Two tanks are interconnected. Tank A contains 60 grams of salt in 50 liters of water, and Tank B contains 80 grams of salt in 40 liters of water.
A solution of 2 gram/L flows into Tank A at a rate of 5 L/min, while a solution of 3 grams/L flows into Tank B at a rate of 7 L/min. The tanks are well mixed.
The tanks are connected, so 8 L/min flows from Tank A to Tank B, while 3 L/min flows from Tank B to Tank A. An additional 12 L/min drains from Tank B.
Letting x represent the grams of salt in Tank A, and y represent the grams of salt in Tank B, set up the system of differential equations for these two tanks.
Answers
Let a(t) and b(t) denote the amounts of salt in tanks A and B, respectively.
The volume of liquid in tanks A and B after t minutes are
A: 50 L + (5 L/min + 3 L/min - 8 L/min)t = 50 L
B: 40 L + (7 L/min + 8 L/min - 3 L/min - 12 L/min)t = 40 L
so the amount of solution in the tanks stays constant.
Salt flows into tank A at a rate of
(2 g/L)*(5 L/min) + (b(t)/40 g/L)*(3 L/min) = (10 + 3/40 b(t)) g/min
and out at a rate of
(a(t)/50 g/L)*(8 L/min) = 4/25 a(t) g/min
so the net flow rate is given by the differential equation
[tex]\dfrac{\mathrm da(t)}{\mathrm dt}=10+\dfrac{3b(t)}{40}-\dfrac{4a(t)}{25}[/tex]
We do the same for tank B: salt flows in at a rate of
(3 g/L)*(7 L/min) + (a(t)/50 g/L)*(8 L/min) = (21 + 4/25 a(t)) g/min
and out at a rate of
(b(t)/40 g/L)*(3 L/min + 12 L/min) = 3/8 b(t) g/min
and hence with a net rate of
[tex]\dfrac{\mathrm db(t)}{\mathrm dt}=21+\dfrac{4a(t)}{25}-\dfrac{3b(t)}8[/tex]
Replace a(t) and b(t) with x and y. Then the system is (in matrix form)
[tex]\dfrac{\mathrm d}{\mathrm dt}\begin{bmatrix}x\\y\end{bmatrix}=\dfrac1{200}\begin{bmatrix}-32&15\\32&-75\end{bmatrix}\begin{bmatrix}x\\y\end{bmatrix}+\begin{bmatrix}10\\21\end{bmatrix}[/tex]
with initial conditions x(0) = 60 g and y(0) = 80 g.
Related Questions
A driveway is 25 meters long how long the driveway in centimeters
Answers
Answer:
2500
Explanation : a meter is 100 centimeters long so you would multiply 25 by 100 to get 2500
Answer: 2,500 centimeters
Step-by-step-Explanation: To convert 25 meters into centimeters, we use the conversion factor for meters and centimeters
which is 100 centimeters = 1 meter.
Next, notice that we're converting from a larger unit, meters, to a smaller unit, centimeters and when we go from a larger unit to a smaller unit, we multiply by the conversion factor.
So we multiply 25 by the conversion factor, 100 which gives us 2,500.
So 25 meters = 2,500 centimeters.
I need help ! I don’t understand pleaseee. ASAP!
Answers
Answer:
[tex]h=\frac{V}{\pi r^2}[/tex] this is the formula to find height
Step-by-step explanation:
Triangle ABC is reflected over the x-axis. Triangle ABC has points A (10, 2), B (9,5), and C
(6,4). What is the B' coordinate?
Answers
A reflection over a line l moves every point P of the plane to the point P ′ on the perpendicular from P to the line l and on the same distance from l .
If the line is the x -axis, a point P = ( p 1 p 2 ) moves to the point P ′ = ( p 1 , − p 2 ) .
The image of the triangle A B C is the triangle A ′ B ′ C ′ with B ′ = ( 9 , − 5 )
c. two hundred thirty-one and five tenths - in decimal standard form
Answers
Answer:
231.5
five tenths = 0.5
67.7% of males over the age of 50 have had a sigmoidoscopy or colonoscopy. If two males over the age of 60 are randomly selected, what is the probability that they both have had a sigmoidoscopy or colonoscopy?
Answers
Answer:
Hello,
45.8%
Step-by-step explanation:
67.7% x 67.7% = 0.677 x 0.677 = 0.677² = 0.458329 ≈ 45.8%
Tickets to a concert cost either $12 or $15. A
total of 300 tickets are sold, and the total
receipts were $4,140. How many of each kind
of ticket were sold?
