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
iogann1982 [59]
2 years ago
10

A cylindrical tank with radius 3 m is being filled with water at a rate of 4 m3/min. How fast is the height of the water increas

ing (in m/min)
Mathematics
2 answers:
slavikrds [6]2 years ago
6 0

Answer:

Let R be the radius of the tank, H(t) the height of the water at time t, and V(t) the volume of the water. The quantities V(t), R and H(t) are related by the equation

V(t) = πR²H(t) ___(1)

The rate of increase of the volume is the derivative with respect to time,

dV/dt

and the rate of increase of the height is

dH/dt

We can therefore restate the given and the unknown as follows

<u>Given</u>:

dV/dt = 4m³/min

<u>Unknown</u>:

dH/dt

Now we take derivative of each side of (1) with respect to t:

dV/dt = πR²dH/dt

So

dH/dt = 1/πR²dV/dt

Substituting R = 3 m and dV/dt = 4m³/min we have

dH/dt = 1/π(3)² ⋅ 4 = 4/9π

<u>Answer</u>: the height of the water increasing at a rate of

dH/dt = 4/9π²

<h3>≈ 0.14 m/min</h3>
Fittoniya [83]2 years ago
4 0

Height of the water increasing is at rate of  #(dh)/(dt)=3/(25 pi)m/(min)#

<h3>How to solve?</h3>

With related rates, we need a function to relate the 2 variables, in this case it is clearly volume and height. The formula is:

#V=pi r^2 h#

There is radius in the formula, but in this problem, radius is constant so it is not a variable. We can substitute the value in:

#V=pi (5m)^2 h#

Since the rate in this problem is time related, we need to implicitly differentiate wrt (with respect to) time:

#(dV)/(dt)=(25 m^2) pi (dh)/(dt)#

In the problem, we are given #3(m^3)/min# which is #(dV)/(dt)#.

So we need to substitute this in:

#(dh)/(dt)=(3m^3)/(min (25m^2) pi)=3/(25 pi)m/(min)#

Hence,  Height of the water increasing is at rate of  #(dh)/(dt)=3/(25 pi)m/(min)#

<h3>Formula used: </h3>

#V=pi r^2 h#

To Learn more visit:

brainly.com/question/4313883

#SPJ4

You might be interested in
Which model represents a fraction greater than 3/5? ​
Olin [163]

Answer:

The last one is your answer :))

Step-by-step explanation:

8 0
3 years ago
Read 2 more answers
Help can't figure this problem out
Darya [45]
(x^1/2 y^-2/3)^-6
= x^(1/2*-6) y^[(-2/3) *(-6)]
= x^-3 y ^4
= y^4 / x^3

answer is D.  y^4 / x^3  
8 0
3 years ago
Use the diagram of a T with an arrow, as shown.
mote1985 [20]

Answer:

After each rotation of the figure after giving

3 0
3 years ago
What is 4 to the 2/3 power
Anna11 [10]
\bf a^{\frac{{ n}}{{ m}}} \implies  \sqrt[{ m}]{a^{ n}} \qquad \qquad&#10;\sqrt[{ m}]{a^{ n}}\implies a^{\frac{{ n}}{{ m}}}\\\\&#10;-------------------------------\\\\&#10;4^{\frac{2}{3}}\implies \sqrt[3]{4^2}\implies \sqrt[3]{(2^2)^2}\implies \sqrt[3]{2^4}\implies \sqrt[3]{2^{3+1}}\implies \sqrt[3]{2^3\cdot 2}&#10;\\\\\\&#10;2\sqrt[3]{2}
8 0
3 years ago
A kilometer is larger than a meter True or false
stira [4]

A Kilometer is 1,000 times larger than a meter

5 0
3 years ago
Read 2 more answers
Other questions:
  • HELLPPPP I WILL GIVE BRAINIEST!!!!!!!!!!!!<br><br> 2x+3=20-15
    6·2 answers
  • Hello can you please help me posted picture of question
    14·1 answer
  • If a formula had addition, division, exponents, and brackets which would the spreadsheet calculate first?
    9·2 answers
  • eric can spend a maximum of $270 on office supplies. Each rem of paper costs $6. Each ink catridge costs $18. Which of the follo
    12·1 answer
  • A fair coin is tossed three times in succession. The set of equally likely outcomes is StartSet HHH comma HHT comma HTH comma TH
    6·1 answer
  • When 12 is multiplied by 6, the result is what?
    15·2 answers
  • An object’s weight on Earth varies directly to its weight on the Moon. If a man weighs 180 kg on Earth, then he will weigh 30 kg
    12·1 answer
  • Plzzz help zoom in to see hurry!!!
    6·2 answers
  • Which equation in slope-intercept form is equivalent to y+2 = -2(x+4)?
    8·2 answers
  • lucy has 4 less quarters then nicklesand 3 more dimes then nickels; she has a total of 35 coins. How many of each coind does she
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!