A tank contains 5,000 L of brine with 13 kg of dissolved salt. Pure water enters the tank at a rate of 50 L/min. The solution is kept thoroughly mixed and drains from the tank at the same rate.
Required:
a. How much salt is in the tank after t minutes?
b. How much salt is in the tank after 20 minutes?
Answers
Answer:
a) \(x(t) = 13*e^(^-^\frac{t}{100}^)\)
b) 10.643 kg
Step-by-step explanation:
Solution:-
- We will first denote the amount of salt in the solution as x ( t ) at any time t.
- We are given that the Pure water enters the tank ( contains zero salt ).
- The volumetric rate of flow in and out of tank is V(flow) = 50 L / min
- The rate of change of salt in the tank at time ( t ) can be expressed as a ODE considering the ( inflow ) and ( outflow ) of salt from the tank.
- The ODE is mathematically expressed as:
\(\frac{dx}{dt} =\) ( salt flow in ) - ( salt flow out )
- Since the fresh water ( with zero salt ) flows in then ( salt flow in ) = 0
- The concentration of salt within the tank changes with time ( t ). The amount of salt in the tank at time ( t ) is denoted by x ( t ).
- The volume of water in the tank remains constant ( steady state conditions ). I.e 10 L volume leaves and 10 L is added at every second; hence, the total volume of solution in tank remains 5,000 L.
- So any time ( t ) the concentration of salt in the 5,000 L is:
\(conc = \frac{x(t)}{1000}\frac{kg}{L}\)
- The amount of salt leaving the tank per unit time can be determined from:
salt flow-out = conc * V( flow-out )
salt flow-out = \(\frac{x(t)}{5000}\frac{kg}{L}*\frac{50 L}{min}\\\)
salt flow-out = \(\frac{x(t)}{100}\frac{kg}{min}\)
- The ODE becomes:
\(\frac{dx}{dt} = 0 - \frac{x}{100}\)
- Separate the variables and integrate both sides:
\(\int {\frac{1}{x} } \, dx = -\int\limits^t_0 {\frac{1}{100} } \, dt + c\\\\Ln( x ) = -\frac{t}{100} + c\\\\x = C*e^(^-^\frac{t}{100}^)\)
- We were given the initial conditions for the amount of salt in tank at time t = 0 as x ( 0 ) = 13 kg. Use the initial conditions to evaluate the constant of integration:
\(13 = C*e^0 = C\)
- The solution to the ODE becomes:
\(x(t) = 13*e^(^-^\frac{t}{100}^)\)
- We will use the derived solution of the ODE to determine the amount amount of salt in the tank after t = 20 mins:
\(x(20) = 13*e^(^-^\frac{20}{100}^)\\\\x(20) = 13*e^(^-^\frac{1}{5}^)\\\\x(20) = 10.643 kg\)
- The amount of salt left in the tank after t = 20 mins is x = 10.643 kg
Related Questions
Joseph is buying tomato seed packets and cucumber seed packets at the store. He plans to buy 7 seed packets of EACH type of plant. Cucumber seed packets cost $1.89 each.
Joseph spends a total of $23.24 on all the seed packets. Which of the following equations can be used to find how much each tomato seed packet (t) costs? Select ALL that apply.
A
23.24=1.89(7)+t
B
7(1.89)+7t=23.24
C
7t=10.00
D
23.24−13.23=7t
Answers
Answer:
B
Step-by-step explanation:
Elimanited C and D
2. Rewrite the expression below using the Associative Property of Multiplication: (ab)c
A. (ba)c
B. c(ab)
C. abc
D. a(bc)
E. All of the above
Answers
As long as the letters are all multiplying each other, the letters can be arranged in any way in accordance with the property
Does the data follow a normal distribution? Why or why not?
