Look at the picture.
Thank u!

Answer:

[tex]dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex] g/min

Step-by-step explanation:

The mass flow rate dA(t)/dt = mass flowing in - mass flowing out

Since water is pumped in at a rate of 3 L/min, and it contains no salt, the concentration in is thus 0 g/L. the mass flow in is thus 0 g/L × 3 L/min = 0 g/min.

Let A(t) be the mass present at any time, t. The concentration at any time ,t is thus A(t)/volume = A(t)/210. Since water flows out at a rate of 3 L/min, the mass flow out is thus, A(t)/210 g/L × 3 L/min = A(t)/70 g/min.

So, dA(t)/dt = mass flowing in - mass flowing out

dA(t)/dt = 0 g/min - A(t)/70 g/min

dA(t)/dt =  - A(t)/70 g/min

 Since the tank initially contains 30 g of salt, the initial mass of salt in the tank is 30 g. So A(0) = 30

So, the initial value problem is thus  

dA(t)/dt =  - A(t)/70 , A(0) = 30

Separating the variables, we have

dA(t)/A(t) = -dt/70

Integrating both sides, we have

∫dA(t)/A(t) = ∫-dt/70

㏑A(t) = -t/70 + C

taking exponents of both sides, we have

A(t) = exp(-t/70 + C)

A(t) = exp(-t/70)expC

[tex]A(t) = e^{-t/70}e^{C}\\A(t) = Ce^{-t/70} whereC = e^{C}[/tex]

A(0) = 30, So

[tex]A(0) = Ce^{-0/70}\\30 = Ce^{0}\\C = 30[/tex]

[tex]A(t) = 30e^{-t/70}[/tex]

The rate at which the number of grams of salt in the tank is changing at time t is

[tex]dA(t)/dt = \frac{d30e^{-t/70} }{dt} \\dA(t)/dt = -\frac{30e^{-t/70} }{70}\\dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex]

So, the rate at which the number of grams of salt in the tank is changing at time t is

[tex]dA(t)/dt = -\frac{3}{7}e^{-t/70}[/tex] g/min

Answer:

√13

Yes you are right

Step-by-step explanation:

The law of cos again

BC^2 = 18 + 25 - 2 * 3√2 * 5 cos(45 degrees)

= 13

==>

BC = √13

Answer:

yes the answer is correct

Answer:

110.1

Step-by-step explanation:

Answer:

Cavalieri's principle tells us that if 2 figures have the same height and the same cross-sectional area at every point along that height, they have the same volume.

Answer:

.9x 6.2= $5.58

.............

Answer:

34.4

Step-by-step explanation:

(54/11) --> ratio of one side of the larger triangle to the smaller one multiplied by 7 = 34.36363636... Rounding it to the nearest tenth is 34.4

Answer:

B. Team B has a larger median and the same interquartile range.

The correct statement is,

D. Team B has a smaller median and the same interquartile range.

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Now, We know that;

Based on the given data, the correct comparison of Team B to Team A is A. Team B has a larger median and a smaller interquartile range.

This is because the median score for Team B is 70, which is higher than the median score for Team A, which is 70.

The interquartile range for Team B is smaller because the scores are more tightly clustered around the median, indicating less variability in scores compared to Team A.

Thus, The correct statement is,

D. Team B has a smaller median and the same interquartile range.

Learn more about the mathematical expression visit:

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Answer: .012

Step-by-step explanation: 6*2 is 12, and you can simply use the number of decimal points on the smaller term to get .012

Answer:

should be .12

Step-by-step explanation:

.06 multiplied by 2 is .12

Options A and D are true for the inverse matrices.

We need to determine which statement about inverse matrices is true.

The inverse of the matrix is another matrix, which on multiplication with the given matrix gives the multiplicative identity. For a matrix A, its inverse is [tex]A^{-1}[/tex], and  [tex]A.A^{-1}=I[/tex] A = I, where I is the identity matrix. The matrix whose determinant is non-zero and for which the inverse matrix can be calculated is called an invertible matrix.

The matrix should have a non-zero determinant for getting the inverse of it.

An inverse matrix should be a square matrix.

