For parts a & b below, derive only the initial value problem set up.
A tank of capacity 200 gallons holds 100 gallons of water with 25 pounds of sugar in solution. Pure water is poured into it at the rate of 2 gallons per minute, and the well-stirred mixture flows out of this tank at a rate of gallon per minute and into the second tank that initially contained 50 gallons of fresh water. The well-stirred mixture in the second tank is allowed to leave the tank at the same rate (1 gal/min).
1. Determine an Initial value problem that satisfied by the amount of sugar in the first tank (Tank A).
2. Determine an Initial value problem that satisfied by the amount of sugar in the second tank (Tank B).

Answers

Answer 1

Answer:

Explanation:

From the given information:

Let y(t) be the amount of sugar in tank A at any time.

Then, the rate of change of sugar in the tank is given by:

[tex]\dfrac{dy}{dt}= (rate \ in ) - ( rate \ out )[/tex]

The rate of the sugar coming into the tank is 0

[tex]\text{rate of sugar going out }= \dfrac{y(t) \ pound}{100}\times \dfrac{1 }{min} \\ \\ = \dfrac{y}{100} \ pound/min[/tex]

[tex]So; \\ \\ \\ \dfrac{dy}{dt} = 0 - \dfrac{y}{100} \\ \\ \implies \dfrac{dy}{y }= -\dfrac{dt}{100 } \\ \\ \implies dx|y| = -\dfrac{t}{100}+C \\ \\ \implies e*{In|y|}= e^{-\dfrac{t}{100}+C} \\ \\ \implies y = Ce^{-\dfrac{t}{100}}[/tex]

Initial amount of sugar = 25 Pounds

Now; y(0) = 25

25 = Ce⁰

C = 25

So;  y(t) = 25 [tex]e^{-\dfrac{t}{100}[/tex]

Thus, the amount of sugar at any time t = [tex]\mathbf{25 e^{^{-\dfrac{t}{100}}}}[/tex]

B) For tank B :

[tex]\dfrac{dy}{dt}= 1 - \dfrac{y}{50 } \\ \\ \dfrac{dy}{dt}= \dfrac{50-y}{50} \\ \\ \dfrac{dy}{50-y }= \dfrac{dt}{50}[/tex]


Related Questions

2. A spider builds his web in the horns of a deer. What is the symbiotic
relationship?
I point
O MUTUALISM
COMMENSALISM
PARASITISM
O Other

Answers

Answer:

COMMENSALISM

Explanation:

Commensalism refers to the relationship that exists between two different organism that belong to different species. In this relationship neither of the organisms are harmed while either of them is benefitted. The web made by the spider between the horns of the deer increases the probability of the spider to catch its prey. The random movement of the deer helps the spider and at the same time it do not harm the deer.

Please help me!!! this is due now​

Answers

it’s on the opposite side of earth from the sun basically making a sandwich which earth in the middle

* Urgent Bet no one knows this *

Answers

Answer: The name of the super continent that existed millions of years ago.

Explanation:

Our continents as they exist today were once joined together into a super continent known as Pangea. Over the millennia, the land masses broke off and drifted away creating the location of the continents we know today.

(つ ^‿^ )つ Hey there!

Answer → Is the second answer, The name of the super continent that existed millions of years ago.  

✨Hope this helps!✨

If 13.5 L of nitrogen gas reacts with 17.8 L of hydrogen gas at STP, according to the following reaction, what mass of ammonia would be produced? N2 + 3 H2 --> 2 NH3 Report your answer with proper significant figures, only a number answer is required, no units needed for this form.

Answers

Answer: N5 + H4 and then do 13.5 * 17.8 then solve so 240.3 divided by 9

Your answer is 26.7  Pretty sure

Explanation: (study)

Answer:

Work is all on the paper

What does purified water and fluorine make?

Answers

Answer:

Adding fluoride to the water supply reduces the incidence of tooth decay. Fluoride protects teeth from decay by demineralization and remineralization. Too much fluoride can lead to dental fluorosis or skeletal fluorosis, which can damage bones and joints.

Explanation:

N/A

why cancer is not a pathogen?​

Answers

Answer:

Because their cells duplicate inside of you not normally!

Explanation:

Hope this helps! Plz mark as brainliest! :)

In which atmospheric layer is the ozone layer? O stratosphere o thermosphere O mesosphere troposphere​

Answers

Answer:

The stratosphere

Explanation:

8) All of the following statements are true except ________. A) Internal energy is a state function. B) The enthalpy change for a reaction is equal in magnitude, but opposite in sign, to the enthalpy change for the reverse reaction. C) The enthalpy change for a reaction depends on the state of the reactants and products. D) The enthalpy of a reaction is equal to the heat of the reaction. E) Enthalpy is an intensive property.