First complete the equations below, where x stands for
$12 tickets and y stands for $15 tickets.
[?]x + [ ]y = 4,140; x + y = U
Answers
Answer:
12x +15y = 4140; x + y = 300x = 120; y = 180Step-by-step explanation:
The first equation is for receipts. Each x ticket generated $12 in receipts, so the first term needs to be 12x. Each y ticket generated $15 in receipts, so the second term needs to be 15y. U in this set of equations is the total number of tickets, said to be 300.
The equations are ...
12x +15y = 4140; x +y = 300
__
Using the second equation to write an expression for x, we have ...
x = 300 -y
Substituting this into the first equation gives ...
12(300 -y) +15y = 4140
3600 +3y = 4140
y = (4140 -3600)/3 = 180
x = 300 -180 = 120
The number of tickets sold is ...
$12 tickets -- 120
$15 tickets -- 180
_____
You might want to notice that the equation we ended up with:
4140 -12(300) = 3y
is equivalent to this "word solution." This can be done in your head; no equations required.
If all the tickets sold were $12 tickets, the revenue would be $3600. The revenue is $540 more than that. Each $15 ticket generates $3 more revenue than a $12 ticket, so to have $540 more revenue, we must have 540/3 = 180 $15 tickets.
Answer: tickets: 120………180
Step-by-step explanation:
. The pet store salesman told Evan to feed his dog 8 ounces of food per day. The food is sold in pounds. How many pounds does Evan need to buy for 2 weeks of feeding his dog? (16 ounces = 1 pound)?
Answers
Figure A is translated 3 units right and 2 units up. The translated figure is labeled figure B. Figure B is reflected over the x-axis. The reflected figure is labeled figure C. Which best explains why figure A is congruent to figure C? On a coordinate plane, triangle A has points (1, negative 2), (3, negative 2), (3, negative 5). Triangle B has points (4, 0), (6, 0), (6, negative 3). Triangle C has points (4, 0), (6, 0), (6, 3). A Is congruent to B and B Is congruent to C A Is congruent to A, B Is congruent to B, C Is congruent to C Each triangle is a right triangle. Each triangle is an isosceles triangle.
Answers
Answer:
A Is congruent to B and B Is congruent to C
Step-by-step explanation:
Let's look at the answer choices:
A: "A Is congruent to B and B Is congruent to C"
Well, clearly, if A ≅ B and B ≅ C, then by the transitive property, we can say that A ≅ C. So, A is very likely correct.
B: "A Is congruent to A, B Is congruent to B, C Is congruent to C"
Just because A is congruent to itself (and same with B and C) doesn't necessarily mean that they're congruent to each other. So, B is wrong.
C: "Each triangle is a right triangle."
Again, there are so many right triangles out there with different dimensions. For example, there are some with sides 3, 4, and 5, and others with sides 5, 12, and 13. They are not congruent, however. So, rule out C.
D: "Each triangle is an isosceles triangle."
This is just like choice C since there are so many variations of isosceles triangles. So D is wrong.
The answer is thus A.
Answer:
First one:
A Is congruent to B and B Is congruent to C
Step-by-step explanation:
Since B is obtained by translating A, it has the same measure angles and sides as A, hence B is congruent to A
C is obtained by reflecting B, which doesn't alter the measure of sides and angles, so C is congruent to B
Therefore by transition, C is congruent to A
The difference between twice the product of a and b and the quotient of these
numbers.
Pls hurry
Answers
Answer:
DIFFERENCE – The difference of two numbers is the result of subtracting these two numbers. PRODUCT – The product of two or more numbers is the result of multiplying these numbers. QUOTIENT – The quotient of two numbers is the result of the division of these numbers.
Step-by-step explanation:
Answer:
2(a*b)-a/b
Step-by-step explanation:
So, read the problem and anlyze it.
To simplify what it says: The difference (subtraction), of twice the product(multiplacation) , and quotient of a & b.
So:
2(a*b)- a/b
Keep in mind that, they are not asking for twice of a/b. Only tice of the multiplacation part. They are asking the difference between both!
WILL RATE BRAINLIEST PLZ HELP
MUST EXPLAIN THO
Answers
Answer:
A -- base 3, height 4B -- base 4, height 4C -- base 3, height 3D -- base 3, height 5Step-by-step explanation:
A sort of straightforward way to approach this is to define base and height variables for each of the figures: ba, ha, bb, hb, bc, hc, bd, hd. Then the statements can be used to make equations in these variables.
