a) Suppose that a large mixing tank initially holds 300 gallons of water in which 50 pounds ofsalt have been dissolved. Pure water is pumped into the tank at a rate of 3gal/min, and whenthe solution is well stirred, it is then pumped out at the same rate. Determine a differentialequation for the amount of salt, , in the tank at time .

Answers

Answer 1

Answer:

x  =  50*e∧ -t/100

Step-by-step explanation:

We assume:

1.-That the volume of mixing is always constant 300 gallons

2.-The mixing is instantaneous

Δ(x)t   =  Amount in  - Amount out

Amount  =  rate * concentration*Δt

Amount in  =  3 gallons/ min * 0  =  0

Amount out  = 3 gallons/min *  x/ 300*Δt

Then

Δ(x)t/Δt  =  - 3*x/300    Δt⇒0   lim Δ(x)t/Δt  =  dx/dt

dx/dt  =  - x/100

dx/ x  =  - dt/100

A linear first degree differential equation

∫ dx/x   =  ∫ - dt/100

Ln x  =  - t/100  +  C

initial conditions to determine C

t= 0     x =  50 pounds

Ln (50) = 0/100 * C

C =  ln (50)

Then final solution is:

Ln x  =  - t/100  + Ln(50)   or

e∧ Lnx   =  e ∧ ( -t/100 + Ln(50))

x  =  e∧ ( -t/100) * e∧Ln(50)

x  = e∧ ( -t/100) * 50

x  =  50*e∧ -t/100


Related Questions

3 3/4 - 1 2/3 iready

Answers

Answer: 2 1/12

Step-by-step explanation:

Find the volume of the cone.
Either enter an exact answer in terms of \piπpi or use 3.143.143, point, 14 for \piπpi.

Answers

Right circular cone

Solve for volume

V≈37.7

r Radius

2

h Height

9

V=πr2h3=π·22·93≈37.69911

Answer:

37.7

Step-by-step explanation:

One consequence of the popularity of the Internet is that it is thought to reduce television watching. Suppose that a random sample of 35 individuals who consider themselves to be avid Internet users results in a mean time of 1.99 hours watching television on a weekday.

Required:
Determine the likelihood of obtaining a sample mean of 1.99 hours or less from a population whose mean is presumed to be 2.45 hours.

Answers

Answer:

Step-by-step explanation:


54, 46, 43, 40, 34, 20, 28, 50, 45, 42, 38. What is the mean?

Answers

Answer:

40

Step-by-step explanation:

Average = Sum / Count

= 440 / 11

= 40

Answer:

Step-by-step explanation:

The mean is the total number to add .them you divide the total for of value ,

in this case     your add   al number 54+46+43+40+34+20+28+50+45+42=382

   in /     382/11 = 34.727272... = 35

a bag contains 13 1/2 cups of sugar. a serving of sugar 3/4 cup. how many total servings are in the bag?

Answers

Answer:

18 servings

Step-by-step explanation:

13 1/2 divided by 3/4

13.5/.75=18

Tim left $3000 in an account that
paid 8% interest compounded
annually. How much interest did
Tim earn in 2 years?

Answers

Answer:

499.20

Step-by-step explanation:

3000

x.08.    Interest rate

=   240 interest after one year

+. 3000

=3,240 principal plus interest after one year

x. .08

  259.20. Interest in year two

+ 240.00 interest in year one

= 499.20. Interest earned in 2 years

Click on the graph below to create a triangle with vertices at the following points.
(-5,0), (-5,9), (0,9)

Answers

Well, since you didn’t upload the picture we can’t really show you the points, but all you do, is for the first one you go 5 up on the graph, and 0 to the side. and then just keep going!

Insurance company records indicate that 12% of all teenage drivers have been ticketed for speeding and 9% for going through a red light. If 4% have been ticketed for both, what is the probability that a teenage driver has been issued a ticket for speeding if they ran a red light?

