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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.

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Answer:

a mixture is a material made up of two or more different substances which are physically combined.

4 0
3 years ago
Consider the generic reaction: 2 A(g) + B(g) → 2 C(g). If a flask initially contains 1.0 atm of A and 1.0 atm of B, what is the
irina1246 [14]

Answer:

b. 1.5 atm.

Explanation:

Hello!

In this case, since the undergoing chemical reaction suggests that two moles of A react with one moles of B to produce two moles of C, for the final pressure we can write:

P=P_A+P_B+P_C

Now, if we introduce the stoichiometry, and the change in the pressure x we can write:

P=1.0-2x+1.0-x+2x

Nevertheless, since the reaction goes to completion, all A is consumed and there is a leftover of B, and that consumed A is:

x=\frac{1.0atm}{2}=0.5atm

Thus, the final pressure is:

P=1.0-2(0.5)+1.0-(0.5)+2(0.5)\\\\P=1.5atm

Therefore the answer is b. 1.5 atm.

Best regards!

3 0
2 years ago
How many sodium ions are in 1.4 kg of sodium chloride, NaCl?
Whitepunk [10]

Answer:

1.44 x 10²⁵ ions of Na⁺

Explanation:

Given parameters:

Mass of NaCl  = 1.4kg  = 1400g

Unknown:

Number of ions of sodium  = ?

Solution:

The compound NaCl in ionic form can be written as;

      NaCl →  Na⁺ + Cl⁻

In 1 mole of NaCl we have 1 mole of sodium ions

 Now, let us find the number of moles in NaCl;

  Number of moles  = \frac{mass}{molar mass}  

    Molar mass of NaCl  = 23 + 35.5 = 58.5g/mol

Number of moles  =  \frac{1400}{58.5}     = 23.93mol

 So;

   Since 1 mole of NaCl gives 1 mole of Na⁺  

    In 23.93 mole of NaCl will give 23.93 mole of Na⁺

1 mole of a substance  = 6.02 x 10²³ ions of a substance

  23.93 mole of a substance  =  6.02 x 10²³ x  23.93

                                                   = 1.44 x 10²⁵ ions of Na⁺

7 0
3 years ago
What is an open-loop system?
Naddika [18.5K]

A.  A group of related objects that do not send out or receive feedback and cannot modify themselves

Explanation:

An open-loop system is a a group of related objects or systems that cannot send out or receive feedback and modify themselves.

  • It is a non-feedback system.
  • In this system, the output control system has no effect on whatever input that is fed into the system.
  • Output and input in such systems are independent of one another.
  • The input and output has no control whatever on each other.

learn more:

Computer programs brainly.com/question/9409412

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5 0
3 years ago
Sodium hydroxide, NaOHNaOH; sodium phosphate, Na3PO4Na3PO4; and sodium nitrate, NaNO3NaNO3, are all common chemicals used in cle
nadya68 [22]

Answer:

NaOH > Na3PO4 > NaNO3

Explanation:

in NaOH

23/40 * 100 = 57.5%

in Na3PO4

3 * 23/164 * 100 = 42%

In NaNO3

23/85 * 100 = 27.1%

Hence;

NaOH > Na3PO4 > NaNO3

4 0
3 years ago
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