The stream function for a flow is given as: Ψ=x^2+y^2−2xy a) What are the expressions for velocity in the x and y directions? b) Is the flow incompressible? c) Determine the magnitude of flow rate in between streamlines passing through (1,1) and (3,2)

Answers

Answer 1

The magnitude of flow rate in between directions passing through (1,1) and (3,2) is 2ρ.

The flow is incompressible when the mass flow rate is constant. Let us find out whether this flow is incompressible or not, using the continuity equation.The continuity equation in two dimensions is given as:

∂ρ/∂t + ∂(ρVx)/∂x + ∂(ρVy)/∂y = 0

where ρ is the density, Vx is the velocity in the x direction, and Vy is the velocity in the y direction.

∂ρ/∂t = 0

because the density is constant.

Let's find out whether the other terms in the equation sum up to zero or not.

∂(ρVx)/∂x + ∂(ρVy)/∂y = 0

Vx = 2y - 2x and

Vy = -2x + 2y

Substituting these values in the continuity equation we get,

∂(ρVx)/∂x + ∂(ρVy)/∂y = 2ρ

The terms do not sum up to zero. Therefore, this flow is not incompressible. c) The flow rate in between streamlines passing through (1,1) and (3,2) is given by,

Q = ρ(VxΔy)

where Δy is the distance between the two streamlines and ρ is the density.

Q = ρ(VxΔy) = ρ

((2(2) - 2(1))(2 - 1)) = 2ρ

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Related Questions

A beam is subjected to a moment of 786 k-ft. If the material the beam is made out of has a yield stress of 46ksi, what is the required section modulus for the beam to support the moment. Use elastic beam design principles. Submit your answer in in^3 with 2 decimal places.

Answers

The required section modulus for the beam to support the moment of 786 k-ft with a yield of the stress of 46ksi is around 204.87 [tex]in^3[/tex].

For the calculation of the section modulus for the beam to support the moment given, let's use the elastic beam design principles.

The required formula is:

[tex]S = M/ f[/tex]

S = required section modulus

M = moment

f = yield stress of the material

The known values are

M = 786 k-ft

f = 46 ksi

We need to convert the units from k-ft to standard form in-lb.

As we know

1 k-ft = 12,000 in-lb

So required unit of M = 786 k-ft × 12,000 in-lb = 9,432,000 in-lb

Let's now calculate the  required section modulus:

[tex]S = M/f[/tex] = 9,432,000 in-lb/ 46 ksi

We will need to convert the kips per square unit from cubic inches to square inches.

[tex]1in^3 = 1/12 ft^3[/tex]

[tex]= 1/12 *12^2 = 1/12 ft^2[/tex]

= 1/12 [tex]in^2[/tex]

S = 9,432,000 in-lb / 46,000 psi

S = 204.87 [tex]in^3[/tex].

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3 pts Question 10 The continuous flow in a horizontal, frictionless rectangular open channel is subcritical. A smooth step-up bed is built downstream on the channel floor. As the height of the step-up bed is increased, choked condition is attained. With further increase in the height of the step-up bed, the water surface O flow will stop. over the step-up bed will decrease to the extent that it will be below the critical depth. O over the step-up bed will decrease to the extent that it will be above the critical depth. O upstream will increase to the extent that it will create supercritical flow over the step-up bed.

Answers

The continuous flow in a horizontal, frictionless rectangular open channel is subcritical. A smooth step-up bed is built downstream on the channel floor. With further increase in the height of the step-up bed, the water surface over the step-up bed will decrease to the extent that it will be below the critical depth.

A flow that is slower than critical velocity is known as subcritical flow. The Froude number in subcritical flow is less than one. Subcritical flow occurs when water is flowing slowly, and the water surface is higher than the critical depth of flow.

The critical depth of flow is the depth of flow at which the specific energy of flow is minimum. The flow is critical if the velocity of water is equal to the velocity of the wave. In open channels, the critical depth is determined by the specific energy equation.

When a flow is restricted, choked conditions occur. When a flow in a channel reaches the maximum possible velocity, the flow becomes choked. The flow will be choked, and the water surface will rise if the depth of the flow exceeds the critical depth in a horizontal, frictionless rectangular open channel with a smooth step-up bed built downstream. With further increase in the height of the step-up bed, the water surface over the step-up bed will decrease to the extent that it will be below the critical depth.

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Compute the following probabilities. Assume the values are on a
standard normal curve.
P (-1.12 < z < 1.82) =
P (z < 2.65) =
P (z > 0.36) =
P (-2.89 < z < -0.32) =

Answers

The probabilities are as follows: 1. P(-1.12 < z < 1.82) ≈ 0.845 , 2. P(z < 2.65) ≈ 0.995 , 3. P(z > 0.36) ≈ 0.6406 , 4. P(-2.89 < z < -0.32) ≈ 0.4954

In order to compute the probabilities given, we need to refer to the standard normal distribution table or use appropriate statistical software. The standard normal distribution has a mean (μ) of 0 and a standard deviation (σ) of 1.

1. P(-1.12 < z < 1.82): This is the probability of the standard normal random variable, z, falling between -1.12 and 1.82. By looking up the values in the standard normal distribution table or using software, we find this probability to be approximately 0.845.

2. P(z < 2.65): This represents the probability of z being less than 2.65. By consulting the standard normal distribution table or using software, we find this probability to be approximately 0.995.

