Suppose that a large mixing tank initially holds 500 gallons of water in which 60 pounds of salt have been dissolved. Pure water is pumped into the tank at a rate of 5 gal/min, and when the solution is well stirred, it is then pumped out at the same rate. Determine a differential equation for the amount of salt A(t) in the tank at time t > 0. What is A(0)

Answers

Answer 1

Answer:

The answer is "[tex]\frac{dA}{dt}+ \frac{A}{100}=0\ \ and \ \A(0)=60[/tex]"

Step-by-step explanation:

[tex]A(0)=60\\\\ \frac{dA}{dt}=Rin-Rout\\\\Rin=0\\\\Rout=\frac{A(t)}{500} \times (5)\\\\ =\frac{A}{100}\\\\ so,\\\\\frac{dA}{dt}=Rin-Rout\\\\\frac{dA}{dt}=0- \frac{A}{100}\\\\\frac{dA}{dt}+ \frac{A}{100}=0\\\\A(0)=60[/tex]


Related Questions

Find the 8th term of the geometric sequence 7, 28, 112, ...

Answers

I got 114688 by going up x4



The distance from Kevin's home to his school is 2 kilometers. Adrian lives 750
meters from the same school. How much closer does Adrian live to school than
Kevin?
1>) 250 meters
1>) 550 meters
» 1,250 meters
2,750 meters

Answers

Answer:

see my explanation!!

Step-by-step explanation:

2000-750=1250m

NEED HELP ASAP! Translate into symbols

1. Fifteen more than a number

2. Decreased the quotient of forty eight and 6 by two is six

Answers

Answer:

x-6+6(6+6+6)X I am a pro boiiiiii

15 < x

6 = (48/6) - 2

Molly hit 6 home runs. Molly hit 3 fewer home runs than Jerry. How many home runs did Jerry hit?

Answers

Answer:

9

Step-by-step explanation:

jerry-3 = molly

molly = 6

jerry - 3 = 6

jerry = 9

Answer:

9

Step-by-step explanation:

Remember Molly hit 6 home runs

and3 less than Jerry

that means the equation is

6 + 3 = x

and as you know

6 + 3 = 9

Mark as Brainliest

please help will give brainliest

Answers

Answer:

B

Step-by-step explanation:

There are thirteen shirts in your closet,
eight blue and five green. You randomly
select one to wear on Monday and then a
different one on Tuesday. You wear a blue
shirt on Monday and a green shirt on
Tuesday.

Answers

11 shirts

Step-by-step explanation:

You start off with 13, wear one monday, 12, then another tuesday 11

13-2=11

HELPPP HELPPP HELPPP!!!!

Answers

Answer:

Step-by-step explanation:

area =8*4 cm

=32 cm^2

Answer:

area of the figure=8×4

=32 cm²

The number of manatee deaths along the Florida coast was recorded each year from 1977 to 1990. Below is a regression printout for number of deaths versus number of boats for each of the 14 years. Which of the following would give a 95% confidence interval for the slope of the regression line?Regression AnalysisThe regression equation isDeaths = - 41.4 + 0.125 BoatsPredictorCoefStdevt-ratiopConstant-41.4307.412-5.590.000Boats0.124860.012909.680.000s = 4.276 n = 15 R-sq = 88.6% R-sq(adj) = 87.7%0.125± 2.160(.013)0.125± 2.145(.013)0.125± 2.179(.013)0.125± 2.179(4.276)0.125± 2.145(4.276)

Answers

the anser is 333399999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999

pls help!! person with correct answer will be marked brainliest

Answers

27.9!
Hope this helps

Which is an equivalent scale factor of Mr. Barrow's height to the height of the power pole?
A. 162:18
B. 6:54
C. 18:162
D. 54:6

Answers

9514 1404 393

Answer:

  C. 18:162

Step-by-step explanation:

Both B and C are the same scale factor, and both correctly express the ratio of the shorter height to the longer one.

The ratio of choice C is directly obtained from the figure, so is probably the best choice.

What are the algebraic properties of the logarithm function?