Answers
Ling has $6 to buy 42-cent postage stamps. What is the greatest number of stamps that she can buy?*
Answers
Answer:
14 stamps
Step-by-step explanation:
She has 6.00 dollars in total so you would divide 2.00 by 0.42 to get 14.286, but you can't but .286 of a stamp so the answer is 14
Hope this helps :-)
A bag contains 1 red, 1 yellow, 1 blue, and 1 green marble. What is the probability of choosing a green marble, not replacing it, and then choosing a red marble?
Answers
Answer:
if its fractions then 1/4 if its percentage then 25%
Step-by-step explanation:
Getting it in that order is 2/12
1/6
What differences would you expect to observe between a random walk of a molecule in a gas and a random walk of a protein molecule in water
Answers
The main difference between the random walk of a gas molecule and that of a protein molecule in water is that the gas molecule will have a lower random walk.
Random Walk This refers to the random movements taken by a molecule in a state of matter. Is heavily affected by the collisions the molecule makes with other molecules.When there is a high frequency of molecules, as is the case in a liquid, there will be more random walks because molecules will keep bumping into each other. In gas however, the random walk will be less because molecules are more spaced out.
In conclusion, the gas molecule will have less random walk.
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2(3x - 1) + 2(4x + 5) = 8
Answers
Answer:
0
Step-by-step explanation:
2(3x -1) + 2(4x + 5) = 8 Distribute the 2's
2(3x) + 2(-1) + 2(4x) + 2(5) = 8
6x - 2 + 8x +10 = 8 Combine like terms
14x + 8 = 8 Subtract 8 from both sides of the equaion
14x = 0 Divide both sides by 14
x = 0
An olive farmer has 1,140 olives to put into jars. It takes 89 olives to fill each jar. After the farmer fills as many jars as possible, how many olives will be left over?
Answers
Answer:
72 olives will be left
Step-by-step explanation:
1140÷89= 12 with 72 left over
Calc
Maximize Q=xy, where x and y are positive numbers such
that x + 3y² = 25.
Write the chiective function in terms of y
Q=
Answers
Q = 25y - 3y³
Step-by-step explanation:
To write the objective function in terms of y, we need to express x in terms of y using the constraint equation:
x + 3y² = 25
x = 25 - 3y²
Now we can substitute this expression for x in the objective function:
Q = xy = y(25 - 3y²)
Expanding this expression gives:
Q = 25y - 3y³
Therefore, the objective function in terms of y is Q = 25y - 3y³
searched everywhere but can't find the answer for this one question, help por favor
Answers
Answer:
Step-by-step explanation:
30.8%
Explanation- Did the maths
sove for N
A.
n = 196
B.
n = 8
C.
n = 32
D.
n = 4
Answers
Answer: B
Step-by-step explanation:
n/56 = 4/28
Simplify:
n/56 = 1/7
Cross multiply:
7x = 56
7x/7 = 56/7
x = 8
\([Hello,BrainlyUser]\)
Answer:
n = 8
Step-by-step explanation:
Divide the numbers
\(\frac{n}{56}=\frac{4}{28}\)
\(\frac{n}{56}=\frac{1}{7}\)
Multiply all terms by the same value to eliminate fraction denominators
\(56*\frac{n}{56}=56*\frac{1}{7}\)
Cancel multiplied terms that are in the denominator
\(n = 56*\frac{1}{7}\)
Multiply the numbers
\(n=8\)
\([CloudBreeze]\)
the ratio of the number of girls to all students in the class is 4:9 can there be 20 students in that class?
I need help asap my sister isn't here so i can't ask her for help
Answers
Answer:
nooo.......how there can only be 20 students.....!
The answer is no!
There can't be 20 students in that class because the ratio is 4:9 so its either 4 boys and 9 girls or 4 girls and 9 boys.This is a total of 13 students because (4+9=13).The answer is That there can not be 20 students in that class because there is only 13 students.
