}](https://tex.z-dn.net/?f=V%20%3D%20%5Cfrac%7B1%7D%7B27%7D%5Cpi%5Ctimes%20h%5E%7B3%7D)
Differentiate with respect to t
![\frac{dV}{dt} = \frac{1}{9}\pi\times h^{2} \frac{dh}{dt}](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B1%7D%7B9%7D%5Cpi%5Ctimes%20h%5E%7B2%7D%20%5Cfrac%7Bdh%7D%7Bdt%7D)
![\frac{dV}{dt} = \frac{\pi}{9}\times 200^{2}\times 20](https://tex.z-dn.net/?f=%5Cfrac%7BdV%7D%7Bdt%7D%20%3D%20%5Cfrac%7B%5Cpi%7D%7B9%7D%5Ctimes%20200%5E%7B2%7D%5Ctimes%2020)
dV/dt = 279111.11 cm³/min
This is the volume of water increasing per minute in the tank.
Let C be the rate of volume of water pumped into the tank.
So, C = 279111.11 + 9500
C = 288611.11 cm³/min