A large tank is partially filled with 100 gallons of fluid in which 20 pounds of salt is dissolved. Brine containing 1 2 pound of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is then pumped out at a slower rate of 4 gal/min. Find the number of pounds of salt in the tank after 35 minutes.

Answers

Answer 1

Answer:

Step-by-step explanation:

From the given information:

[tex]R_{in} = ( \dfrac{1}{2} \ lb/gal) (6)\ gal /min \\ \\R_{in} = 3 \ lb/min[/tex]

Given that the solution is pumped at a slower rate of 4gal/min

Then:

[tex]R_{out} = \dfrac{4A}{100+(6-4)t}[/tex]

[tex]R_{out}= \dfrac{2A}{50+t}[/tex]

The differential equation can be expressed as:

[tex]\dfrac{dA}{dt}+ \dfrac{2}{50+t}A = 3 \ \ \ ... (1)[/tex]

Integrating the linear differential equation; we have::

[tex]\int_c \dfrac{2}{50 +t}dt = e^{2In |50+t|[/tex]

[tex]\int_c \dfrac{2}{50 +t}dt = (50+t)^2[/tex]

multiplying above integrating factor fields; we have:

[tex](50 +t)^2 \dfrac{dA}{dt} + 2 (50 + t)A = 3 (50 +t)^2[/tex]

[tex]\dfrac{d}{dt}\bigg [ (50 +t)^2 A \bigg ] = 3 (50 +t)^2[/tex]

[tex](50 + t)^2 A = (50 + t)^3+c[/tex]

A = (50 + t) + c(50 + t)²

Using the given conditions:

A(0) = 20

⇒ 20 = 50 + c (50)⁻²

-30 = c(50) ⁻²

c = -30 × 2500

c =  -75000

A = (50+t) - 75000(50 + t)⁻²

The no. of pounds of salt in the tank after 35 minutes is:

A(35) = (50 + 35) - 75000(50 + 35)⁻²

A(35) = 85 - [tex]\dfrac{75000}{7225}[/tex]

A(35) =69.6193 pounds

A(35) [tex]\simeq[/tex] 70 pounds

Thus; the number of pounds of salt in the tank after 35 minutes is 70 pounds.


Related Questions

AMONG US!
CODE-MRXLFF

Answers

Answer:

I have no idea but thanks for point

Answer:

YASSS AMOUNG USSSSSS

Darius paid 8.5% sales tax when he bought a new phone for $100. What was the total price of his new phone?
A. $108.05
B. $109
C. $105.50
D. $108.50

Answers

Answer:

To get the total amount plus sales tax you simply multiply 100 by .085 and you’d get 8.50$. So the answer is ‘D’.

Answer:

D

Step-by-step explanation:

108.5

Use the inequality 24 ≥ 58 + 5(x - 3.8)
Solve for the inequality X.
Pls help I need to hand it in by 4:00..

Answers

Answer:

Work shown below!

Step-by-step explanation:

24 ≥ 58 + 5(x - 3.8)

Distribute;

24 ≥ 58 + 5x - 19

Collect like terms;

24 ≥ 39 + 5x

Subtract 39 from both sides;

-15 ≥ 5x

Divide both sides by 5;

x ≥ -3

An art teacher buys 4 packs of oil paints. Each pack contains 18 tubes of paint. Which equations represent the total
number of tubes of paint the teacher bought? Check all that apply.
4x 18 = 72
18 + 18 + 18 + 18 = 72
22-4 = 18
18 + 4 = 22
72 - 18 = 4
I’m

Answers

Answer: it’s answer 18+18+18+18

Step-by-step explanation:it’s basically18 times 4

Answer:

4 × 18 = 72

18 + 18 + 18 + 18 = 72

72 ÷ 18 = 4

Step-by-step explanation:

Please help me please

Answers

Answer:

it is A and C

Step-by-step explanation:

If you do the math and equations of all of these, you will find that:

10 is 2.5x bigger than 4 (Side lengths DE and BA)

and if we do the equation:

x · 2.5

(the x variable stands for the different side lengths of triangle ABC)

it will equal the side lengths of the bigger triangle.

and when I finished doing that, I multiplied all of the answers to find the area:

12.5 x 7.5 x 10 which altogether is 937.5

none of the other answers for the total of the triangle add up to be that, but side length EF is 7.5, which I used to get my total answer of 937.5.

