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BigorU [14]
3 years ago
14

A valve in a full 6000 gallon water tank is slowly opening. Water flows out of the tank through the valve. The flow rate in gall

ons per hour is given by the function f(t)=300 t^2 where t is in minutes.
How much water flows out the tank in the first 7 minutes?
How many minutes does it take for the tank to be completely empty?,
Mathematics
2 answers:
Wittaler [7]3 years ago
8 0
The volume of the gallon is 6000 gallon
the rate of water flow per min is f(t)=300t^2
a] amount of water that flowed in the first 7 minutes=7/60 hours will be:
f(7)=300(7/60)^2
solving the above we get
f(7)=7/12 gallons

b] The time taken for the tank to be empty will be as follows:
amount of water that will flow out for the tank to be empty will be 6000 gallons
thus,
6000=300t^2
this can be simplified to
20=t^2
t^2-20=0
solving this we get:
t=-2√5 or 2√5
the time taken for the tank to be empty will be t=2√5 hours=5.4721 hours



weqwewe [10]3 years ago
4 0

Answer:

a) entire tank is empty hence 6000 gallons

b) 3.915 mins

Step-by-step explanation:

a)

\int\limits^7_0 {f(t)} \, dt =  \int\limits^7_0 {300t^2} \, dt \\\\= 100t^2\limits^7_0\\= 34300 > 6000 \\Hence, entire tank empt

b) V (t) = 100t^3

6000 = 100t^3

t = \sqrt[3]{60} = 3.915 mins

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3 years ago
Will someone plz help me this us due and I am confused
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Hey there! I would love to help you.

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If you know how too solve systems of equations by elimination, we need to to do something similar to eliminate all of the repeating parts so we can solve for x.

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