Answers

Answer:

344343234

Step-by-step explanation:

The hypotenuse function is correct, but the main function has a problem. Explain why it may not work, and show a way to fix it. Your fix must be to the main function only; you must not change the hypotenuse function in any way.

Answers

Answer: hello your question is incomplete attached below is the missing codes

Answer : It may not work because; the double pointer P was not allotted a double using a new double ( I.e. Error in the main function ) also the cout statement was not written in the main function

Step-by-step explanation:

It may not work because; the double pointer P was not allotted a double using a new double ( I.e. Error in the main function ) also the cout statement  should be moved to the Main

The correction  is below

{

   double* p = new double;

   hypotenuse(1.5, 2.0, p);

  cout << "The hypotenuse is " << *p << endl;

}

Please help me solve (with each step) the following:
log7 -2b-9=-6

Answers

The answer is -10b and it can be solved by any one who put his mind forward

z=−12i+11
What are the real and imaginary parts of z ?

Answers

Answer:

it is easy simply you can answer-12 imaginary 11 is real

Cube roots of 1 are +1 and -1 (true and false)​

Answers

False cube root of 1 is plus 1 only.

What is the value of log6 49?

Round your answer to two places.

Answers

Answer: 2.17

Step-by-step explanation: To get the answer you count the first two numbers on the Decimal Form, starting behind the period.

(2.17206626)

The following diagram shows part of the graph off with x-intercept (5,0) and y-intercept (0,8).

Find the y-intercept of the graph of f(x) + 3.

Answers

Step-by-step explanation:

By question , it's given that the X intercept is (5,0) and the y intercept is (0,8) . And we need to find the y-intercept of the graph of f(x) + 3 . For that , firstly let's find out the equation of the line.

We can use here two point form of the line .So that , the equation would be ,

[tex]\sf\implies y- y_1 = \bigg(\dfrac{y_2-y_1}{x_2-x_1}\bigg) ( x - x_1) \\\\\sf\implies y - 0 = \bigg(\dfrac{0-8}{5-0}\bigg)( x - 5 ) \\\\\sf\implies y = \dfrac{-8}{5}( x - 5 ) \\\\\sf\implies 5y = -8x +40 \\\\\sf\implies 8x + 5y - 40 = 0 [/tex]

Let us say that this is f(x) :-

[tex]\\\\\sf\implies f(x) = 8x + 5y - 40 \\\\\sf\implies \boxed{\sf\red{ f(x)+3 = 8x +5y -37 }}[/tex]

Plot its graph :-

We can either convert it into intercept form but plotting a graph can also be done to find y intercept .

[tex]\implies \boxed{\pink{\sf y - intercept = 7.4}}[/tex]

Refer to attachment for graph .

Hence the y Intercept is 7.4 .

The height of the triangle is 4 inches less than four times its
base. The area of the triangle is 112 in2. What is the height of
the triangle?

Answers

Answer:

h = 28 inches

Step-by-step explanation:

Let the base of the triangle is b.

the height of the triangle is 4 inches less than four times its  base.

h = 4b-4

The area of the triangle is 112 inch².

The formula for the area of a triangle is given by :

[tex]A=\dfrac{1}{2}bh\\\\112=\dfrac{1}{2}\times b\times (4b-4)[/tex]

It is a quadratic equation, whose solution is as follows :

b = -7 and b = 8 inches

Height, h = 4(8)-4

= 32-4

= 28 inches

Hence, the height of the triangle is 28inches.

pls answer pls pls hurry

Answers

Answer: This can not be answered unless you choose a bigger photo.

Step-by-step explanation:

Sorry

NEED HELP ASAP OR NOW!!!

1. Which of the following statements best represents the graph?

A. After one month of service, the cost of internet is $45.

B. After 60 months of service, the cost of internet is $1.

C. After one months of service, the cost of internet is $60.

D. After 5 months of service, the cost of internet is $210.


PLEASE ALSO ANSWER THE QUESTION BELOW.


