1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
BlackZzzverrR [31]
3 years ago
13

Water is leaking out of a large barrel at a rate proportional to the square rooot of the depth of the water at that time. If the

water level starts at 36 inches and drops to 34 inches in 1 hour. How long will it take for all of the water to drain out of that barrel?
Mathematics
1 answer:
sdas [7]3 years ago
5 0

Answer:

It will take about 35.49 hours for the water to leak out of the barrel.

Step-by-step explanation:

Let y(t) be the depth of water in the barrel at time t,  where y is measured in inches and t in hours.

We know that water is leaking out of a large barrel at a rate proportional to the square root of the depth of the water at that time. We then have that

                                                 \frac{dy}{dt}=-k\sqrt{y}

where k is a constant of proportionality.

Separation of variables is a common method for solving differential equations. To solve the above differential equation you must:

Multiply by \frac{1}{\sqrt{y}}

\frac{1}{\sqrt{y}}\frac{dy}{dt}=-k

Multiply by dt

\frac{1}{\sqrt{y}}\cdot dy=-k\cdot dt

Take integral

\int \frac{1}{\sqrt{y}}\cdot dy=\int-k\cdot dt

Integrate

2\sqrt{y}=-kt+C

Isolate y

y(t)=(\frac{C}{2} -\frac{k}{2}t)^2

We know that the water level starts at 36, this means y(0)=36. We use this information to find the value of C.

36=(\frac{C}{2} -\frac{k}{2}(0))^2\\C=12

y(t)=(\frac{12}{2} -\frac{k}{2}t)^2\\\\y(t)=(6 -\frac{k}{2}t)^2

At t = 1, y = 34

34=(6 -\frac{k}{2}(1))^2\\k=12-2\sqrt{34}

So our formula for the depth of water in the barrel is

y(t)=(6 -\frac{12-2\sqrt{34}}{2}t)^2\\\\y(t)=\left(6-\left(6-\sqrt{34}\right)t\right)^2\\

To find the time, t, at which all the water leaks out of the barrel, we solve the equation

\left(6-\left(6-\sqrt{34}\right)t\right)^2=0\\\\t=3\left(6+\sqrt{34}\right)\approx 35.49

Thus, it will take about 35.49 hours for the water to leak out of the barrel.

You might be interested in
What is the measerment of the missing angle? ​
Ede4ka [16]

Answer:

80°

Step-by-step explanation:

Since they are vertical angles, they are congruent to each other.

∠r ≅ 80°

3 0
3 years ago
Read 2 more answers
2 Points
Gnesinka [82]
Answers are A, C, and D!
3 0
3 years ago
How can I learn to round better in math
love history [14]
I have always followed an easy rule: "five or more raises the score". What it means is if the number is 5 or more, it goes to the next whole. Make sense?
3 0
3 years ago
Read 2 more answers
Angelica painted 1/20 of her bedroom walls in 1/2 an hour. How long will it take Angelica to paint her whole bedroom?
julsineya [31]

Angelica would have painted the bedroom in 20 hours if every hour she painted 1/20. But she doesn't paint 1/20 of a room per hour but rather 30 minutes. That means it will take her 10 hours to paint the whole room.

Hope this helps.

4 0
3 years ago
Read 2 more answers
Click on the picture to look at some equivalent fractions. Look at them closely. Can you see a relationship of any kind between
Vera_Pavlovna [14]

when you simplify 2/4 it equals 1/2. Making them both equal the same.


2/3 when you double the numbers to make a bigger fraction you make 4/6.

2x2 = 4/ 3x3= /6 = 4/6


3/9 simplified is 1/3. Three goes into three one time, making the top one and three goes into 9 three times making the bottom 3.


When 9/12 is rounded down it is equivalent to 3/4

5 0
3 years ago
Read 2 more answers
Other questions:
  • The power P (in watts) generated by a windmill that has efficiency E is given by the formula P = 0.31ED^2V^3, where D is the dia
    8·1 answer
  • Have y'all ever experienced Deja Vu before?
    15·2 answers
  • What is the leading coefficient of the polynomial when written in standard<br> form?<br> 872 +9+ 5x
    15·1 answer
  • Solve the following: 32 ÷ 4 + 4 × 8 = ? A. 96 B. 40 C. 42 D. 32
    7·1 answer
  • Victor is at the art store and wants to buy a box of markers with the most number of markers to donate to a school in Haiti. The
    9·1 answer
  • Slope = 1; y-intercept = -4<br><br><br> Write the linear equation in slope intercept form
    8·1 answer
  • PLEASE ANSWER ASAP!!!
    12·1 answer
  • Find the slope: (1,6) and (4,1)​
    5·1 answer
  • Factorise : 17px-51py ​
    14·1 answer
  • Expand the brackets and simplify: 2(5x-y)-3(3x-y)​
    14·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!