0. hc = bc . . . . figure C is a square
1. ba = bd
2. ba = bb -1
3. hc = ba
4. hb = ha = bb
5. hc·bc = 9
6. (1/2)ha·ba +(1/2)hb·bb +hc·bc+hd·bd = 38
__
Using equations 0 and 5, we find ...
hc² = 9 ⇒ hc = 3
From equation 3, ...
ba = 3
From equation 2, ...
3 = bb -1 ⇒ bb = 4
From equation 1, ...
bd = 3
From equation 4, ...
ha = hb = 4
Filling in the values we know in equation 6, we get ...
(1/2)(4)(3) +(1/2)(4)(4) +9 +hd(3) = 38
23 +3hd = 38
hd = 15/3 = 5
The dimensions are:
A -- base 3, height 4B -- base 4, height 4C -- base 3, height 3D -- base 3, height 5Classify this relation as direct, inverse, or neither:
On Sarah's 16 GB flash drive, she can fit 16 video clips of about 1 GB each, two movies of about 8 GB each, or 4000 songs of about 4 MB each.
A. Inverse; there is a constant product of 8 GB.
B. Inverse; there is a constant product of 16 GB.
C. Direct; the ratio of corresponding x- and y-values is constant.
D. Neither
Answers
Answer:
b option im not sure but
Step-by-step explanation:
Suppose a quality control engineer wishes to estimate the proportion of defective items in a production line. i. (4 points) To estimate the proportion within 0.02 and with 98% confidence, what is the minimum required sample size if the company currently has no idea about the
Answers
Answer:
The minimum sample size required is 3385.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
98% confidence level
So [tex]\alpha = 0.02[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.02}{2} = 0.99[/tex], so [tex]Z = 2.327[/tex].
To estimate the proportion within 0.02 and with 98% confidence, what is the minimum required sample size if the company currently has no idea about the
The minimum sample size required is n.
We find n when [tex]M = 0.02[/tex]
We don't know the true proportion, so we use [tex]\pi = 0.5[/tex], which is when the largest minimum sample size will be needed.
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.02 = 2.327\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.02\sqrt{n} = 2.327*0.5[/tex]
[tex]\sqrt{n} = \frac{2.327*0.5}{0.02}[/tex]
[tex](\sqrt{n})^{2} = (\frac{2.327*0.5}{0.02})^{2}[/tex]
[tex]n = 3384.33[/tex]
Rounding up
The minimum sample size required is 3385.
What’s the volume of the solid ?
Answers
Answer:
I think its 70in hope it helps
Step-by-step explanation:
A researcher is interested in whether or not there is any association between normal method of transportation taken to work and reported mood at the beginning of a typical Monday morning. He classifies participants into three transportation groups (those who: bike/walk, take public transit or drive) and asks them how they typically feel on a normal Monday morning: happy/excited, angry/irritated, or sleepy. Data from his survey on 200 participants are presented below.
Happy Angry sleepy Total
Bike/Walk 20 7 13 40
Public transit 13 5 42 7
Drive 17 18 65 100
Total 50 30 120 200
You would like to test his question of whether or not there is any association between normal method of transportation taken to work and reported mood at the beginning of a typical Monday morning. Calculate a two variable chi-square test using an alpha (α) level of 0.01.
You will use the information above to complete the question parts below for a two variable chi-square test.
Part A: Which of the following represents the appropriate null hypothesis(H0), given your research question of interest?
Part B: Which of the following represents the appropriate alternative hypothesis (H1), given your research question of interest?
Part C: What is your degrees of freedom (df)?
Part D: What is the critical chi-square value (from the Chi-square table) appropriate for your test, testing at an alpha level (α) of 0.01?
Part E: What is your calculated chi-square statistic?
Part F: What is your decision about the null hypothesis based on your test results?
Answers
Answer:
Check the explanation
Step-by-step explanation:
Kindly check the attached image below to see the step by step explanation to the question above.
Find the value of P(7,2)
Answers
Answer: 42
Step-by-step explanation:Its a permutation problem!
(8.2×10^2)+(3.41×10^-1)
Answers
Answer:
820.341
Step-by-step explanation:
(8.2×10^2)+(3.41×10^-1)=
(8.2×100)+(3.41×0.1)=
820+0.341=
820.341
Answer:820.341
Step-by-step explanation:
(8.2x10^2)+(3.41x10^-1)
(8.2x10x10)+(3.41 x 1/10)
(8.2x100)+(3.41x0.1)
820+0.341=820.341
What’s the correct answer?