Help pls I’ll mark you brainliest
Answers
Answer:
9
Step-by-step explanation:
9
Complete the following tables with values for the functions f _ and h given that: (a) f is an odd function: (b) g is an even function. (c) h = g(f(x)) h(x)
Answers
The result is that h(x) = 0 for all x except for x = -2 and x = 2, where h(x) = 6.
f(x) | -2 | -1 | 0 | 1 | 2
-------|----|----|----|----|----
f(x) | 5 | -3 | 0 | -3 | 5
g(x) | -2 | -1 | 0 | 1 | 2
-------|----|----|----|----|----
g(x) | 6 | 0 | 0 | 0 | 6
h(x) | -2 | -1 | 0 | 1 | 2
-------|----|----|----|----|----
h(x) | 6 | 0 | 0 | 0 | 6
h(x) = g(f(x))
For x = -2, h(x) = g(f(-2)) = g(5) = 6
For x = -1, h(x) = g(f(-1)) = g(-3) = 0
For x = 0, h(x) = g(f(0)) = g(0) = 0
For x = 1, h(x) = g(f(1)) = g(-3) = 0
For x = 2, h(x) = g(f(2)) = g(5) = 6
Since f is an odd function and g is an even function, then h(x) = g(f(x)) will be an even function. This means that for any given x, h(x) will always equal 0 or a positive value. For the set of values provided above, the result is that h(x) = 0 for all x except for x = -2 and x = 2, where h(x) = 6.
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if 6 people can walk 12 dogs, how many people are needed to walk 24 dogs
Answers
Answer:
12 people are need to walk 24 dogs
Step-by-step explanation:
12/2=6
24/2=12
Answer:
12 people can walk 24 dogs.
Step-by-step explanation:
Given information,
→ 6 people can walk 12 dogs.
→ People required for 24 dogs = ?
Let us assume that,
→ Missing value = p
Forming the equation,
→ 6/12 = p/24
Then the value of p will be,
→ 6/12 = p/24
→ p/24 = 6/12
→ p × 12 = 6 × 24
→ 12p = 144
→ p = 144/12
→ [ p = 12 ]
Hence, the value of p is 12.
Which equation has no solution?
Answers
Answer:
number 3
Step-by-step explanation:
What is the meaning of "A group G whose order is a prime number has only two subgroups, G itself and 1 = {1}"?
Answers
If G is not a cyclic group, then it does not have a subgroup of order p. Conversely, if G is cyclic, then it has a unique subgroup of order p.
The statement "A group G whose order is a prime number has only two subgroups, G itself and 1 = {1}" means that if G is a group with a prime number of elements, then the only subgroups of G are the trivial subgroup {1} and the group G itself.
In other words, there are no other proper subgroups of G besides these two.
The statement "A group G whose order is (p-1) where p is a prime number has a subgroup of order p if and only if G is cyclic" means that if G is a group with (p-1) elements, where p is a prime number, then G has a subgroup of order p if and only if G is a cyclic group.
In other words, if G is not a cyclic group, then it does not have a subgroup of order p. Conversely, if G is cyclic, then it has a unique subgroup of order p.
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2.414114111 is a rational number true or false
Answers
Question 2 The current report quantitatively analyzes three variables - load factors, revenue passenger mile, and available seat miles for American Airlines. The data retrieved for the analysis was extracted from the Bureau of Transportation Statistics, focusing on domestic flights from January 2006 to December 2012. The quantitative analysis focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. Table 2: Summary Statistics of American Airlines (Domestic) Revenue Passenger Miles Mean 6,624,897 Median 6,522,230 Mode NONE Minimum 5,208,159 Maximum 8,277,155 Standard Dev 720,158.571 Variance 518,628,367,282.42 Load Factors Mean 82.934 Median 83.355 Mode 84.56 Minimum 74.91 Maximum 89.94 Standard Dev 3.972 Variance 15.762 Revenue Passenger Miles 9000000 8000000 7000000 6000000 5000000 4000000 3000000 2000000 1000000 0 0 10 American Airlines (Domestic) Performance 20 30 ● Revenue Passenger Miles 40 50 Load Factors Available Seat Miles 60 Mean 7,984,735 Median 7,753,372 Mode NONE Minimum 6,734,620 Maximum 9,424,489 Standard Dev 744,469.8849 Variance 554,235,409,510.06 70 80 Linear (Revenue Passenger Miles) 90 100 Figure 1: American Airlines (Domestic) Performance Write a report based on the given data. Please include additional tests such as hypothesis testing, skewness, z statistic, level of significance, and other necessary tests, as well as a discussion of the results obtained.
