Consider a lake of constant volume 12200 km^3, which at time t contains an amount y(t) tons of pollutant evenly distributed throughout the lake with a concentration y(t)/12200 tons/km^3.
assume that fresh water enters the lake at a rate of 67.1 km^3/yr, and that water leaves the lake at the same rate. suppose that pollutants are added directly to the lake at a constant rate of 550 tons/yr.
A. Write a differential equation for y(t).
B. Solve the differential equation for initial condition y(0)=200000 to get an expression for y(t). Use your solution y(t) to describe in practical terms what happens to the amount of pollutants in the lake as t goes from 0 to infinity.

Answer:

B) 11

Step-by-step explanation:

PEMDAS=parenthesis, exponents, multiplication, division, addition, and subtraction.

First start with the parenthesis:

20 x 1/4=5

9 + (5) - 6 ÷ 2

We don't have exponents or multiplication, so go onto division:

-6 ÷ 2 = -3

9+5-3

Finally addition and subtraction:

9+5-3=11

Hope this helps!

The slope of the parametric curve x=-4t^2-4, y=6t^3 at the point corresponding to t is -9t/4.

To find the slope of the parametric curve x=-4t^2-4, y=6t^3 at the point corresponding to t, follow these steps:
1.  Find the derivatives of both x and y with respect to t:
   dx/dt = -8t
   dy/dt = 18t^2
2. The slope of the parametric curve is the ratio of the derivatives, dy/dx.

    To find this, divide dy/dt by dx/dt:

    dy/dx = (dy/dt) / (dx/dt)

              = (18t^2) / (-8t)
3. Simplify the expression:
   dy/dx = -9t / 4
So, the slope of the parametric curve x=-4t^2-4, y=6t^3 at the point corresponding to t is -9t/4.

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In a Nyquist plot, If G(s) has one pole in the right-half s plane, the system is marginally stable.

If G(s) has no pole in the right-half s plane, but has one zero in the right-half s plane, the system is stable.

In a Nyquist plot, the stability of a system can be determined by examining the number of encirclements of the -1 point. If the number of encirclements is equal to the number of right-half plane poles, then the system is unstable. If the number of encirclements is less than the number of right-half plane poles, then the system is marginally stable. If the number of encirclements is greater than the number of right-half plane poles, then the system is stable.

In the first case where G(s) has one pole in the right-half s plane, the Nyquist plot will encircle the -1 point once in the clockwise direction. Therefore, the number of encirclements is less than the number of right-half plane poles, which means the system is marginally stable.

In the second case where G(s) has one zero in the right-half s plane, the Nyquist plot will not encircle the -1 point at all. Therefore, the number of encirclements is less than the number of right-half plane poles, which means the system is stable.

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Answer:

LO=6

Step-by-step explanation:

MO/KO=NO/LO

5/10=3/LO

5LO=30

LO=6cm

Answer:

Step-by-step explanation:

1=a

Answer:

Step-by-step explanation:

Identity means to get itself

For multiplication,

if you  multiplied a number by 0, you would not get that number again, you would get 0.  so multiplying by 0 is not and identity

ex.  (a)(0)=0   does not = a so this is not an identity

if you multiplied a number by 1, yes that would be an identity because any number times 1 is itself

ex. a(1)=a    multiplied by 1 the number is itself, so yes this is an identity.

Answer:

2 1/3

Step-by-step explanation:

V = LWH

V = 1 3/4 ft × 2/3 ft × 2 ft

V = 7/4 × 2/3 × 2/1 ft³

V = 28/12 ft³

V = 7/3 ft³

V = 2 1/3 ft³

The watch gains 4 min till 8:00 PM in the next evening and show 8:04 pm the next evening.

Considering that,

A broken watch adds ten seconds per hour.

Find the number of hours between 8:00 PM this evening and 8:00 PM the following evening.

There are 24 hours in a day.

number of seconds the defective watch gained.