Answers
Answer:
B.
Step-by-step explanation:
Answer:b
Step-by-step explanation:you need to add both
How to convert 100 inches per minute to feet per minute?
Answers
Answer:
8 1/3 ft/min
Step-by-step explanation:
12 inches = 1 foot
100 inches = 8 1/3 feet
Evaluate using factors:(7.62)² - (2.38)²?
Answers
Answer:
52.4.
Step-by-step explanation:
This is the difference of 2 squares:
a^2 - b^2 = (a - b)(a + b)
(7.62^2 - (2.38)^2
= (7.62 - 2.38)(7.62 + 2.38)
= 5.24 * 10
= 52.4
Answer:
52.4
Step-by-step explanation:
a²-b² = (a-b)(a+b)
Similarly,
(7.62)²-(2.38)²
= (7.62-2.38)(7.62+2.38)
= (5.24)(10)
= 52.4
Find the digit in the tenths place of 25.391
Answers
Answer:
Step-by-step explanation: The digit in the tenths place will be 1 place to the right of the decimal point.
So in this problem, the digit in the tenths place is 3.
In a class of 28 students, 12 earned an A on the final exam, 6 earned a B, 4 earned a C, and the remaining students failed. Based on these results, what is the experimental probability that a student will not earn an A or a B?
Answers
Answer:
5/14 ≈ 35.7%
Step-by-step explanation:
(12 +6) = 18 of the 28 students earned an A or a B. So, the experimental probability that a student did not earn that grade is ...
p(<B) = (28 -18)/28 = 10/28
p(<B) = 5/14 ≈ 35.7%
how many times does 8 go into 11
Answers
Answer:
8 goes into 11 one time with a remainder of 3
Look at recent question
Answers
Answer:
ok was it college math if so the I don't know
The area of a rectangular swimming pool is 360 square feet. If the length of the pool is 9 feet more than it’s width, find the length of the pool
Answers
Answer:
The length of the pool is [tex]L=24\:ft[/tex].
Step-by-step explanation:
The area of a rectangle is given by [tex]A=L\cdot W[/tex] where L is the length, W is the width.
If the length of the pool is 9 feet more than it’s width, this means that [tex]L=9+W[/tex]
We know that the area of a rectangular swimming pool is 360 [tex]\:ft^2[/tex]. So we simple insert the length ([tex]L=9+W[/tex]), width ( [tex]W[/tex]) and area (360) into the formula and solve the resulting equation.
[tex]360=\left(9+W\right)W\\\\360=9W+W^2\\\\9W+W^2=360\\\\W^2+9W-360=0[/tex]
[tex]\mathrm{Solve\:with\:the\:quadratic\:formula}\\\\\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}\\\\x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex][tex]\mathrm{For\:}\quad a=1,\:b=9,\:c=-360:\quad W_{1,\:2}=\frac{-9\pm \sqrt{9^2-4\cdot \:1\left(-360\right)}}{2\cdot \:1}\\\\W=\frac{-9+\sqrt{9^2-4\cdot \:1\left(-360\right)}}{2\cdot \:1}= 15[/tex]
[tex]W=\frac{-9-\sqrt{9^2-4\cdot \:1\left(-360\right)}}{2\cdot \:1}= -24[/tex]
A length cannot be negative. So [tex]W=15[/tex] and the length of the pool is [tex]L=9+15=24\:ft[/tex]
U(x)=x^2+9 and w(x)=sqrt x+8. Find (wu)(8) and (uw)(8)
Answers
Answer:
¿cual es la influencia que tiene la revolución cubana en el surgimiento de grupos armados en Colombia?
Step-by-step explanation:
Paul owns a mobile wood-fired pizza oven operation. A couple of his clients complained about his dough at a recent catering, so he changed his dough to a newer product. Using the old dough, there were 6 complaints out of 385 pizzas. With the new dough, there were 16 complaints out of 340 pizzas. Let p 1 be the proportion of customer complaints with the old dough and p 2 be the proportion of customer complaints with the new dough. State the competing hypotheses to determine if the proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough g
Answers
Answer:
[tex]z=\frac{0.0156-0.0471}{\sqrt{0.0303(1-0.0303)(\frac{1}{385}+\frac{1}{340})}}=-2.469[/tex]
Now we can calculate the p value with this probability:
[tex]p_v =P(Z<-2.469)= 0.0068[/tex]
Since the p value is a very low value and using any significance level 5% or 10% we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough.
