If a tank holds 6000 gallons of water, which drains from the bottom of the tank in 50 minutes, then Toricelli's Law gives the volume V of water remaining in the tank after t minutes as V=5000 (1-1/50*t)^2 0⤠t ⤠50.

1. Find the rate at which water is draining from the tank after the following amount of time. (Remember that the rate must be negative because the amount of water in the tank is decreasing.)

a. 5 min
b. 10 min
c. 20 min
d. 50 min

2. At what time is the water flowing out the fastest?
3. At what time is the water flowing out the slowest?

hello from the question the volume of tank = 6000 gallons while the value in the Torricelli's equation = 5000 hence I resolved your question using the Torricelli's law equation

1) a) -180  gallons/minute ,

  b)  -160 gallons/minute

  c)  -120 gallons/minute

  d) 0

2) The water is flowing out fastest when t = 5 min

3) The water is flowing out slowest after t = 20 mins

Step-by-step explanation:

Volume of tank = 5000 gallons

Time to drain = 50 minutes

Volume of water remaining after t minutes by Torricelli's law

V = 5000 ( 1 - )^2 ----- ( 1 )

1) Determine the rate at which water is draining from the tank

First step : differentiate equation 1 using the chain rule to determine the rate at which water is draining from the tank

V' =

a) After t = 5minutes

V' = - 10000[ ( 1 - 0.1 ) * ( 0.02 ) ]

   = -180  gallons/minute

b) After t = 10 minutes

V' = - 10000[ ( 1 - 0.2 ) * ( 0.02 ) ]

   = - 160 gallons/minute

c) After t = 20 minutes

V' = - 10000 [ ( 1 - 0.4 ) * ( 0.02 ) ]

   = -120 gallons/minute

d) After t = 50 minutes

V' = - 10000 [ ( 1 - 1 ) * ( 0.02 ) ]

   = 0 gallons/minute

2) The water is flowing out fastest when t = 5 min

3) The water is flowing out slowest after t = 20 mins  because no water flows out after 50 minutes

the answer is b.

step-by-step explanation:

identity property is where 0+whatever number=whatever number. basically 0+ a number.

fabric (square meters)                   cloaks

7                                                           21

4/3                                                         4

step-by-step explanation:

we are told that harry needs 2 square meters of fabric for every 6 wizard cloaks he makes.

1. first of all we will find how many cloaks can be made from 1 square meter of fabric by dividing 6 by 2.

we can see that 3 cloaks can be made from 1 square meter of fabric. now we will multiply 3 by 7 to find number of cloaks made from 7 square meters of fabric.

therefore, harry will make 21 cloaks from 7 square meters of fabric.

2. let us find how many square meters of fabric will be needed to make 4 cloaks.

first of all we will find fabric needed for 1 cloak by dividing 2 by 6.

we can see that fabric needed for 1 cloak is   square meter. now we will multiply   by 4 to find fabric needed for 4 cloaks.