So the answer is A and C




Triangle ABC has vertices of A(-6, 7), B(4, -1), and C(-2, -9). Find the length of the median from
A. 4
B. Square Root of 18
C. 8
D. Square Root of 68

Answers

Answer:

A

Step-by-step explanation:

Solve the system by finding the determinants and using Cramer's Rule:
2x - y = 4
3x + y = 1

Answers

Answer:

(1, - 2)

Step-by-step explanation:

2x - y = 4

3x + y = 1

A = [tex]\left[\begin{array}{cc}2&-1\\3&1\end{array}\right][/tex] = 2(1) - 3( - 1) =2 + 3 = 5

[tex]A_{x}[/tex] = [tex]\left[\begin{array}{cc}4&-1\\1&1\end{array}\right][/tex] = 4(1) - 1(- 1) = 4 + 1 = 5

[tex]A_{y}[/tex] = [tex]\left[\begin{array}{cc}2&4\\3&1\end{array}\right][/tex] = 2(1) - 4(3) = 2 - 12 = - 10

x = [tex]\frac{A_{x} }{A}[/tex] = 1

y = [tex]\frac{A_{y} }{A}[/tex] = - 2

(1, - 2)

Classify the following triangle by its side lengths:

Answers

With two equal sides it’s called isosceles triangle

Answer:

Isosceles triangle

Step-by-step explanation:

all sides the same=scalene triangle

2 sides the same=isosceles triangle

all sides the same=equilateral triangle

plesase solve this

Prove that a line parallel to one side of a triangle divides the other two sides proportionally. Be sure to create and name the appropriate geometric figures. (10 points)

Answers

Diagram:-

Required Answer:-

Tools Needed:

pencil, paper, ruler

Draw:-[tex]\begin{align*}\triangle ABC\end{align*}.[/tex] Label the vertices.

[tex]\begin{align*}\overline{XY}\end{align*} so that \begin{align*}X\end{align*} is on \begin{align*}\overline{AB}\end{align*} and \begin{align*}Y\end{align*} is on \begin{align*}\overline{BC}\end{align*}. \begin{align*}X\end{align*} and \begin{align*}Y\end{align*}[/tex] can be anywhere on these sides.

Is [tex]\begin{align*}\triangle XBY \sim \triangle ABC\end{align*}? Why or why not? Measure \begin{align*}AX, XB, BY,\end{align*} and \begin{align*}YC\end{align*}. Then set up the ratios \begin{align*}\frac{AX}{XB}\end{align*} and \begin{align*}\frac{YC}{YB}\end{align*}.[/tex] Are they equal?

Draw:-

a second triangle,[tex] \begin{align*}\triangle DEF\end{align*}.[/tex] Label the vertices

Draw:-

[tex]\begin{align*}\overline{XY}\end{align*} so that \begin{align*}X\end{align*} is on \begin{align*}\overline{DE}\end{align*} and \begin{align*}Y\end{align*} is on \begin{align*}\overline{EF}\end{align*} AND \begin{align*}\overline{XY} \ || \ \overline{DF}\end{align*}.

Is \begin{align*}\triangle XEY \sim \triangle DEF\end{align*}? Why or why not? Measure \begin{align*}DX, XE, EY,\end{align*} and \begin{align*}YF\end{align*}. Then set up the ratios \begin{align*}\frac{DX}{XE}\end{align*} and \begin{align*}\frac{FY}{YE}\end{align*}.[/tex] Are they equal?

From this investigation, it is clear that if the line segments are parallel, then [tex]\begin{align*}\overline{XY}\end{align*}[/tex] divides the sides proportionally.