1 hour equals 10 seconds

24 hours ÷ by 10

24 * 10 is 240 seconds.

Now figure out how many minutes your defective watch has gained.

60 s = 1 minute

240 sec = 240/60

= 4 min

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Missing parts;

A faulty watch gains 10 seconds an hour. If it is set correctly at 8:00 pm one evening, what time will it show when the correct time is 8:00 pm the following evening

Answer:

-1(-4)=-5

Step-by-step explanation:

as h = -1

The height of the pillar is 14 feet.

We can use the ratio of the building's height to the length of its shadow to solve for the pillar's height and apply it to the pillar as well. This is because similar-shaped objects will produce shadows that are proportional to their size.

Let h represent the pillar's height, and let's establish a proportion:

height of building / length of building's shadow = height of pillar / length of pillar's shadow

Substituting the given values:

70 / 50 = h / 10

We can simplify this proportion by cross-multiplying:

70 x 10 = 50h

700 = 50h

And solving for h:

h = 700 / 50 = 14

Therefore, the height of the pillar is 14 feet.

In conclusion, we can solve for the pillar's height by establishing a ratio between the building's height and the length of its shadow and applying that ratio to the pillar.

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If the curve x2/3+y2/3=4 and Let L be the tangent line to this curve at the point (1,3√3), and let A and B be the x- and y-intercepts of L, then the length of line segment AB is √38 (option b).

Explanation:

To find the length of line segment AB, follow these steps:

Step 1: We need to first find the equation of tangent line L at the given point (1, 3√3) on the curve x^(2/3) + y^(2/3) = 4.

Step 1. Find the derivative dy/dx using implicit differentiation:
(2/3)x^(-1/3) + (2/3)y^(-1/3)(dy/dx) = 0

Step 2. Solve for dy/dx (the slope of tangent line L) at point (1, 3√3):
(2/3)(1)^(-1/3) + (2/3)(3√3)^(-1/3)(dy/dx) = 0
dy/dx = -1/2

Step 3. Use the point-slope form to find the equation of tangent line L:
y - 3√3 = -1/2(x - 1)

Step 4. Find the x- and y-intercepts (A and B) of line L:
x-intercept (A): y = 0
0 - 3√3 = -1/2(x - 1)
x = 2 + 6√3

y-intercept (B): x = 0
y - 3√3 = -1/2(0 - 1)
y = 3√3 + 1/2

Step 5. Calculate the length of the line segment AB using the distance formula:
AB = √[(2 + 6√3 - 0)^2 + (3√3 + 1/2 - 0)^2] = √38

The length of line segment AB is √38 (option b).

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The shape and size of the figure are unchanged. and other soltuions are below

The rule for translating a point 4 units left and 8 units up is (x, y) → (x - 4, y + 8).

Using the above rule

After the translation, the new coordinates of A are (3, 13).

The rule for reflecting a point over the y-axis is (x, y) → (-x, y).

Using the above rule

After the reflection, the coordinates of A become (-7, 5).

The final figure is congruent to the original figure because translation and reflection are both rigid transformations, which preserve distance and angles between points.

Therefore, the shape and size of the figure are unchanged.

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No, W is not a subspace of R3 because it is not closed under vector addition and scalar multiplication, even though it contains the zero vector.

A set must meet three requirements to be a subspace of a vector space: (1) it must include the zero vector, (2) it must be closed under vector addition, and (3) it must be closed under scalar multiplication.

While W includes the zero vector (0, 0, 0), vector addition does not close it. For example, the triples (3, 4, 5) and (5, 12, 13) are both Pythagorean, but their addition (8, 16, 18) is not. As a result, W does not meet the second requirement and is not a subspace of R3.

Under scalar multiplication, W is likewise not closed. When we multiply the Pythagorean triple (3, 4, 5) by -1, we obtain (-3, -4, -5), which is not a Pythagorean triple. Therefore, W does not satisfy the third condition and is not a subspace of R.

