![abbeyeasterwood](/avatars/36116.jpg)
abbeyeasterwood
14.09.2019 •
Mathematics
initially tank i contains 100 litres of salt brine with a concentration of 1 kilogram per litre, and tank ii contains 100 litres of water. liquid is pumped from tank i into tank ii at a rate of 1 litre per minute, and liquid is pumped from tank ii into tank i at a rate of 2 litres per minute. the tanks are kept well stirred. let a1 be the amount of salt in kilograms in tank i and a2 be the amount of salt in pounds in tank ii.
(a) calculate a1(t) and c1(t). for which range of values of t are the expression for a1(t) and c1(t) valid?
(b) what is the concentration in tank i after 10 minutes?
Solved
Show answers
More tips
- A Auto and Moto Experience the World of the Most Expensive Cars on the Planet...
- S Style and Beauty How to Get Rid of a Double Chin?...
- F Food and Cooking How to Cook Julienne? Recipes and Tips...
- D Dating, Love, Relationships 10 Useful Tips on How to Survive a Breakup?...
- F Food and Cooking Apple Cider Vinegar: The Ultimate Health and Beauty Solution...
- C Computers and Internet Е-head: How it Simplifies Life for Users?...
- F Family and Home How to Choose the Best Diapers for Your Baby?...
- F Family and Home Parquet or laminate, which is better?...
- L Leisure and Entertainment How to Properly Wind Fishing Line onto a Reel?...
- L Leisure and Entertainment How to Make a Paper Boat in Simple Steps...
Answers on questions: Mathematics
- M Mathematics Shade some or all of the grids to show that 2 one is the same as 20 tenths explain...
- M Mathematics Consider the function 2 x a bx a b ( ) ; ( , 0) where a and b are some positive constants; x is an independent variable. find x that maximizes 1. 1/2 x y / 2. x y / 3....
- M Mathematics The quinn family drove 228 miles in 4 hours at a constant rate. which equation can be used to determine how far they traveled each hour?...
- M Mathematics Last year the profit for a company was $560,000. this year s profit decreased by 7.1%. find this year s profit....
- M Mathematics A$10 bill is worth how many \pennies....
- M Mathematics If f(x) = 2x and g(x)=1/x, what is the domain of (f o g)(x)? x_ 0 all real numbers except x = 0 x _0 all real numbers...
- M Mathematics Is it possible for one ray of an angle to be longer than the other ray?...
- M Mathematics What are the solutions of the equation 2x2=2 use a graph of the related function...
- M Mathematics Acube has a surface are of 3750 find the length on one side...
- M Mathematics The following is an arithmetic sequence. 1, 2.5, 4, 5.5,… is this true of falseme...
Ответ:
a)![A1(t)=\frac{100000000}{(100-t)(100+t)^{2} } \\C1(t)=\frac{A1(t)}{100+t}](/tpl/images/0230/8735/3d705.png)
b) C1 = 0.8348 [kg/lt]
Step-by-step explanation:
Explanation
First of all, the rate of change of the amount of salt in the tank I is equal to the rate of change of salt incoming less the rate change of the salt leaving, so:
We know that the incoming rate is greater than the leaving rate, this means that the fluid in the tank I enters more than It comes out, so the total rate is :
This total rate means that 1 lt of fluid enters each minute to the tank I from the tank II, with the total rate we can calculate the volume in the tank I y tank II as:
Now we have the volume of both tanks, the next step is to calculate the incoming and leaving concentration. The concentration is the ratio between the amount of salt and the volume, so:
Since fluid is pumped from tank I into tank II, the concentration of the tank II is a function of the amount of salt of the tank I that enters into the tank II, thus:
If we substitute the concentrations and the rates into the differential equation we can get:
The obtained equation is a homogeneous differential equation of first order and the solution is:
a)![A1(t)= \frac{100000000}{(100-t)(100+t)^{2} }](/tpl/images/0230/8735/5174b.png)
and the concentration is:
This equations A1(t) and C1(t) are only valid to 0<=t<100 because to t >=100 minutes the tank II will be empty and mathematically A1(t>=100) tends to the infinite.
b) To calculate the concentration in the tank I after 10 minutes we have to substitute t=10 in C1(t), thus:
Ответ:
the lines are neither parallel nor perpendicular
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Rearrange both equations and compare their slopes.
If slopes are equal then they are parallel.
If slopes are the negative inverse of each other then perpendicular.
5x + 6y = 18 ( subtract 5x from both sides )
6y = - 5x + 18 ( divide all terms by 6 )
y = -
+ 3
with m = -![\frac{5}{6}](/tpl/images/0233/1356/2bbce.png)
2x + 14y = 21 ( subtract 2x from both sides )
14y = - 2x + 21 ( divide all terms by 14 )
y = -
+ ![\frac{3}{2}](/tpl/images/0233/1356/dbf42.png)
with m = -![\frac{1}{7}](/tpl/images/0233/1356/53e0d.png)
Since slopes are neither equal nor negative inverses, then they are neither parallel nor perpendicular.