Answers

Answer:

E. Enthalpy is an intensive property Is false.

Explanation:

The false or wrong option in this question is that Enthalpy is an intensive property.

To explain this, I would first explain an intensive property. An intensive property is one that does not depend on the quantity or the mass of matter. Examples are temperature and pressure.

But an extensive property is a property which depends on the mass and the quantity of the system. Enthalpy, volume are all extensive.

What volume in

L

of a 0.724 M Nal solution contains 0.405 mol of Nal ?

Answers

Answer:

[tex]0.5594\ \text{L}[/tex]

Explanation:

Mol of NaI = 0.405 mol

Molarity of solution = 0.724 M

Molarity is given by

[tex]M=\dfrac{\text{mol}}{\text{Volume of solution in }NaI}\\\Rightarrow \text{Volume of solution in }NaI=\dfrac{0.405}{0.724}\\\Rightarrow \text{Volume of solution in }NaI=0.5594\ \text{L}[/tex]

The required volume is [tex]0.5594\ \text{L}[/tex].

In order for heat to flow there must be... *

A. identical tempatures

B. a difference in tempatures

C. a difference in altitude

D. an electrical current present

Answers

Answer:

B. a difference in temperatures.

Explanation:

Conduction involves the transfer of electric charge or thermal energy due to the movement of particles. When the conduction relates to electric charge, it is known as electrical conduction while when it relates to thermal energy, it is known as heat conduction.

In the process of heat conduction, thermal energy is usually transferred from fast moving particles to slow moving particles during the collision of these particles.

Also, thermal energy is typically transferred between objects that has different degrees of temperature and materials (particles) that are directly in contact with each other but differ in their ability to accept or give up electrons.

In order for heat to flow there must be a difference in temperatures.

This ultimately implies that, the driving force responsible for heat to flow is a difference in temperature between the points from which heat originates and where heat is received.

Additionally, the higher the temperature difference, the greater would be the heat flow; which is usually from a high temperature level to a low temperature level.

How many grams do 4.5 moles of oxygen atoms weigh

Answers

Answer:

71.99100

Explanation:

The mass of oxygen equal to one mole of oxygen is 15.998 grams and the mass of one mole of hydrogen is 1.008 g. 15.998*4.5 = 71.99100

#12 don’t understand need help significantly

Answers

Answer:

C. 8.80 mol H₂

General Formulas and Concepts:

Math

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Chemistry

Atomic Structure

Reading a Periodic TableMoles

Stoichiometry

Using Dimensional AnalysisAnalyzing Reactions RxNExplanation:

Step 1: Define

[RxN - Balanced] N₂ (g) + 3H₂ (g) → 2NH₃ (g)

[Given] 100 g 2NH₃

[Solve] moles H₂

Step 2: Identify Conversions

[RxN] 2 mol NH₃ (g) → 3 mol H₂ (g)

[PT] Molar Mass of N - 14.01 g/mol

[PT] Molar Mass of H - 1.01 g/mol

Molar Mass of NH₃ - 14.01 + 3(1.01) = 17.04 g/mol

Step 3: Stoich

[DA] Set up conversion:                                                                                 [tex]\displaystyle 100 \ g \ NH_3(\frac{1 \ mol \ NH_3}{17.04 \ g \ NH_3})(\frac{3 \ mol \ H_2}{2 \ mol \ NH_3})[/tex][DA] Multiply/Divide [Cancel out units]:                                                         [tex]\displaystyle 8.80282 \ mol \ H_2[/tex]

What volume, in milliliters, of a 0.140 M solution of KCl contains 2.65 g of the compound?
Express the volume to three significant figures and include the appropriate units.

Answers

Answer:

Calculate moles KCl: 2.55 g / 74.55 g/mol = 0.0342 moles KCl

Volume KCl = 0.0342 mol X (1 L/0.150 mol) = 0.228 L X 1000 mL/L = 228 mL

Explanation:

Volume=288mL

Given:

Molarity=0.140 M

Mass=2.65 g

To find:

Volume=?

Molar mass of KCl = 74.55 g/mol

Firstly, we need to calculate the number of moles of KCl:

[tex]\text{Number of moles}=\frac{\text{Given mass}}{\text{Molar mass}} \\\\\text{Number of moles}=\frac{2.65g}{74.55g/mol} \\\\\text{Number of moles}=0.0355 moles[/tex]

In order to calculate the volume,

[tex]\text{ Volume of KCl} = 0.0342 mol * (1 L/0.150 mol) \\\\\text{ Volume of KCl} = 0.228 L * 1000 mL/L \\\\\text{ Volume of KCl} = 228 mL[/tex]

The volume in mL will be 228mL.