4. There were 2000 students at the university.
After some students graduated, there were
1600 students remaining. By what percent did
the number of students at the university
decrease?

Answers

Answer:

20%

Step-by-step explanation:

you  take away the zeros and make it 16/20. 16/20=80%. 100%-80%=20%

Answer:

20%

Step-by-step explanation:

2000-1600=400

400/2000=1/5=20%

Which of the following values are solutions to the inequality 1 + 5x < 4?

Answers

Step-by-step explanation:

you cant add 1 to 5x, so subtract 1 on both sides leaving you with 1 + 5x < 4 that equals 5x < 3 -1 -1

then divide 5 from both sides 5x < 3 This leaves 5 5

you with x < 3/5

Triangle ABC is congruent to Triangle A’B’C’. Describe a sequence of transformations on triangle ABC that would result in triangle A’B’C’.

Answers

Answer:A

Step-by-step explanation:

The triangle ΔABC is rotated 180° about the origin, then the ΔA'B'C' is obtained.

What is a transformation of a point?

A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.

Triangle ABC is congruent to Triangle A’B’C’.

ΔABC ≅ ΔA'B'C'

The triangle ΔABC is rotated 180° about the origin, then the ΔA'B'C' is obtained.

More about the transformation of a point link is given below.

https://brainly.com/question/27224339

#SPJ2

Please help & thank you.

Answers

Answer:

9

Step-by-step explanation:

2(5y°) = 90° ⇒ y = 9

A tank initially contains 130 gallons of water. It is then filled with more water, at a constant rate of 8 gallons per minutes. Write an equation that represents how much water is in the tank after m minutes.

Answers

Answer: 130+8(m)

Step-by-step explanation: you want to add how much water times m is added to your very first amount

A die is rolled twice. Find the chance that the ace (single dot) comes up on one of the two rolls, but not both. Record your answer as a percentage rounded to the nearest tenth of a percent.

Answers

Answer:

13.9%

Step-by-step explanation:

In order to calculate the probability of this happening, we would need to multiply the probability of one of the rolles being an ace with the probability of one of the roles NOT being an ace. Since the probability of rolling an ace is 1/6 (since there is only one ace in a six-sided die) then the probability of NOT rolling an ace is 5/6

[tex]\frac{1}{6} * \frac{5}{6} = \frac{5}{36}[/tex] or 0.1388     multiply by 100 to get percentage value

0.1388 * 100 = 13.9%

Therefore, the probability of getting one ace and one non-ace roll is 13.9%

Which probability indicates that an event is not likely to occur?


14

12

34

1

Answers

Answer:

its 14 or 1/4 as you said     |     if it is not fractions and is whole numbers it is 1

Step-by-step explanation:

1/4 is the smallest value out of all of them, making it the least probable to happen

if they are not fractions, it is 1 because that is the smallest value, making it the least probable

hope this helped!

Answer:

Step-by-step explanation:its 1/4

Keith wants to plot -8 and -9 and on a number line. Which statement is true? *

Answers

Where the statements at lol

12. If 3x + 4y = -1 and x - 2y = 3, then y=
a) 1
b) 2
c)-1
d) 3
e) 4

13. If 2x - 4y = 8 and y=2x + 1, then x
a) 2 b) 4
c) -3
d) 3
e) -2

Answers

y=3 and x= 5

Step-by-step explanation:

3×+×=-1 and 4y-2y=34×=1 and 2y=3×=4-1 and y=3+2x=3 and y=5

13/3 = 26/c help ASAP PLZ!!!!!!!!!!!!!

Answers

C=6
13 is half of 26
All you’re doing is basically adding 13+13 together which is 26 and then 3 plus 3 which is 6

61 meters = _____ feet

I'LL GIVE BRAINLIEST!

Answers

Answer:

200.131234

Step-by-step explanation:

Calculate each unit rate. Round to the nearest hundredth if necessary. 175 Calories in 12 ounces

Answers

Answer:

L

Step-by-step explanation:

Rewrite 38/7 as a mixed number.

