A tank initially has 300 gallons of a solution that contains 50 lb. of dissolved salt. A brine solution with a concentration of 2lb of salt/gallon is admitted into the tank at a rate of 6 gallons per minute. The well-stirred solution is drained at the same rate. How long will it take for the tank to have 100 lb. of dissolved salt

Answers

Answer 1

Let s(t) be the amount of salt in the tank at time t. Then s(0) = 50 lb.

Salt flows into the tank at a rate of

(2 gal/min) (6 lb/gal) = 12 lb/min

and flows out at a rate of

(2 gal/min) (s(t)/300 lb/gal) = s(t)/150 lb/min

so that the net rate at which salt is exchanged through the tank is

ds(t)/dt = 12 - s(t)/150 … (lb/min)

Solve for s(t). The DE is separable, so we have

ds/dt = 12 - s/150

150 ds/dt = 1800 - s

150/(1800 - s) ds = dt

Integrate both sides to get

-150 ln|1800 - s| = t + C

Solve for s :

ln|1800 - s| = -t/150 + C

1800 - s = exp(-t/150 + C )

1800 - s = C exp(-t/150)

s = 1800 - C exp(-t/150)

Now given that s(0) = 50, we solve for C :

50 = 1800 - C exp(-0/150)

50 = 1800 - C

C = 1750

Then the amount of salt in the tank at any time t ≥ 0 is

s(t) = 1800 - 1750 exp(-t/150)

To find the time it takes for the tank to hold 100 lb of salt, solve for t in

100 = 1800 - 1750 exp(-t/150)

1700 = 1750 exp(-t/150)

34/35 = exp(-t/150)

ln(34/35) = -t/150

t = -150 ln(34/35) ≈ 4.348

So it would take approximately 4.348 minutes.

By the way, we didn't have to solve for s(t), we could have instead stopped with

-150 ln|1800 - s| = t + C

Solve for C - this C is not the same as the one we found using the other method. s(0) = 50, so

-150 ln|1800 - 50| = 0 + C

C = -150 ln|1750|

==>   t = 150 ln(1750) - 150 ln|1800 - s|

Then s(t) = 100 lb when

t = 150 ln(1750) - 150 ln(1700)

t = 150 ln(1750/1700)

t = 150 ln(35/34)

t ≈ 4.348


Related Questions

find the measure of the missing side in the right triangle

Answers

12.2 ft because the Pythagorean theorem ( a^2 +b^2 = c^2) given this c is square root of 149 which is 12.2

Answer:

[tex]12.2\text{ ft}[/tex]

Step-by-step explanation:

In any right triangles, the Pythagorean Theorem states that the sum of the squares of both legs is equal to the hypotenuse squared ([tex]a^2+b^2=c^2[/tex], where [tex]c[/tex] is the hypotenuse, or longest side).

In this case, the length we're solving for is the hypotenuse of the triangle and the two legs of the triangle are 7 and 10. Therefore, we have:

[tex]7^2+10^2=c^2,\\49+100=c^2,\\c^2=149,\\c=\sqrt{149},\\c\approx \boxed{12.2\text{ ft}}[/tex]

Find the missing measure if a and b are the legs of the right triangle and c is the hypotenuse, with a = 11 and c =18.

Answers

Answer:

[tex]\sqrt{203}[/tex]

Step-by-step explanation:

1. [tex]11^{2} + b^{2} = 18^{2}[/tex]

2. [tex]b^{2} =203[/tex]

3. b = [tex]\sqrt{203}[/tex]

Can't be simplified.

Answer 16

Step-by-step explanation:

Can someone help me with these two

Answers

Answer:

10. D. 1 / 216

11. B. - ( 8^0 )

Step-by-step explanation:

10.

6^5 x 6^-8

= 6^( 5 - 8 )

= 6^-3

= 1 / 6^3

= 1 / 216

11.

- ( 8^0 )

= - 1

- 1 < 0

Instructions: Find the missing side lengths. Leave your answers as radicals in simplest
form.
60°
22

Answers

Answer:

A. x = 11√3

B. y = 11

Step-by-step explanation:

A. Determination of the value of x.

Angle θ = 60°

Hypothenus = 22

Opposite = x =?