Learn more:

brainly.com/question/15356425

Rubbing alcohol is 70.% (v/v) isopropyl alcohol by volume. How many mL of isopropyl alcohol are in a 1 pint (473 mL) container? Rubbing alcohol is 70.% (v/v) isopropyl alcohol by volume. How many mL of isopropyl alcohol are in a 1 pint (473 mL) container? 330 mL 470 mL 70. mL 680 mL 0.15 mL

Answers

Answer:

helped

The number  of ml of isopropyl  alcohol  that are 1 pint (473 Ml)   is  331.1 Ml

  calculation

assume  that  the 1 pint  is in  a  container

  This implies  that the 1 pint (473 ml)  is  in 100 %  M/V

     what about 70 %(M/V)

that is  473 Ml  = 100 %

                  ?   =   70 %

by  cross  multiplication

   =  473 x70/100 = 331.1 Ml

Explanation:

Where are the most reactive nonmetals located on the periodic table?

Answers

The most reactive nonmetals are located in the upper right portion of the periodic table

Please help me I’m not sure with that

Answers

What I can’t see the pic ?hhbc639l73773 ghcbhjbch

Answer:

i cant see the picture sorry

Explanation:

MULTIPLE CHOICE QUESTION
When the frequency increases, the waves
become?
Shorter
Longer

Answers

Answer:

Shorter

Explanation:

As a wavelength increases in size, its frequency, and energy (E) decrease. From these equations, you may realize that as the frequency increases, the wavelength gets shorter. As the frequency decreases, the wavelength gets longer. There are two basic types of waves: mechanical and electromagnetic.

Which blood vessels carry blood away from the heart?

veins
arteries
capillaries

Answers

Answer:

Arteries

Explanation:

Answer:         arteries.    :)

Explanation:

the top one is right trust me and i took the test.      :)

have agreat day.     :)

What are two things that interact that determine if there is a phase change or not HELP

Answers

Answer:

phase change always has two phases in contact during the change. melting => solid & liquid; evaporation (boiling) => liquid & vapor. If only one phase is present, then phase change is not occurring. Also, when two phases are in contact, no temperature changes occur. Only the pure phase demonstrates temperature change when measured. Example, when ice is added to water, at thermal equilibrium (temp = 0°C) the water temp will not continue to change. Only when all the ice has melted will the water temperature demonstrate a measured temperature change.

Explanation:

2) A common "rule of thumb" -- for many reactions around room temperature is that the

rate will double for each ten degree increase in temperature. Does the reaction you hav

studied seem to obey this rule.

Answers

The question is incomplete. The complete question is :

A common "rule of thumb" for many reactions around room temperature is that the rate will double for each ten degree increase in temperature. Does the reaction you have studied seem to obey this rule? (Hint: Use your activation energy to calculate the ratio of rate constants at 300 and 310 Kelvin.)

Solutions :

If we consider the activation energy to be constant for the increase in 10 K temperature. (i.e. 300 K → 310 K), then the rate of the reaction will increase. This happens because of the change in the rate constant that leads to the change in overall rate of reaction.

Let's take :

[tex]$T_1=300 \ K$[/tex]

[tex]$T_2=310 \ K$[/tex]

The rate constant = [tex]$K_1 \text{ and } K_2$[/tex] respectively.

The activation energy and the Arhenius factor is same.

So by the arhenius equation,

[tex]$K_1 = Ae^{-\frac{E_a}{RT_1}}$[/tex]  and [tex]$K_2 = Ae^{-\frac{E_a}{RT_2}}$[/tex]

[tex]$\Rightarrow \frac{K_1}{K_2}= \frac{e^{-\frac{E_a}{RT_1}}}{e^{-\frac{E_a}{RT_2}}} $[/tex]

[tex]$\Rightarrow \frac{K_1}{K_2}= e^{-\frac{E_a}{R}\left(\frac{1}{T_1}-\frac{1}{T_2}\right)}$[/tex]

[tex]$\Rightarrow \ln \frac{K_1}{K_2}= - \frac{E_a}{R} \left(\frac{1}{T_1} -\frac{1}{T_2} \right)$[/tex]

[tex]$\Rightarrow \ln \frac{K_2}{K_1}= \frac{E_a}{R} \left(\frac{1}{T_1} -\frac{1}{T_2} \right)$[/tex]

Given, [tex]$E_a = 0.269$[/tex] J/mol

           R = 8.314 J/mol/K

[tex]$\Rightarrow \ln \frac{K_2}{K_1}= \frac{0.269}{8.314} \left(\frac{1}{300} -\frac{1}{310} \right)$[/tex]

[tex]$\Rightarrow \ln \frac{K_2}{K_1}= \frac{0.269}{8.314} \times \frac{10}{300 \times 310}$[/tex]

[tex]$\Rightarrow \ln \frac{K_2}{K_1}= 3.479 \times 10^{-6}$[/tex]

[tex]$\Rightarrow \frac{K_2}{K_1}= e^{3.479 \times 10^{-6}}$[/tex]

[tex]$\Rightarrow \frac{K_2}{K_1}= 1$[/tex]

∴ [tex]$K_2=K_1$[/tex]

So, no this reaction does not seem to follow the thumb rule as its activation energy is very low.

