summerhumphries3
14.06.2020 •
Mathematics
A tank contains 300 liters of fluid in which 40 grams of salt is dissolved. Pure water is then pumped into the tank at a rate of 5 L/min; the well-mixed solution is pumped out at the same rate. Let the A(t) be the number of grams of salt in the tank at time t. Find the rate at which the number of grams of salt in the tank is changing at time t. dA dt = Find the number A(t) of grams of salt in the tank at time t. A(t) = g
Solved
Show answers
More tips
- G Goods and services How to Choose a Coffee Maker? The Ultimate Guide for Coffee Lovers...
- O Other How to Accidentally Get a Rare Coin with Your Change and How to Know Its Value?...
- S Society and Politics How Could Nobody Know About the Dead Mountaineers?...
- D Dating, Love, Relationships Why do we feel shame?...
- F Family and Home Why Does God Punish Us Constantly and How Can We Fix It?...
- F Family and Home Do Lullabies Help Babies Sleep or Is it Just a Myth?...
- B Business and Finance How to Get Your Money Back When Lending? Top 7 Ways...
- S Society and Politics Выборы: Смысл, Значение и Отражение...
- D Dating, Love, Relationships Why Should the Man be Active and the Woman Passive during Foreplay?...
- P Philosophy How did the concept of module arise in computer science?...
Answers on questions: Mathematics
- M Mathematics 9.476, 9.427, 9.43, 9.347, 9.4, 9.38 HELP ASAP LESSER GREATER...
- M Mathematics Question What is the degree of the polynomial function f(x) = 4x + 3x2 +52 + 7?...
- M Mathematics In a simple regression model, if the coefficient of determination is found to be 0.64 and slope is estimated to be - 3.2, then the sample correlation coefficient...
- M Mathematics Need help for finals pls...
- M Mathematics What is the slope of the line that contains the points (-1,2) and(3,3)...
- M Mathematics When the quantities of different units are being compared change them to the same unit before comparing a. trueb. false...
- M Mathematics Hint Two shaded sections of the bar model represent 18 cards. So, how How many cards does 1 section represent?...
- M Mathematics Stitches Inc can make at most 30 jean jackets and 20 leather jackets in a week. It takes a worker 10 hours to make a jean jacket and 20 hours to make a leather...
- M Mathematics Escribir ecuaciones para la recta horizontal y la recta vertical que atraviesan el punto (6, -3)....
- M Mathematics X = z - m for x My teacher says the answer is x = -z + m, so I am wondering how to get that. I still do not understand literal equations....
Ответ:
Step-by-step explanation:
Solution:-
- The amount of salt in the solution is ( A ) at any time t.
- Pure water enters the tank ( no salt ( A = 0 ) ).
- The volumetric rate of flow in and out of tank is V(flow) = 5 L / min
- The rate of change of salt in the tank at time ( t ) can be expressed as a first order ordinary differential equation for the salt solution that flows in and out of the tank
- The first order ordinary differential equation is expressed as:
= ( salt flow in ) - ( salt flow out )
- Fresh water with zero salt content flows in then ( salt flow in ) = 0
- The concentration of salt within the tank changes with time ( t ).
- The volume of water in the tank remains constant ( steady state conditions ). I.e 5 Liters volume leaves and 5 Liters is added; hence, the total volume of solution in tank remains 300 Liters.
- So at any instant the concentration of salt in the 300 Liter tank is:
- The amount of salt-solution flowing out of the tank per unit time would be:
- The differential equation becomes:
- Separate the variables and integrate both sides:
- Initial conditions: A ( 0 ) = 4 grams. Use the initial conditions to evaluate the constant of integration:
- The solution to the differential equation becomes::
Ответ:
1 meter= 0.001 kilometer
56 meters = 0.056 kilometers
Therefore, the height of Niagara falls is 0.056 kilometers