We can obtain the value of x by using sine ratio as illustrated below:

Sine θ = Opposite / Hypothenus

Sine 60 = x / 22

√3/2 = x / 22

Cross multiply

2 * x = 22√3

Divide both side by 2

x = (22√3) / 2

x = 11√3

B. Determination of the value of y.

Angle θ = 60°

Hypothenus = 22

Adjacent = y =?

We can obtain the value of y by using cosine ratio as illustrated below:

Cos θ = Adjacent / Hypothenus

Cos 60 = y / 22

½ = y / 22

Cross multiply

y = ½ × 22

y = 11

grade 6 math any one willing to answer ONE question??? pls answer due in 30 minutes 10 points and brainliest

Answers

Answer:

2 and 5 is the gcf and lcm is 360

Step-by-step explanation:

Answer:

GCF is 120 and LCM is 1440

Step-by-step explanation:

-To find the GCF, take a look at the orange section(the intersection) and multiply all the numbers in there. 2^3x3x5=120

-To find the LCM, multiply all the numbers in the entire venn diagram. 2^5x3^2x5=1440

Help me pleaseeeeeeeee

Answers

Get y by itself
6y= -3x-18
Divide by 6
Y= -3x/6 -18
Slope is -1/2.
Line perpendicular is 2/1 or 2

Which expression is equivalent to 3(m - 3) + 4?
3m + 1
O
3m-
5
O
3m + 13
O 3m - 3

Answers

Answer:

3m -5

Step-by-step explanation:

3(m - 3) + 4

Distribute

3m -9 +4

Combine like terms

3m -5

Answer:

3m - 5

Step-by-step explanation:

3(m - 3) + 4

3m - 9 + 4

3m - 5

if you is equals to 1 2 3 4 5 6 7 8 9 10 and a is equal to 1267 b is equals to 2 3 5 6 and C is equals to 4 5 6 7 then verify that a union B complement is equal to a complement intersection b complement​

Answers

This should be the answer

Finish the following table for the given function with x as the independent variable

Answers

Answer:

hi?

Step-by-step explanation:

why e=mc2?why not e=mc3?​

Answers

Step-by-step explanation:

E = mc^2

E is Energy

M is Mass

C is Speed of light

This is Albert Einstein's General theory of relativity.

According to The principle of homogeneity,

E = mc^2 is dimensionally correct.

E = mc2 Explained. E = mc2. It's the world's most famous equation, but what does it really mean? "Energy equals mass times the speed of light squared." On the most basic level, the equation says that energy and mass (matter) are interchangeable; they are different forms of the same thing.

A student skipped a step when she tried to convert 18 hours into seconds, and she got the following incorrect result:

Answers

Answer:

She's, "HOT"!

Step-by-step explanation:

Which coordinate pair identifies a point in the third quadrant of the coordinate plane? A) (0, 5) B) (1, −5) C) (1, 5) D) (−1, −2)

(IF YOU USE THIS QUESTION FOR POINTS I WILL REPORT YOU)
(NVM IT'S (-1,-2)

Answers

Answer:

Me need my points :D                    

Step-by-step explanation:

I don't have time to do this before my class, could someone help? Thanks so much

Answers

Answer:

AD=27

Step-by-step explanation:

please anyone help no wrong asnwers plss ------

Answers

(-1/4, 2 1/4)

I graphed the equations and that was the other solution. See the attached photo to view the graph.

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

simplify.
[(1+5)⋅2−5]⋅2

Answers

Answer:

14

Step-by-step explanation:

[(1+5)⋅2−5]⋅2

[(6)⋅2−5]⋅2

[12−5]⋅2

[7]⋅2

14

Step-by-step explanation:

[6.2-5].2

[12-5].2

7.2

14 answer

Akili has two tests next week. The probability that he will pass the first test, science, is 34 . How he does on that test affects how he will do on his math test. If he passes science, then the probability that he will also pass the math test is 45; otherwise, the probability is only 13 that he will pass the math test. If the probability he passes exactly one test can be expressed as mn for two relatively prime positive integers m and n, what is m n

Answers

Answer:

Following are solutions to the given question:

Step-by-step explanation:

First-test probability: [tex]\frac{3}{4}[/tex]

A person's chances of passing a second test are reduced if he fails the first test: [tex]\frac{1}{3}[/tex]

However, the chance of failing the first test is 1 in 4. As just a result, the probability of these events is low.