The value of the equilibrium constant for a reaction
a. changes with temperature.
b. changes with time.
c. is the same under all conditions.
d. changes with concentration.

Answers

Answer:

a. changes with temperature.

Explanation:

Hello there!

In this case, according to the thermodynamic definition of the equilibrium constant in terms of the Gibbs free energy of reaction and the temperature of the system:

[tex]lnK=-\frac{\Delta G}{RT}[/tex]

It is possible to figure out that the equilibrium constant varies as temperature does, not only on the aforementioned definition, but also in the Gibbs free energy as it is also temperature-dependent. Therefore, the appropriate answer is a. changes with temperature.

Best regards!

1. If 3.2 L of nitrogen monoxide and 4.3 g of oxygen gas are combined, what volume of nitrogen dioxide will be formed? 2NO + 0, -> 2NO,​

Answers

Answer:

[tex]3.2 \div 22.4 = \frac{1}{7} mol \: no[/tex]

[tex]4.3 \div 32 = 0.134mol \: o2[/tex]

Explanation:

NO is limit reactant so:

1÷7×46=6.57 grams of NO2 will form

320.0 g of NaCl would contain how many formula units? (Molar mass of
NaCl is 58.44 g/mol) *

Answers

Answer:

Formula unit = 32.9746×10²³

Explanation:

Given:

Mass of NaCl = 320 g

Molar mass of  NaCl = 58.44 g/mol

Find:

Formula unit

Computation:

Formula unit = [Mass of NaCl / Molar mass of  NaCl]Avogadro's number

Formula unit = [320 /58.44]6.022×10²³

Formula unit = 32.9746×10²³

#15 need help don’t understand

Answers

I got B. Lmk if u need explanation

Four flasks each contain 100 milliliters of aqueous solutions of equal concentrations at 25°C and 1 atm.

KCI
CH3OH
Ba(OH)2
CH3COOH

Which solutions contain electrolytes?

Answers

Answer:

KCl and Ba(OH)₂.

Explanation:

Hello there!

In this case, since electrolytes are substances characterized by presence of covalent bonds between the atoms forming the compound, it is possible to realize that just KCl and Ba(OH)₂ as they are species composed by cations (K and Ba) and anions (OH and Cl); therefore, they have the capacity to get ionized in aqueous solution and thus transfer electricity when present.

Best regards!

The solution containing electrolytes is the flask of KCI and [tex]Ba(OH)_2[/tex].

The correct options are a and c.

What is an electrolyte?

An electrolyte is a medium that contains ions and conducts electricity through the movement of ions, but not electrons.

They are minerals present in the body, that are electrically charged.

Electrolytes help in maintaining the water balance in the body, and pH of the body.

The three primary electrolytes are sodium, potassium, and chloride.

Thus, the correct options are a, KCI, and b, [tex]Ba(OH)_2[/tex].

Learn more about electrolyte

https://brainly.com/question/14566383

What is the formula for the ionic compound made up of the ions Cd+3 and SO4-2?

Answers

Answer: since the sodium ion is Na+, and sulfate is SO4(2-), you'll need 2 sodiums for a sulfate, making sodium sulfate Na2SO4.

Explanation:

As a raindrop falls from a cloud to the surface of Earth,
A. its speed increases due to gravity.
B. its speed increases due to air resistance,
C. it moves at a constant speed,
<
OD. it moves at a constant velocity

Answers

Answer:

The answer is C!

Explanation:

Hope it helps

Answer D

Explanation: did the quiz ψ(`∇´)ψ

What is the pH of 2.88*10^-5 M LiOH?

Answers

Answer: 9.46

Explanation: in LiOH solution concentration of OH- ions is 2.88·10^-5 M

And pOH = -log( 2.88·10^-5 M) = 4.54. Because PH + pOH = 14.00

Then pH = 14-4.54

CuCl2(aq) + Na3PO4(aq) =>?
Net ionic equation

Answers

If you are balancing the equation, your final one should be

Cu3(PO4)2 +6 NaCl.
The reaction is a double replacement reaction

A key process common to all organisms is the ability to reproduce. Where do all cells come from?
A. from ova
B. from atoms
C. from gametes
D. from pre-existing cells

Answers

Answer:

It’s d

Explanation:

It’s d 100%

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