I need this ASAP

Answers

Answer:

5 3/7

Step-by-step explanation:

Answer:

[tex]5\frac{3}{7}[/tex]

Step-by-step explanation:

Seven goes into 38 five times. Giving you 5 from 5×7=35.

I hope this explantion was helpful.

Write the equation of the line that passes through the point (-2, 7) and is PARALLEL to the line y = -4x + 1.​

Answers

Answer:

The equation is [tex]y=x-9[/tex]

Step-by-step explanation:

If we want a line parallel to the line in the problem it will have the same slope. The equation given in the problem is already in slope intercept form so we can take the slope for the new equation directly from this equation.

The slope-intercept form of a linear equation is:  [tex]y=mx+b[/tex]

Where  m  is the slope and  b  is the y-intercept value.  

[tex]y=1x-2[/tex]

Therefore the slope is  

[tex]m=1[/tex]

We can now use the point-slope formula to write the equation of the parallel line:

The point-slope formula states:  

[tex](y-y1)=m(x-x1)[/tex]

Where  m  is the slope and  [tex](x1,y1)[/tex] is a point the line passes through.  

Substituting the information from the problem gives:

[tex](y- (-7)=1(x-2)[/tex]

[tex](y+7)=1(x-2)[/tex]

Or, we can solve for  y  to put the equation in slope-intercept form:

[tex]y+7=x-2[/tex]

[tex]y+7-7=x-2-7[/tex]

[tex]y+0=x-9[/tex]

[tex]y=x-9[/tex]

whats is the only solution of 2x2+8x2-16?​

Answers

Answer:

4

Step-by-step explanation:

If x is the principal square root of 7, what must be true.

A. x = 7², and x is negative

B. x² = 7, and x is positive

C. x = 7², and x is positive

D. x² = 7, and x is negative ​

Answers

Answer:

B

Step-by-step explanation:

x=√7

squaring

x²=7

PLEASE HELP PLEASE
question: Your mass on earth is 50 kilograms. What is your mass on the moon?

Answers

Answer:

No matter if you are on Earth, the moon or just chilling in space, your mass does not change. But your weight depends on the gravity force; you would weigh less on the moon than on Earth, and in space you would weigh almost nothing at all. Where ever you are, your mass will always stay the same.

Answer:

50 kilograms

Step-by-step explanation:

Mass never changes, and is constant everywhere. The weight is what changes. If you weigh 50 kg on Earth, you'll weigh 50 kg everywhere else in the universe. That's because the amount of matter in you cannot change.

I need help on this one please

Answers

Answer:

here is what i think

(07.03)
How many solutions does the equation 5x + 10 = 5x - 8 have? (4 points)
a
Zero
Ob
One
ос
Two
Od
Infinitely many

Answers

Answer:

0 I think

Step-by-step explanation:

0 solutions because 5x will cancer each other making de solutions undefined

Matrix, help.
So I was instructed to use a calculator rather than solving by hand, so I did try to use my TI-84 but I'm having trouble, Is it possible to solve this by hand and if so- how do I go about it? Thank you (:

Answers

Answer:

i knew it but i forgot

Step-by-step explanation:

Answer:

8

Step-by-step explanation:

Determine the value of y, if x = -3.
y = |x + |1|

Answers

Answer:

Step-by-step explanation:

, if x = -3.

y = |x + |1|

So value of Y is

Y=|-3|+|1|

Y=3+1

Y=4

Answer is 4

Answer:

[tex]y = 4[/tex]

Step-by-step explanation:

[tex]y = |x + |1|\\[/tex]

| | = absolute value (how far it is from 0)

[tex]y = |-3 + |1|\\\\\\|-3| =3\\\\|3 +1| =3 + 1 \\3 + 1= 4\\[/tex]

[tex]\LARGE\boxed {y = 4}[/tex]

Let me know if you have any other questions or concerns!

~[tex]InLoveWithPugs[/tex]

[tex]Moderator\\Math\ Enthusiast[/tex]

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