SOLUTION: PLEASE PLEASE HELP I can't seem to figure out how to do these four problems.
My kids’ bathtub is being drained. Since it is an ordinary tub, it can be modeled by the function
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Question 987202: PLEASE PLEASE HELP I can't seem to figure out how to do these four problems.
My kids’ bathtub is being drained. Since it is an ordinary tub, it can be modeled by the function
V(t) = -15t + 45 where V(t) is the volume of the tub in gallons and t is the time that has passed in minutes.
1.Based on the function V(t) = -15t + 45, when will the tub be half full?
2.What is the practical domain in this problem? Use appropriate notation in your answer.
3.What is the practical range? Use the appropriate notation in your answer.
4.My tub is a garden tub. When I drain it I can model the volume of water in it by
v(T) = -20T + 50 where v(T) is the volume of the tub in gallons and T is the time that has passed
in minutes. Given all this, which tub drains faster, my kids’ tub, or mine? Explain your reasoning.
Found 3 solutions by stanbon, solver91311, macston:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
My kids’ bathtub is being drained. Since it is an ordinary tub, it can be modeled by the function
V(t) = -15t + 45 where V(t) is the volume of the tub in gallons and t is the time that has passed in minutes.
Note: Your volume equation implies the capacity of the tub is 45
1.Based on the function V(t) = -15t + 45, when will the tub be half full?
22.5 = -15t + 45
-22.5 = -15t
time = 1.5 minutes
----------------------------
2.What is the practical domain in this problem? Use appropriate notation in your answer.
Solve::
0 = -15t + 45
t = 3 minutes
----
Domain:: 0<= t <=3
-----------------------------
3.What is the practical range? Use the appropriate notation in your answer.
0<= V(t) <= 45
----------------------------
4.My tub is a garden tub. When I drain it I can model the volume of water in it by v(T) = -20T + 50 where v(T) is the volume of the tub in gallons and T is the time that has passed in minutes. Given all this, which tub drains faster, my kids’ tub, or mine? Explain your reasoning.
Solve:
0 = -20T + 50
T = 50/20
T = 2.5 minutes
----
Ans: Your tub has 50 gallons and empties in 2.5 minutes.
Your's drains faster.
--------------
Cheers,
Stan H.
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Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
\ =\ -15t\ +\ 45)
Since this model gives the volume of water in the tub over time as it is draining, the value of the function at time zero must be the capacity of a full tub. Substitute zero for 
and solve for )
, the volume of water in a full tub.
Once you know the volume of a full tub, you can divide that number by 2 to find the volume of a half-full tub.
Set 
equal to the volume of a half full tub and solve for 
, the time at which the tub will be half full.
Since the Volume function is a linear function, there is another way to do this. Set the function equal to zero and then solve for 
, the time when the tub will be empty. Since the function is linear, the tub will be half-empty when half the time to empty it completely has passed. I recommend that you solve this both ways to verify.
Part of your particular problem with mathematics is that you either cannot, or refuse to, read and follow written instructions. I refer to the very clear instruction on the page where you posted these questions that says "One problem per submission".
John
My calculator said it, I believe it, that settles it
Answer by macston(5194) (Show Source): You can put this solution on YOUR website!
.
1. When t=0, the tub has not yet started to drain:
The total volume of the tub is 45 gallons.
The tub will be half full when V(t)=(1/2)(45gal)=22.5gal:
Subtract 45 from each side.
Divide each side by -15.
ANSWER: The tub will be half empty in 1.5 minutes.
.
2. Domain: [0,3]
Since t is time, it is not less than zero. So 0<=t.
If t>3, the volume is negative so t<=3.
.
3. Range: [0,45]
V(t) is volume, cannot be less than zero: 0<+V(t)
At t=0, the tub is full at 45 gallons, so: V(t)<=45
.
4. Kid's tub, t when V(t)=0 is time to drain fully:
It takes 3 minutes to drain this tub completely.
.
For the garden tub when V(t)=0:
It takes 2.5 minutes to completely drain the garden tub.
.
ANSWER: The garden tub drains faster.
REASONING: The kid's tub drains 45 gal/3 min=15 gal/min.
The garden tub drains 50 gal/2.5 min=20gal/min.
The garden tub drains more water in less time.
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