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Answer:5/6

Step-by-step explanation: Theres 6 people that you are splitting 5 oranges among. so you do the equation 5÷6 or 5/6 which is the answer your looking for

Answer:

5/6

Step-by-step explanation:

=0.8333.......................

Therefore, the margin of error for a 95% confidence interval for the population mean of AAA batteries (with a population standard deviation of 0.5 hours and a population mean of 9 hours) based on a sample size of 25 batteries is 0.196 hours.

What is margin error?

Margin of error is a statistical term that refers to the amount of error that is allowed in a survey or poll's results. It is a measure of the precision of the results and indicates the range within which the true value is likely to fall.

In statistical terms, the margin of error is calculated as a percentage of the total number of respondents in a survey, and it takes into account factors such as the size of the sample, the level of confidence desired, and the variability in the responses.

For example, if a poll has a margin of error of +/- 3%, it means that the actual value of the result could be up to 3% higher or 3% lower than the reported value in the survey.

The formula for the margin of error for a 95% confidence interval is:

Margin of error = z * (σ / [tex]\sqrt(n)[/tex])

Where:

z = the z-score for the desired confidence level (95% confidence level corresponds to z = 1.96)

σ = the population standard deviation

n = the sample size

Substituting the given values into the formula:

Margin of error = 1.96 * (0.5 /[tex]\sqrt(25)[/tex])

Margin of error = 1.96 * (0.5 / 5)

Margin of error = 1.96 * 0.1

Margin of error = 0.196

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The solution of inequality is -9 < x < 12.

The correct option is B.

We have,

-2 < x/3 + 1 < 5

Now, solving the inequation in parts as

-2 < x/3 + 1

-2 - 1 < x/3

-3 < x/3

-9 < x

and, x/3 + 1 < 5

x/3 < 4

x <12

Thus, the solution of inequality is -9 < x < 12.

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z = 2√13(cos 5.49 + i sin 5.49) in polar form.

We can use Euler's formula, e^(iθ) = cos(θ) + i sin(θ), to write complex numbers in polar form.

1. For e^(iπ/3), we have:

e^(iπ/3) = cos(π/3) + i sin(π/3) = 1/2 + i√3/2

Therefore, a = 1/2 and b = √3/2.

2. For e^(i4π/3), we have:

e^(i4π/3) = cos(4π/3) + i sin(4π/3) = -1/2 - i√3/2

Therefore, a = -1/2 and b = -√3/2.

3. For z = 6 - 4i, we can find the magnitude (or modulus) of z, r, using the Pythagorean theorem:

|r| = √(6^2 + (-4)^2) = √52 = 2√13

To find the angle, theta, we can use the inverse tangent function:

tan⁻¹(-4/6) = -tan⁻¹(2/3) ≈ -0.93 radians

However, since we want the angle to satisfy 0 ≤ θ < 2π, we need to add 2π to the angle if it is negative:

θ = 2π - 0.93 ≈ 5.49 radians

Therefore, z = 2√13(cos 5.49 + i sin 5.49) in polar form.

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The singular, affirmative and formal command for each of the following are as follows: 1.tener: tenga, 2.conocer: conozca 3.buscar:busque 4.ir:vaya 5.ser:sea

What Spanish Affirmative and Negative commands?

The indicative, subjunctive, and imperative verb moods are the three primary categories of verb moods in Spanish.

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The corresponding z-score for a random variable x that is normally distributed with a mean of 395 and a standard deviation of 23, when  x = 35 is:  -15.65

To find the z-score, you can use the following formula:

z = (x - μ) / σ

where z is the z-score, x is the value of the random variable, μ is the mean, and σ is the standard deviation.

Step 1: Identify the values.
x = 35, μ = 395, and σ = 23.

Step 2: Substitute the values into the formula.
z = (35 - 395) / 23

Step 3: Calculate the z-score.
z = (-360) / 23 = -15.65

So, the corresponding z-score for x = 35 is approximately -15.65.