Answers

Answer:

four out of 100 (4%)

Step-by-step explanation:

log (w2+21) - log (10)

Answers

Answer:

[tex]w =7\ or\ w =3[/tex]

Step-by-step explanation:

Given

The right question is:

[tex]\log(w^2+ 21) = \log(10w)[/tex]

Required

Solve for w

[tex]\log(w^2+ 21) = \log(10w)[/tex]

Cancel log on both sides

[tex]w^2+ 21 = 10w[/tex]

Equate to 0

[tex]w^2 - 10w+ 21 = 0[/tex]

Split

[tex]w^2 - 3w - 7w+ 21 = 0[/tex]

Factorize

[tex]w(w - 3) - 7(w-3) = 0[/tex]

Factor out w - 3

[tex](w - 7)(w-3) = 0[/tex]

Solve for w

[tex]w - 7 = 0\ and\ w - 3 = 0[/tex]

[tex]w =7\ or\ w =3[/tex]

amplitude of h(x)=-4sin(2x-7)+3

Answers

Answer:

Use the form asin(bx−c)+d to find the variables used to find the amplitude, period, phase shift, and vertical shift.

a=−4

b=2

c=7

d=3

Find the amplitude |a| .

Amplitude: 4

Find the period using the formula 2[tex]\pi[/tex] / |b|.

Find the phase shift using the formula c / b .

Phase Shift: 7/2

List the properties of the trigonometric function.

Amplitude: 4

Period: [tex]\pi[/tex]

Phase Shift: 7/2 (7/2 to the right)

Vertical Shift: 3

Step-by-step explanation:

URGENT WILL MAKE BRANLIEST AND POINTS

Answers

Answer:

first one is c and second one is acute

Step-by-step explanation:

acute angle which is 45

Answer:

Q.11 x=11

Q.12 complementary angles

Q.10 142 degrees

Use the information to answer the question.
There are 2.54 centimeters in 1 inch. There are 100 centimeters in 1 meter.
To the nearest meter, how many meters are in 158 inches? Enter the answer in the box.
meters

Answers

There are about 4 because the final answer will be 3.81

Write the expression with your terms. 10x-2x

Answers

Answer:

Step-by-step explanation: first you do 10 minus 2 you get 8

-90 + x = 180
What is the answer ?

Answers

Answer:

x = 270

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Step-by-step explanation:

Step 1: Define

Identify

-90 + x = 180

Step 2: Solve for x

[Addition Property of Equality] Add 90 on both sides:                                  x = 270

Answer:

x = 270

Step-by-step explanation:

- 90 + x = 180

Add 90 to each side of the equation.

- 90 + 90 + x = 180 + 90

Combine like terms.

x = 270

A rectangle with a length of 5cm and width of 2cm is cut diagonally. What is the area of one of the triangles formed?

PLEASE LEAVE STEPS!

Answers

Answer:

5cm^2

Step-by-step explanation:

l=5 w=2

Area= 5×2

=10cm^2

Area of triangle= 10/2

=5cm^2

Jared has some birds and dogs in his backyard. He counts a total of 12 heads and 30 legs. How many birds and dogs are in Jared's garden?

Answers

Answer:

12, because both dogs and birds only have 12 heads

12 Jared has 12 birds


4. For his garden, Clay has a mixture of 12
white corn seeds, 24 yellow corn seeds, and
16 bicolor corn seeds. If he reaches for a
seed without looking, what is the probability
that Clay will plant a bicolor corn seed first?

Answers

Answer:

I believe about 30.8%

Two houses on the same side of the street have house numbers that are consecutive
even integers. The sum of the integers is 58. What are the two house numbers?

Answers

Answer:

28 and 30

Step-by-step explanation:

'x' = 1st consecutive #

'x+2' = 2nd consecutive #

x + x+2 = 58

2x + 2 = 58

2x = 56

x = 28

x+2 = 30

Plz help me well mark brainliest if correct.....?

Answers

Answer:

B. 8 x 12

Step-by-step explanation:

First of all, it has an area of 96

So lets find the multiplication pair that equals 96.