The inverse of the matrix can be calculated by two approaches:

1) Adjoint method

2) Row/Column elementary method

Therefore, options A and D are true for the inverse matrices.

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Answer:

1st one: 16

2nd one: 16

3rd one: 64

4th one: 27

5th one: 1000

Step-by-step explanation:

Have a great day

I think 710 is the answer

266+266+89+89= 710

Answer:

I think it's C im not certain

Answer:

1st, third and last options are correct answers

Step-by-step explanation:

e + 3 + e + 3

2e + 6

2(e + 3)

Answer:

5

Step-by-step explanation:

25 / ( 12-7)  = 25 / 5 = 5

I hope im right!!

2y

Step-by-step explanation:

16y^5-3/4)

16y²/4)

4y²)1/2

2y

Answer:

1,050

Step-by-step explanation:

3.5x

12x

25

=

1,050

Answer:

139

Step-by-step explanation:

x^2 + y^3 2+x = 3^2 + 5^3 + 2 + 3

= 9 + 125 + 5

= 139!

Answer:

9,-7 hope this helps :))))))))

Answer:

The maximum rent each will pay is $1,333.

Step-by-step explanation:

They want the monthly rent to be no more than $3,999.

It will be split evenly between all of them, with each contributing with x.

This means that the maximum rent each will pay is given by:

[tex]3x = 3999[/tex]

[tex]x = \frac{3999}{3}[/tex]

[tex]x = 1333[/tex]

The maximum rent each will pay is $1,333.

Answer:

the three consecutive numbers are 14, 15, 16

Answer:

Since the consecutive numbers, so the first one is x, the next one is x+1, and so on....I hope this will help

Step-by-step explanation:

x + (x + 1) + (x + 2) = 45

x + x + 1 + x + 2 = 45

3x + 3 = 45

3x = 42

x = 14

Now that we know x = 14, let's add one to it.

x + 1 = 14 + 1 = 15.

Now we have our middle number, which is 15. You can always check your answer by adding 14 + 15 + 16 = 45. Whoo!

Given:

The coordinates of the points are B(-4,3), G(-2, 4), H(1, -2), L(-1, -3).

To find:

Whether GL and BH are parallel or not by using their slopes.

Solution:

If a line passes through the two points, then the slope of the line is

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

Using the slope formula, the slope of GL is

[tex]m_1=\dfrac{-3-4}{-1-(-2)}[/tex]

[tex]m_1=\dfrac{-7}{-1+2}[/tex]

[tex]m_1=\dfrac{-7}{1}[/tex]

[tex]m_1=-7[/tex]

Using the slope formula, the slope of BH is

[tex]m_2=\dfrac{-2-3}{1-(-4)}[/tex]

[tex]m_2=\dfrac{-5}{1+4}[/tex]

[tex]m_2=\dfrac{-5}{5}[/tex]

[tex]m_2=-1[/tex]

We know that slopes of parallel lines are always equal.

The slopes of GL and BH are -7 and -1 respectively but they are not equal, therefore GL and BH are not parallel lines.

Answer:

72.8

Step-by-step explanation:

16 is 8 times 2. 36.4 times 2 would be 72.8

Answer:Ok Don't freak out What do you need help with

Step-by-step explanation:

1/3 * 7/9 kg = (1 * 7)/(3 * 9) kg = 7/27 kg

He used 7/27 kg of sugar.

Answer:

x=8 x=16

Step-by-step explanation:

Given function:

Thinks:

Rewrite as:

Thereform, x=8 and x=16.

Answer:

72 cm²

Step-by-step explanation:

Given:

m<ABC = 44°

x = 16 cm

y = 13 cm

Required:

Area of the triangle

Solution:

Formula for finding area of a triangle using the Side-Angle-Side method is given as:

Area = ½*ab*sin C

where,

a = 16

b = 13

C = 44°

Plug in the values

Area = ½(16*13)*sin 44

Area = 72.2444705 ≈ 72 cm²

Answer:

8.66

Step-by-step explanation:

If it helps, volume is LENGTH x WIDTH x HEIGHT, and for a triangular prism, each side is the same. :)

Answer:

13

Step-by-step explanation:

5²+12²=c²

25+144=c²

169=c²

c=√169

c=13