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det(A) = ad - bc.

Matrix X is X = [8/5 -6/5, -2, 2/5 2/5]

We know that the adjugate of a 2x2 matrix is:

adj(A) = [d -b, -c a]

A = [a b, c d]

det(A) = ad - bc.

So, from the given adj(A), we have:

d - b = 1

-c = 2

-a = 1

d - c = 1

We have c = -2. Then, from the fourth equation, we have d = 1 - c = 3. Substituting these values into the first and third equations, we get:

b = 2

a = -1

So, the matrix A is:

A = [-1 2, -2 3]

We are given that AX = A + X. Substituting the matrix A and simplifying, we get:

AX = A + X

=> A(X - I) = X - A

=> (X - I)(-A) = X - A

=> X - I = (-A)⁻¹ (X - A)

=> X - I = A⁻¹ (X - A)

=> X = A⁻¹ X - A⁻¹ A + I

=> X = A⁻¹ (X - A) + I

Since we know A, we can find its inverse:

A⁻¹ = 1/(ad - bc) [d -b, -c a] = 1/5 [3 -2, 2 -1]

Substituting this into the above equation, we get:

X = 1/5 [3 -2, 2 -1] (X - [-1 2, -2 3]) + I

Simplifying this, we get:

X = 1/5 [4X + 5, -6X - 10, -2X - 10, 3X + 5]

Equating the corresponding elements on both sides, we get the following system of equations:

4x + 5 = x

-6x - 10 = 2

-2x - 10 = 1

3x + 5 = 3

Solving this system of equations, we get:

x = -1

Therefore, det(A) = ad - bc = (-1)(3) - (2)(-2) = -1 + 4 = 3.

And, matrix X is:

X = [8/5 -6/5, -2, 2/5 2/5]

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(a) P{L1 = 0}: Since L1 is the last Poisson event time before m, and m is uniformly distributed on [0, 1], we have:

P{L1 = 0} = P{no Poisson events in [0, m]} = e^(-λm)

(b) P{L1 < x}, 0 < x < m: We have:

P{L1 < x} = P{there is at least one Poisson event in [0, x]} = 1 - P{no Poisson events in [0, x]} = 1 - e^(-λx)

(c) P{R1 = 1}: Since R1 is the first Poisson event time after m, we have:

P{R1 = 1} = P{no Poisson events in [m, 1]} = e^(-λ(1-m))

(d) P{R1 = x}, m < x < 1: We have:

P{R1 = x} = P{there is no Poisson event in [m, x]} * P{there is at least one Poisson event in [x, 1]}

= e^(-λ(x-m)) * (1 - e^(-λ(1-x)))

(e) E[R-L]: We have:

E[R-L] = E[(R1-L1) + (R2-L2) + ... + (Rn-Ln)]

= E[R1-L1] + E[R2-L2] + ... + E[Rn-Ln] (by linearity of expectation)

= nE[R1-L1] (since the n copies are identical)

To find E[R1-L1], note that R1-L1 represents the length of the fragment that contains the marked position. This length is distributed as an exponential random variable with parameter λ, since it is the time until the next Poisson event in a Poisson process with rate λ. Therefore:

E[R1-L1] = 1/λ

Thus, we have:

E[R-L] = n/λ

This means that as n (the number of copies) becomes large, the expected length of the interval containing the marked position becomes smaller and smaller, converging to 0 as n approaches infinity.

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The resultant matrix represents the vertices of the translated triangle, with A' at (-3, 7), B' at (-2, 0), and C' at (1, 7).

A transformation matrix is a mathematical matrix that represents a geometric transformation of space.

