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
Whitepunk [10]
3 years ago
5

Water is poured into a conical container at the rate of 10 cm3/sec. The cone points directly down, and it has a height of 20 cm

and a base radius of 15 cm. How fast is the water level rising when the water is 2 cm deep (at its deepest point)?
Chemistry
1 answer:
8090 [49]3 years ago
4 0

Answer:

\frac{dh}{dt}_{h=2cm} =\frac{40}{9\pi}\frac{cm}{2}

Explanation:

Hello,

The suitable differential equation for this case is:

\frac{dV}{dt}=10\frac{cm^3}{s}

As we're looking for the change in height with respect to the time, we need a relationship to achieve such as:

\frac{dh}{dt} = ?*\frac{dV}{dt}

Of course, ?=\frac{dh}{dV}.

Now, since the volume of a cone is V=\pi r^2h/3 and the ratio r/h=15/20=3/4 or r=3/4h, the volume becomes:

V=\pi (\frac{3}{4} h)^2h/3= \frac{3}{16}\pi h^3

We proceed to its differentiation:

\frac{dV}{dh} =\frac{9}{16} \pi h^2\\\frac{dh}{dV} =\frac{16}{9 \pi h^2}

Then, we compute \frac{dh}{dt}

\frac{dh}{dt} = \frac{16}{9 \pi h^2}*\frac{dV}{dt}\\\frac{dh}{dt} = \frac{16}{9\pi h^2}*10\frac{cm^3}{s} =\frac{160}{9 \pi h^2}

Finally, at h=2:

\frac{dh}{dt}_{h=2cm} =\frac{160}{9\pi 2^2}\\\frac{dh}{dt}_{h=2cm} =\frac{40}{9\pi}\frac{cm}{s}

Best regards.

You might be interested in
Which statement correctly describes diamond and graphite, which are different forms of solid carbon?
mart [117]
They differ in their molecular structures and properties.
5 0
3 years ago
Read 2 more answers
Balance the 2 chemical equation below: 1) _____H2 + _____02 ---> _____H20 2) _____CH4 + _____Cl2 ---> _____CCl4 + _____HCl
sergij07 [2.7K]

Answer:

1.)    2H2  +  O2  --->  2H2O

2.)   CH4  +  4Cl2 --->  CCl4  +  4HCl

Explanation:

In order to balance the equation, you have to make sure there are the same amount of each element on both sides.

Ex (#1).  By adding the coefficients infront of H2 and H20, You now have 4 hydrogen's and 2 oxygens on the left side as well as 4 hydrogens and 2 oxygens on the right side.

Sorry if that's confusing, but hope this helps! :)

6 0
2 years ago
vanillin is a flavoring agent in vanilla it has a mass percent composition of 61.15% c,5.3%H,31.55% o determine the empirical fo
Nutka1998 [239]

The empirical and molecular formulas will be  C_5H_5O_2 and  C_1_0H_1_0O_4 respectively.

<h3>Empirical and molecular formula</h3>

The compound contains C, H, and O.

C = 61.15/12 = 5.0958

H = 5.3/1 = 5.3

O = 31.55/16 = 1.9719

Divide by the smallest

C = 2.6

H = 2.7

O = 1

Thus, the empirical formula is C_5H_5O_2

Empirical formula mass = (12x5) + (1x5) + 16x2 = 97

n = 152.15/97 = 2

The molecular formula is C_1_0H_1_0O_4

More on molecular and empirical formulas can be found here: brainly.com/question/14425592

#SPJ1

6 0
2 years ago
Which phrase best describes humidity?
NARA [144]

One phrase that best describes humidity is:

<u><em>Heat</em></u>

7 0
3 years ago
Read 2 more answers
Write a balanced net ionic equation for the following reaction. BaCI2(aq)+H2SO4(aq) -&gt; BaSO4(s)+HCI (aq)
Sever21 [200]
Ba²⁺ + 2Cl⁻ + 2H⁺ + SO₄²⁻ = BaSO₄ (precipitate) + 2H⁺ + 2Cl⁻
Ba²⁺ + SO₄²⁻ = BaSO₄
4 0
3 years ago
Read 2 more answers
Other questions:
  • A neutral atom of chlorine (Cl) has an average mass of 35 amu and 17 electrons. How many neutrons does it have?
    6·2 answers
  • Select all of the following statements which are true of water.
    9·1 answer
  • A concept map for four types of intermolecular forces and a certain type of bond is shown.
    11·1 answer
  • З BaCl2 how many atoms​
    12·1 answer
  • True or False?
    10·1 answer
  • What gas does photosynthesis produce
    5·2 answers
  • Which substance is a type of biomolecule that can be used for energy storage and insulation? O A. Nucleic acid O B. Carbon dioxi
    15·2 answers
  • Newton determined that the attractive force between two masses was DIRECTLY proportional to:
    12·1 answer
  • Can anyone explain this to me?
    14·1 answer
  • Equation for the reaction btn nitric acid and metal X whose valence is 3​
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!