Answers
The z-statistic test was conducted to determine the Deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
Report on the Analysis of American Airlines (Domestic) PerformanceThe quantitative analysis focused on three variables- load factors, revenue passenger miles, and available seat miles for American Airlines.
The Bureau of Transportation Statistics data for domestic flights from January 2006 to December 2012 was retrieved for the analysis. The quantitative analysis also focused on finding critical statistical values like mean, median, mode, standard deviation, variance, and minimum/maximum variables. The results of the data are summarized in Table 2. Revenue Passenger Miles (RPM) mean is 6,624,897, the median is 6,522,230, and mode is NONE. The minimum is 5,208,159 and the maximum is 8,277,155. The standard deviation is 720,158.571, and the variance is 518,628,367,282.42.
Load Factors (LF) mean is 82.934, the median is 83.355, and mode is 84.56. The minimum is 74.91, and the maximum is 89.94. The standard deviation is 3.972, and the variance is 15.762. The Available Seat Miles (ASM) mean is 7,984,735, the median is 7,753,372, and mode is NONE. The minimum is 6,734,620, and the maximum is 9,424,489. The standard deviation is 744,469.8849, and the variance is 554,235,409,510.06.Figure 1 above displays the performance of American Airlines (Domestic).
The mean RPM is 7,984,735, and the linear regression line is y = 50584x - 2.53E+8. The linear regression line indicates a positive relationship between RPM and year, with a coefficient of determination, R² = 0.6806. A coefficient of determination indicates the proportion of the variance in the dependent variable that is predictable from the independent variable. Therefore, 68.06% of the variance in RPM is predictable from the year. A one-way ANOVA analysis of variance test was conducted to determine the equality of means of three groups of variables; RPM, ASM, and LF. The null hypothesis is that the means of RPM, ASM, and LF are equal.
The alternative hypothesis is that the means of RPM, ASM, and LF are not equal. The level of significance is 0.05. The ANOVA results indicate that there is a significant difference in means of RPM, ASM, and LF (F = 17335.276, p < 0.05). Furthermore, a post-hoc Tukey's test was conducted to determine which variable means differ significantly. The test indicates that RPM, ASM, and LF means differ significantly.
The skewness test was conducted to determine the symmetry of the distribution of RPM, ASM, and LF. The test indicates that the distribution of RPM, ASM, and LF is not symmetrical (Skewness > 0).
Additionally, the z-statistic test was conducted to determine the deviation of RPM, ASM, and LF from the mean. The test indicates that RPM, ASM, and LF significantly deviate from the mean.
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Ways to regroup and rename the number
680,000
Answers
Answer:
680,000
Step-by-step explanation:
680,000
Is this answer right?
Answers
Answer:
Step-by-step explanation:
yes!
Can anyone help me that would be great
Answers
Explanation:
The lowest numbers first
Answer:
0.343, 0.424, 0.443
Step-by-step explanation:
What part of an hour passes from 3:12 p.m. to 5:30 p.m.?
Answers
Answer:
2.3 hours
Step-by-step explanation:
From 3:12 pm to 4:12 pm, one hour passes.
From 4:12 pm to 5:12 pm, another hour passes.
From 5:12 pm to 5:30 pm, there are 18 minutes that pass.
Therefore, the total time elapsed is 2 hours and 18 minutes out of 60 minutes in an hour.