[tex]\to \frac{1}{4}\times \frac{1}{3}=\frac{1}{12}\\\\\to \frac{3}{4} + \frac{1}{12} = \frac{9+1}{12} = \frac{10}{12} = \frac{5}{6}[/tex]

One of the other.

Amy flips a coin and rolls a standard number cube. Find the probability that the coin will show heads and the cube will show one.
Write the probability as a fraction in the simplest form.

Answers

Answer:

1/12

Step-by-step explanation:

Mathematically, when a coin is flipped, we either get a head or a tail

These are equal probabilities of 1/2 each

So to show heads, we have a probability of 1/2

In a standard cube, there are 6 numbers (1-6)

now, we have only 1 one

the probability of it showing up would be 1/6

So the probability of both occurring would be the product

So we have this as;

1/6 * 1/2 = 1/12

When creating lines of best fit, do you believe that estimation by inspection of the equation is best or do you think it should be determined exactly? In what situations would it be best to use one over the other?

Answers

Answer:

Estimation by inspection is better than trying to determine the line of best fit exactly

i) For a scatter plot : The use of estimation by inspection

ii) For a straight line graph : The exact determination method

Step-by-step explanation:

To create lines of best fit the estimation by inspection is better than trying to determine the line of best fit exactly .

This is because line of best fit only shows the trend of the data and in most cases it doesn't have to start from origin.

Scenarios :

i) For a scatter plot : The use of estimation by inspection

ii) For a straight line graph : The exact determination method

PLZZZZ HELPPPP… IF NOT 100% SURE PLZZ DONT ANSWER! BRAINLIEST TO FIRST AND CORRECT ANSWER!

Answers

Answer is 7/10 because you need the same denominator so you multiply 1/2 by 5 both top and bottom then multiply 1/5 by 2 both top and bottom and then add numerator

Answer:

7/10

Step-by-step explanation:

½ of a cup of cheddar=½ x 1=½

⅕ of a cup of parmesan=⅕ x 1=⅕

all cheese used=½ + ⅕= 7/10

Heidi solved the equation
3(x + 4) + 2 = 2 + 5(x – 4). Her steps are below:
3x + 12 + 2 = 2 + 5x – 20
3x + 14 = 5x – 18
14 = 2x – 18
32 = 2x
16 = x

Answers

Answer:

The answer is correct

Step-by-step explanation:

3(x + 4) + 2 = 2 + 5(x – 4)

3x + 12 + 2 = 2 + 5x - 20

3x + 14 = 5x - 18

-2x = -32

x = 16

need help with a p e x !!!

Answers

i think B is the right answer

Can someone help with this please

Answers

9514 1404 393

Answer:

  a) (1.75 +1.00d)/4 < (3.50 +1.50d)/5

  b) 3.70

Step-by-step explanation:

a) You want ...

   classic cost < XL cost

Using the given expressions for the costs, the inequality is ...

  (1.75 +1.00d)/4 < (3.50 +1.50d)/5

__

b) For a 10-mile ride, the XL cost is ...

  (3.50 +1.50(10))/5 = (3.50 +15.00)/5 = 18.50/5 = 3.70

Each passenger in a group of 5 friends pays $3.70 for the 10-mile ride.

_____

Additional comment

Each expression can be divided out to give ...

  classic cost per person = $0.4375 +0.25d

  XL cost per person = $0.70 +0.30d

Comparing these, we see there is no positive value of d that will make the XL cost per person be less than the classic cost per person. Both the initial fee and the per-mile cost are lower for the classic.