To translate the triangle by (-2, 4), we need to add -2 to the x-coordinates and add 4 to the y-coordinates of each vertex. The transformation matrix for this translation is:

[tex]\left[\begin{array}{ccc}1&0&-2\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}0&1&4\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}0&0&1\end{array}\right][/tex]

To apply this transformation to the vertices of the triangle, we can represent each vertex as a column vector with a third coordinate of 1:

[tex]A=\left[\begin{array}{ccc}-1&3&1\end{array}\right][/tex]

[tex]B=\left[\begin{array}{ccc}0&-4&1\end{array}\right][/tex]

[tex]C=\left[\begin{array}{ccc}3&3&1\end{array}\right][/tex]

To apply the translation, we multiply each vertex by the transformation matrix:

[tex]A'=\left[\begin{array}{ccc}1&0&-2\end{array}\right] \left[\begin{array}{ccc}-1&3&1\end{array}\right] \left[\begin{array}{ccc}-3&7&1\end{array}\right][/tex]

      [0 1  4] × [ 0 -4  1] = [-2  0  1]

      [0 0  1]   [ 1  3  1]   [-1  7  1]

[tex]B'=\left[\begin{array}{ccc}1&0&-2\end{array}\right] \left[\begin{array}{ccc}0&-4&1\end{array}\right] \left[\begin{array}{ccc}-2&-4&1\end{array}\right][/tex]

      [0 1  4] × [ 0 -4  1] = [-2   0  1]

      [0 0  1]   [ 0  3  1]   [-2   7  1]

[tex]C'=\left[\begin{array}{ccc}1&0&-2\end{array}\right] \left[\begin{array}{ccc}3&3&1\end{array}\right] \left[\begin{array}{ccc}1&7&1\end{array}\right][/tex]

      [0 1  4] × [ 3  3  1] = [ 1  7  1]

      [0 0  1]   [ 3  3  1]   [ 1  7  1]

The resultant matrix represents the vertices of the translated triangle, with A' at (-3, 7), B' at (-2, 0), and C' at (1, 7).

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The final image is real since it is located to the right of the second lens. It is also upright since the magnification is positive.

(a) Using the thin lens formula, 1/f = 1/p + 1/q, where f is the focal length, p is the object distance, and q is the image distance, we have:

1/f = 1/p - 1/q1

Substituting the given values, we get:

1/11.6 = 1/16.2 - 1/q1

Solving for q1, we get:

q1 = 6.97 cm

Therefore, the image formed by the first lens is located 6.97 cm to the right of the lens.

(b) The image formed by the first lens acts as an object for the second lens. Using the thin lens formula again, we have:

1/f = 1/p2 + 1/q1

Substituting the given values, we get:

1/5 = 1/p2 + 1/6.97

Solving for p2, we get:

p2 = 3.32 cm

The distance from the second lens to the image of the first lens is then:

q2 = p2 + q1 = 3.32 + 6.97 = 10.29 cm

Therefore, the image of the first lens is located 10.29 cm to the right of the second lens.

(c) The object distance for the second lens is simply the image distance of the first lens:

p2 = q1 = 6.97 cm

(d) Using the thin lens formula again, we have:

1/f = 1/p2 + 1/q2

Substituting the given values, we get:

1/5 = 1/6.97 + 1/q2

Solving for q2, we get:

q2 = 13.95 cm

Therefore, the final image is located 13.95 cm to the right of the second lens.

(e) The magnification of the first lens is given by:

m1 = -q1/p = -6.97/16.2 ≈ -0.43

(f) The magnification of the second lens is given by:

m2 = -q2/p2 = -13.95/3.32 ≈ -4.20

(g) The total magnification of the system is given by the product of the magnifications of the two lenses:

m = m1 × m2 ≈ 1.81

(h) The final image is real since it is located to the right of the second lens. It is also upright since the magnification is positive.

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The option to the above question is a circle graph titled New York City visitor's transportation, with five sections labelled walk 40 per cent, bicycle 8 per cent, car service 15 per cent, bus 10 per cent, and subway 27 per cent.

