Answer: D
Step-by-step explanation:
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
Let x = smallest number
y = middle number
z = largest number
Equations:
sum of 3 numbers: x + y + z = 15
two times smallest is 1 less than largest: 2x = z - 1
sum of largest and smallest is 10: z + x = 10
z + x = 10 can be solved for z ⇒ z = 10 - x
substitute into 2x = z - 1 ⇒ 2x = 10 - x - 1
3x = 9
x = 3 (divided both sides of equation by 3)
Since z + x = 10 ⇒ z + 3 = 10 ⇒ z = 7
Substitute values for x and z into x + y + z = 15 ⇒ 3 + y + 7 = 15
y + 10 = 15
y = 5
answer: 3, 5, 7