To convert this to a fraction, we can write:
2 hours + 18 minutes = 2 + 18/60 hours = 2.3 hours
So, 2.3/1 hour passes from 3:12 pm to 5:30 pm.
Y=4x+2 -6x+2y=8 what is the value x t y
Answers
Y = 4x + 2
-6x + 2y = 8
We can start by rearranging the second equation to solve for y:
-6x + 2y = 8
2y = 6x + 8
y = 3x + 4
Now we can substitute this expression for y into the first equation:
Y = 4x + 2
3x + 4 = 4x + 2
Subtracting 4x from both sides:
x = -2
To find the value of y, we can substitute x = -2 into either equation:
Y = 4x + 2
Y = 4(-2) + 2
Y = -6
Therefore, the solution to the system of equations is x = -2 and y = -6.
BODDIFinding the percentage increase or decrease: AdvancedEDThe price of a technology stock has dropped to $9.64 today. Yesterday's price was $9.73. Find the percentage decrease. Round your answer to the nearest tenthof a percent.
Answers
To find the percentage decrease, we need to find the actual decrease in price, and then, how much it represents from the original price(on this case, yesterday's price).
The actual decrease is the difference between the prices, and it is given by
\(9.73-9.64=0.09\)Now, to find how much it represents(in decimals) of the original price, we divide this decrease by yesterday's price.
\(\frac{0.09}{9.73}=0.00924974306\ldots\)And finally, to rewrite this value as a percentage, we multiply it by 100.
\(0.00924974306\ldots\times100=0.00924974306\ldots\approx0.9\)There was a 0.9% decrease on the price.
Fill in the blank for this question!
Answers
While an absolute value may be any number, the output from an absolute value expression is always greater than or equal to zero
How to Interpret an Absolute Value Function?The absolute value | x | of a real number x is defined as the non-negative value of x without regard to its sign. For example, the absolute value of 3 is 3, and the absolute value of −3 is also 3. The absolute value of a number may be thought of as its distance from zero along real number line.
The absolute value of any number is seen to be always greater than or equal to zero. Both a number and its opposite are the same distance from zero on the number line. Since they have the same distance from zero, they have the same absolute value.
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Last year, a gardening store ordered 8,910 potted plants. This year, they ordered 9,801 potted plants. What is the percent of increase in the number of potted plants ordered annually?
Answers
Answer:
Step-by-step explanation:
100(9801 - 8910)/8910 = 10%
What is the solution to the system of equations x+y=10 and x+2y=4 using the linear combination method?
Answers
Answer:
The solution:
X = 16 and Y = -6
Step-by-step explanation:
The equations to be solved are:
x+y = 10 ------- equation 1
x+2y = 4 ----------- equation 2
we can multiply equation 1 by -1 to make the value of x and y negative.
This will give us
-x- y = - 10 ------- equation 3
x+2y = 4 ----------- equation 2
We will now add equations 3 and 2 together so that x will cancel itself out.
this will give us
y = -10 +4 = -6
hence, we have the value of y as -6.
To get the value of x, we can put this value of y into any of the equations above. (I will use equation 1)
x - 6 = 10
from this, we have that x = 4
Therefore, we have our answer as
X = 16 and Y = -6
PLZ ANSWER ASASP ALMOST DUE!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Answers
Answer:
D) The third side could be 4 meters long.
Step-by-step explanation:
The third side of a triangle must be greater than the difference and less than the sum of the other two sides.
5-4=1
5+4=9
So the third side must be GREATER THAN 1 and LESS THAN 9. (1<x<9)
Therefore, the answer can't be A or C. The second one could be correct, depending on how much less than 4 it is. But the last one is definitely correct.
QUICK GIVING AWAY BRAINLIESt
Answers
-4
Hope this helps!!! :DDD
Answer:
the answer is -16
Step-by-step explanation:
if you have the problem -10 + 6 then the answer will be -16 because -10 is bigger than 6 and six is a positive number and since -10 is bigger than you would have to go with negative