A circle is a geometric shape that consists of a set of points in a plane that are equidistant from a fixed point called the centre. The distance from the centre to any point on the circle is called the radius, and the distance across the circle passing through the centre is called the diameter.

According to the given information:

The correct circle graph that represents the data in the table would be:

circle graph titled New York City visitor's transportation, with five sections labelled walk 40 per cent, bicycle 8 per cent, car service 15 per cent, bus 10 per cent, and subway 27 per cent.

This is because the percentages shown in this circle graph match the data given in the table for each type of transportation. Specifically, the circle graph shows that 40% of visitors walked, 8% used bicycles, 15% used car service, 10% used the bus, and 27% used the subway, which aligns with the numbers provided in the table.

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Answer:It’s B i got it correct on the quiz

Step-by-step explanation:

Answer:

In this problem it is saying that it is $35 less than the original cost so to find this you need to add. This should be just $149 + $35 to solve it which is a total of $184 which is the original cost for the phone.

$184 is your answer

Step-by-step explanation:

$114

as the question says the price is $35 less than the original cost, which means 149-35 which equal 144.

Each group of four binary digits can be represented by a single hexadecimal digit. The hexadecimal notation of (0111 0111 0111 0111)₂ is (7777)₁₆.

To convert the binary expansion of (0111 0111 0111 0111)2 to hexadecimal, we first group the digits into groups of four starting from the right:
(0111 0111 0111 0111)2 = (7 7 7 7)16
Each group of four binary digits can be represented by a single hexadecimal digit. In this case, each group of four binary digits represents the hexadecimal digit 7. Therefore, the hexadecimal notation of (0111 0111 0111 0111)2 is (7777)16.
To convert the binary expansion (0111 0111 0111 0111)₂ to a hexadecimal expansion, you can group the binary digits into sets of four starting from the right and then convert each group to its corresponding hexadecimal value. Here's the process:
1. Group the binary digits: (0111) (0111) (0111) (0111)
2. Convert each group to hexadecimal:
  - (0111)₂ = 7₁₆
  - (0111)₂ = 7₁₆
  - (0111)₂ = 7₁₆
  - (0111)₂ = 7₁₆
Your answer: The hexadecimal notation of (0111 0111 0111 0111)₂ is (7777)₁₆.

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Answer:

Step-by-step explanation:

let's firstly get the EQUATion, of the graph before we get the inequality.

so we have a quadratic with two zeros, at -6 and 8, hmmm and we also know that it passes through (-2 , 10)

[tex]\begin{cases} x = -6 &\implies x +6=0\\ x = 8 &\implies x -8=0\\ \end{cases} \\\\[-0.35em] ~\dotfill\\\\ \stackrel{original~polynomial}{a ( x +6 )( x -8 ) = \stackrel{0}{y}}\hspace{5em}\textit{we also know that } \begin{cases} x=-2\\ y=10 \end{cases}[/tex]

[tex]a ( -2 +6 )( -2 -8 ) = 10\implies a(4)(-10)=10\implies -40a=10 \\\\\\ a=\cfrac{10}{-40}\implies a=-\cfrac{1}{4} \\\\[-0.35em] ~\dotfill\\\\ -\cfrac{1}{4}(x+6)(x-8)=y\implies -\cfrac{1}{4}(x^2-2x-48)=y \\\\\\ ~\hfill {\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{x}{2}+12=y \end{array}}~\hfill[/tex]

now, hmmm let's notice something, the line of the graph is a solid line, that means the borderline is included in the inequality, so we'll have either ⩾ or ⩽.

so hmmm we could do a true/false region check by choosing a point and shade accordingly, or we can just settle with that, since the bottom is shaded, we're looking at "less than or equal" type, or namely ⩽, so that's our inequality

[tex]{\Large \begin{array}{llll} -\cfrac{x^2}{4}+\cfrac{x}{2}+12\geqslant y \end{array}}[/tex]

Answer:

this is a correct answer 5√6/2