10 x 10 = 100        NO

6 x 16 = 96           YES

8 x 12 = 96           YES

Now we have two equations: 8 x 12 and 6 x 16

Perimeter of 40 means:

2(a+b) = 40

Lets input the two equations:

2(8+12) = 2 x 20 = 40

2(6+16) = 2 x 22 = 44

So the dimensions that works is 8 x 12

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

plwaseeee helppp!! plelalslsllslslz

Answers

Answer:

45 degrees

opposite angles are the same so

30+30=60

105+105=210

210+60=270

360-270=90

but since we have 2 angles we divide it by 2

so angle 1 is 45 degrees

hope it helps :)

1) Which division expression is the given figure below modeling?
10 points
A) 2/3=4
B) 4 = 2/3
C) 4x2/3
D) 2/3 x 4
Figure to use with Problem #1​

Answers

4/8=32 in think that’s the answer

What is the real number of ∞?

Answers

Answer:

Infinity is not a real number, its an idea.

Step-by-step explanation:

An idea of something without an end. Infinity cannot be measured. Even these faraway galaxies can't compete with infinity.

please help!!! urgently i dont get this

Answers

Answer:

4

Step-by-step explanation:

Brie saves her $5 weekly allowance for several weeks and uses the money to buy a game for $32. She has $8 remaining. For how many weeks did Brie save her allowance

Answers

Answer:

8 weeks

Step-by-step explanation:

hope this helps!!

What angle is this
A. Vertical
B. Adjacent
C. Supplementary
D. Complementary
Can be multiple answers ​

Answers

Answer:

A and D

Step-by-step explanation:

I already know the answer I just need someone to explain step by step how to solve it. I need to know the process ​

Answers

Step-by-step explanation:

First Multiply two of the numbers, for example, 15 x 6 and then multiply that by the last number, 90 x 13 and thats your answer. Hope it helps!


$7.36 + 2.23 + 4.86

Answers

The answer for 7.36 + 2.23 + 4.86 is 14.35

$14.45 ps mark me brainless

The process that produces Sonora Bars (a type of candy) is intended to produce bars with a mean weight of 56 gm. The process standard deviation is known to be 0.77 gm. A random sample of 49 candy bars yields a mean weight of 55.82 gm.
(a) State the hypotheses to test whether the mean is smaller than it is supposed to be.
(b) What is the test statistic?
(c) At α = .05, what is the critical value for this test?
(d) What is your conclusion?

Answers

Answer:

|z(s)| <  |z(c)|

Then  z(s) is in the acceptance region we accept H₀.

We don´t have evidence to support that candy bar mean weight is below 56 gm

Step-by-step explanation:

Goal mean     μ  =  56 gm

standard deviation   σ  = 0,77

From random sample:

mean    x  = 55,82

sample size  n  = 49

We assume a normal distribution ( is a manufacturing controlled process)

a) Hypothesis Test:

Null Hypothesis                         H₀          x   =  μ

Alternative Hypothesis             Hₐ           x  <  μ

Alternative hypothesis is telling us that the test is a one-tail test to the left

as n > 30 we use the normal distribution.

b)  z(s) =  ( x  -  μ  ) / σ / √n

z(s)  =  55.82  -  56 ) * 7 / 0,77

z(s)  = 0,18*7/0,77

z(s)  =  - 1.6363

c)  if  significance level is α  = 0.05  then  α/2 = 0,025

Then from  z table, z  score for  0,025     z(c) = -1.96

d)  Comparing  z(c)  and z(s) modules

|z(s)| <  |z(c)|

Then  z(s) is in the acceptance region we accept H₀.

We don´t have evidence to support that candy bar mean weight is below 56 gm

( NEED HELP ASAP )
Drews fish tank measures 32 cm by 22 cm by 26 cm. He pours 20 liters of water into it, and some overflows the tank. Find the volume of water, in milliliters, that overflows.

Answers

Answer:

the answer to the question is 1,696

Step-by-step explanation:im sorry i dont have an exsplanation but its that trust me

rewrite 1/4 with the denominator 24​

Answers

Answer:

6/24.

Step-by-step explanation:

24 = 4 * 6 so we:

multiply by 6/6:

1 * 6

------  =    6 / 24.

4 * 6

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