2. Which is the correct equation best reflects to the graph above on question 1?

A. Y = 90x

B. Y = 180x

C. Y = 45x

D. Both B and C




Answers

the first question would be A and Cis the answer for the second question!!
The second is A and the first one is b

Tienes $20 para gastar en la tarifa del taxi. El viaje cuesta
$5 más $2.50 por kilómetro.
Escribe una desigualdad para determinar la distancia
en kilómetros, d, que podrías recorrer por $20.
¿Cuál es la distancia máxima, en kilómetros, que
puedes recorrer por $20?
kilómetros.

Answers

Answer:

6 kilometers serian15 mas 5

The tallest man alive today is 8 feet 3 inches. How tall is he in inches?

Answers

Answer:

99 inches

It should be correct, you can try and double check with goo gle though.

Answer:

99

Step-by-step explanation:

1 foot = 12 inches

12 × 8 = 96

96 + 3 = 99

99

Hi plz help, if you can ill mark you 5 starz! :)

Answers

Answer:

b and 288

Step-by-step explanation:

ywwwwwwwwwwww

Write the number 9.9 x 10-5 in standard form.

Answers

It’s going to be 94 if it works let me know!

Rewrite the following logarithmic expression as an exponential expression

Answers

Answer:

it should be the same answer....?

Step-by-step explanation:

Please show steps on how to solve
log7 -2b-9=-6

Answers

Answer: b= - -log10(7)+3/2

Step-by-step explanation: log 10 (7) -2b-9=-6 : b= - -log10(7)+3/2 (Decimal : b = -1.07745...)

so these are the steps how I got it I did log 10 (7)-2b-9=-6 subtract log 10 (7) -9 from both sides log 10 (7)-2b-9-(log10(7)-9)=-6-(log 10 (7) -9)

Simplify -2b= -log10(7)+3

Divide both sides by -2  -2b/2= - log 10(7)/-2+ 3/-2 if you simplify it should give you b= - -log10(7)+3/2 that should be your answer but i'm not sure those I think that's how you do it let me know if you got it right bye!

Insurance companies are interested in knowing the population percent of drivers who always buckle up before riding in a car. They randomly survey 387 drivers and find that 298 claim to always buckle up. Construct a 84% confidence interval for the population proportion that claim to always buckle up.

Answers

Answer:

The 84% confidence interval for the population proportion that claim to always buckle up is (0.74, 0.80).

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 z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

They randomly survey 387 drivers and find that 298 claim to always buckle up.

This means that [tex]n = 387, \pi = \frac{298}{387} = 0.77[/tex]

84% confidence level

So [tex]\alpha = 0.16[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.16}{2} = 0.92[/tex], so [tex]Z = 1.405[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 - 1.405\sqrt{\frac{0.77*0.23}{387}} = 0.74[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.77 + 1.405\sqrt{\frac{0.77*0.23}{387}} = 0.8[/tex]

The 84% confidence interval for the population proportion that claim to always buckle up is (0.74, 0.80).

A gumball machine has various colors of gumballs. There is a 10% chance that the next
gumball from the machine is red and 0.8 chance it is orange.
Is the next gumball more likely to be red or orange? Explain your reasoning.

Answers

Answer:

It is red

Step-by-step explanation:

i need the answer to
7(p + 1) = 2(3p + 1)

Answers

Answer:

p = -5

Step-by-step explanation:

7(p + 1) = 2(3p + 1)

Distribute on both sides.

7p + 7 = 6p + 2

Subtract 6p from both sides.

p + 7 = 2

Subtract 7 from both sides.

p = -5

Answer:

p = -5

Step-by-step explanation:

7(p + 1) = 2(3p + 1)

Distribute

7p +7 = 6p +2

Subtract 6p from each side

7p +7 -6p = 6p+2-6p

p+7 = 2

Subtract 7 from each side p+7-7 =2-7

p=-5

Drag each label to the correct location on the image.
Here is a multiplication sentence:
1 x (4 x 4) = 16
Drag the numbers and the parentheses to create an equivalent multiplication sentence that illustrates the associative property of
multiplication

Answers

Answer:

4 x (1 x 4) = 16

Step-by-step explanation:

1 x 4 = 4

4 x 4 = 16

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