Step-by-step explanation:
Information provided
[tex]X_{1}=6[/tex] represent the complaints with the old dough
[tex]X_{2}=16[/tex] represent the complaints with the new dough
[tex]n_{1}=385[/tex] sample 1 selected
[tex]n_{2}=340[/tex] sample 2 selected
[tex]p_{1}=\frac{6}{385}=0.0156[/tex] represent the proportion of complaints with the old dough
[tex]p_{2}=\frac{16}{340}=0.0471[/tex] represent the proportion of complaints with the new dough
[tex]\hat p[/tex] represent the pooled estimate of p
z would represent the statistic
[tex]p_v[/tex] represent the value
Hypothesis to test
We want to verify if the proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough, the system of hypothesis would be:
Null hypothesis:[tex]p_{1} \geq p_{2}[/tex]
Alternative hypothesis:[tex]p_{1} < p_{2}[/tex]
The statitsic is given by:
[tex]z=\frac{p_{1}-p_{2}}{\sqrt{\hat p (1-\hat p)(\frac{1}{n_{1}}+\frac{1}{n_{2}})}}[/tex] (1)
Where [tex]\hat p=\frac{X_{1}+X_{2}}{n_{1}+n_{2}}=\frac{6+16}{385+340}=0.0303[/tex]
Replacing the info provided we got:
[tex]z=\frac{0.0156-0.0471}{\sqrt{0.0303(1-0.0303)(\frac{1}{385}+\frac{1}{340})}}=-2.469[/tex]
Now we can calculate the p value with this probability:
[tex]p_v =P(Z<-2.469)= 0.0068[/tex]
Since the p value is a very low value and using any significance level 5% or 10% we have enough evidence to reject the null hypothesis and we can conclude that the true proportion of customer complaints using the old dough is less than the proportion of customer complaints using the new dough.
The angle θ lies in Quadrant III . cosθ=−1/6 What is tanθ ?
Answers
With θ in quadrant III, we expect to have both cosθ and sinθ negative. Then from the Pythagorean identity, we get
[tex]\cos^2\theta+\sin^2\theta=1\implies\sin\theta=-\sqrt{1-\cos^2\theta}=-\dfrac{\sqrt{35}}6[/tex]
Then from the definition of tangent, that is
tanθ = sinθ / cosθ
we get
[tex]\tan\theta=\dfrac{-\frac{\sqrt{35}}6}{-\frac16}=\boxed{\sqrt{35}}[/tex]
The value of [tex]\tan \theta[/tex] is required.
The required value in quadrant three is [tex]\tan\theta=\sqrt{35}[/tex]
[tex]\cos \theta=-\dfrac{1}{6}[/tex]
We have the identity
[tex]\tan \theta=\dfrac{\sqrt{1-\cos^2\theta}}{\cos \theta}\\\Rightarrow \tan\theta=\dfrac{\sqrt{1-\left(-\dfrac{1}{6}\right)^2}}{-\dfrac{1}{6}}\\\Rightarrow \tan \theta=\dfrac{\sqrt{\dfrac{35}{36}}}{-\dfrac{1}{6}}\\\Rightarrow \tan\theta=\pm\sqrt{35}\times -1\\\Rightarrow \tan\theta=\pm\sqrt{35}[/tex]
The required value in quadrant three is [tex]\tan\theta=\sqrt{35}[/tex]
Learn more:
https://brainly.com/question/11694897
What is an equation of the line that passes through the points (-4, 1) and (4, -1)?
Answers
Answer:
y = 1/4x
Step-by-step explanation:
image attached
A 24 ounce box of cornflakes costs $4.59 the question is find the unit rate off the nearest cent per ounce. Compare.
Answers
Answer$5.22
Step-by-step explanation:
Find the area of this semi-circle with diameter, d = 12cm.
Give your answer as an expression in terms of π.
Answers
Answer:
6pi
Step-by-step explanation:
Area of a circle = 2pi*r
d = 12
r = d/2
r=6
Area of semicircle = (2pi *r)/2 = pi*r
pi*6 = 6pi
Answer:18π cm^2
Step-by-step explanation:
diameter=12
Radius=diameter ➗ 2
Radius=12 ➗ 2
Radius=6
Area of semicircle=0.5 x π x radius x radius
Area of semicircle=0.5xπx6x6
Area of semicircle=18π cm^2