HELPASAP
A circle with an arc length of ____ centimeters is intercepted by a central angle of 3pi/4 radians has a radius of ____ centimeters.

1st Blank Options: 12pi, 4pi, 2pi
2nd Blank Options: 3, 16, 24

Answers

Answer:

add an attachm3nt to make iy clear

What is the solution to this system of equations?
2x+y = 6
- - x - y = 2
0
0
(1, -1)
(0,8)
infinitely many solutions
no solution

Answers

Answer:

Step-by-step explanation:

{ 2/3 x+y=6

+

{ -2/3x-y=2

= 0=6

Hence,no solution.

Jane spent 3 hours exploring a mountain with a dirt bike. First, she rode 48 miles uphill. After she reached the peak she rode for 15 miles along the summit. While going uphill, she went 5 mph slower than when she was on the summit. What was her rate along the summit?

Answers

Answer: [tex]25\ mph[/tex]

Step-by-step explanation:

Given

Jane took 3 hours

First she rode 48 miles with let say with [tex]x[/tex] mph

then she rode 15 miles with speed [tex](x+5)[/tex] mph

Equate the time in each ride and equate it to total time

[tex]\Rightarrow 3=\dfrac{48}{x}+\dfrac{15}{x+5}\\\\\Rightarrow 3x(x+5)=48(x+5)+15x\\\\\Rightarrow 3x^2+15x=48x+48\times 5+15x\\\\\Rightarrow 3x^2-48x-240=0\\\\\Rightarrow (x-20)(x+4)=0\\\\\text{Neglecting the negative value as speed cannot be negative}\\\\\Rightarrow x=20\ mph[/tex]

So, her along the summit is [tex]x+5=25\ mph[/tex]

im doing a exam please help me fast

Seven guests are arriving for dinner. How many possible orders can they arrive in?

5,040!

7!

5!

49!

Answers

Answer:

7!

Hope it is helpful

please help with this on the images

Answers

Answer:

52%

7 more

Step-by-step explanation:

There are 5*5 = 25 boxes in the grid

13 are shaded

13/25 = 13/25 *4/4 = 52/100 = 52% are shaded

We want 80% shaded

80/100

Divide top and bottom by 4

20/25

We need 20 shaded and have 13 shaded

20-13 = 7

We need to shaded 7 more

52%

The grid has 25 squares and 13 are colored.

This translates into the fraction 13/25.

This can become a decimal and become .52

.52 in percentage form is 52%

Hope this helps! Please make me the brainliest, it’s not necessary but appreciated, I put a lot of effort and research into my answers. Have a good day, stay safe and stay healthy.

What is the height of the cylinder?

Answers

Answer:

h = 7 inches

Step-by-step explanation:

WHERE ARE THE EXPERTS AND ACE!!!!!!! I NEED HELP PLS SHARE YO SMARTNESS!!!!! WILL GIVE BRAINLIEST AND RATE AND VOTE!!! EASY IM JUST NOT SMART

PLEASE GIVE EXPLANATION

Answers

Answer:

Ellipse

[tex]✔ \: \: : { \sf{ {x}^{2} + {y}^{2} = 1 }}[/tex]

Step-by-step explanation:

[tex]{ \sf{circle : \: {x}^{2} + {y}^{2} + 2gx + 2fy + c = 0}} \\ { \sf{parabola : \: {y}^{2} = 4ax }} \\ { \sf{hyperbola : \: {x}^{2} - {y}^{2} = 1 }}[/tex]

Sohanlal is a gardener. He is paid ₹160 daily, find how much money will he
get in the month of September?

Answers

Answer:

Give some examples of source documents.

➢  Define an account. What are the two  forms of account posting illustrated in the chapter?➢  What is meant by the term double-entry procedure, or duality?

➢  Describe how you would determine the balance of a T-account.

➢  Define debit and credit.

➢  Do you think this double entry accounting system makes sense? Can you conceive of other possible methods for recording changes in accounts?

➢  Which of the steps in the accounting cycle are performed throughout the accounting period?

➢  What is the purpose of the Dividends account and how is it increased?

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