3. P(z > 0.36): This is the probability of z being greater than 0.36. Again, referring to the standard normal distribution table or using software, we find this probability to be approximately 0.6406.

4. P(-2.89 < z < -0.32): This represents the probability of z falling between -2.89 and -0.32. After consulting the standard normal distribution table or using software, we find this probability to be approximately 0.4954.

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Find or evaluate the integral by completing the square. (Use C for the constant of integration. ) dx 4x Find the derivative of the exponential function. Y = xerºx dy dx Find the integral. (Use C for the constant of Integration. ) dx + 4

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Integral: To evaluate the integral ∫(4x)dx by completing the square, we can rewrite the integrand as a perfect square. The integrand can be expressed as 4(x) = (2x)^2.

∫(4x)dx = ∫(2x)^2 dx

Now, we can integrate using the power rule for integration:

= (2/3)(2x)^3 + C

= (8/3)x^3 + C

Therefore, the integral of 4x with respect to x is (8/3)x^3 + C, where C represents the constant of integration.

Derivative: To find the derivative of the exponential function y = x * e^(r * x), we can use the product rule of differentiation.

Let's differentiate term by term:

dy/dx = d/dx (x * e^(r * x))

Applying the product rule, we have:

dy/dx = x * d/dx(e^(r * x)) + e^(r * x) * d/dx(x)

The derivative of e^(r * x) with respect to x is r * e^(r * x), and the derivative of x with respect to x is 1. Substituting these values, we get:

dy/dx = x * (r * e^(r * x)) + e^(r * x) * 1

dy/dx = r * x * e^(r * x) + e^(r * x)

Therefore, the derivative of the exponential function y = x * e^(r * x) with respect to x is r * x * e^(r * x) + e^(r * x).

Integral: Unfortunately, you haven't provided the function inside the integral. Please provide the function so that I can assist you in finding the integral.

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[-/2 Points] DETAILS HARMATHAP12 12.4.006. MY NOTES Find the cost of producing 30 units (to the nearest dollar). $ 3 PRACTICE ANOTHER Cost, revenue, and profit are in dollars and x is the number of units. If the marginal cost for producing a product is MC = 86-4e-0.01x, with a fixed cost of $8,200, find the total cost function. C(x) #

Answers

The cost function for producing x units is C(x) = 0.01x^2 - 86x + 8,200.

To find the total cost function, we need to calculate the sum of the fixed cost and the marginal cost multiplied by the number of units produced. The fixed cost is given as $8,200.

The marginal cost function is MC = 86 - 4e^(-0.01x). This equation represents the additional cost incurred for producing each additional unit. It is a decreasing exponential function, which means that as the number of units produced increases, the marginal cost decreases.

To obtain the total cost function, we multiply the marginal cost by the number of units produced and add it to the fixed cost:

C(x) = 86x - 4e^(-0.01x) * x + 8,200.

Simplifying the equation, we get:

C(x) = 86x - 0.04x * e^(-0.01x) + 8,200.

This equation represents the total cost of producing x units, taking into account both the fixed cost and the varying marginal cost based on the number of units produced.

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The total cost function is C(x) = 8200 + 86x - 4e^(-0.01x).

The total cost function is determined by adding the fixed cost of $8,200 to the marginal cost of producing x units. The marginal cost function is given as MC = 86 - 4e^(-0.01x). The term "MC" represents the marginal cost, which is the additional cost incurred for producing one additional unit. The formula for marginal cost indicates that the cost decreases exponentially as the number of units increases. The term "e" represents Euler's number (approximately 2.71828), and the exponent in the formula ensures the exponential decrease in cost.

To find the total cost, we add the fixed cost of $8,200 to the marginal cost. This gives us the total cost function C(x) = 8200 + 86x - 4e^(-0.01x). This equation allows us to calculate the total cost for any given number of units produced.

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Find y as a function of t if with y(0) = 7, y'(0) = 7. y = 1600y" - 9y = 0

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Given the differential equation y = 1600y" - 9y = 0, with initial conditions y(0) = 7 and y'(0) = 7, we need to find y as a function of t.

To solve the differential equation, we can assume a solution of the form y = e^(rt), where r is a constant. We substitute this solution into the equation to find the characteristic equation:

1600r^2e^(rt) - 9e^(rt) = 0.

Factoring out e^(rt) gives us:

e^(rt)(1600r^2 - 9) = 0.

For this equation to hold, either e^(rt) = 0 (which is not possible) or 1600r^2 - 9 = 0.

Solving 1600r^2 - 9 = 0, we find r = ±3/40.

Using these values of r, the general solution to the differential equation is:

y(t) = Ae^(3t/40) + Be^(-3t/40),

where A and B are constants determined by the initial conditions.

Using the given initial condition y(0) = 7, we can substitute t = 0 and y = 7 into the general solution:

7 = Ae^(0) + Be^(0),

7 = A + B.

Using the other initial condition y'(0) = 7, we differentiate the general solution:

y'(t) = (3A/40)e^(3t/40) - (3B/40)e^(-3t/40).

Substituting t = 0 and y'(0) = 7 into this expression, we have:

7 = (3A/40)e^(0) - (3B/40)e^(0),

7 = (3A/40) - (3B/40).

From these equations, we can solve for A and B. Upon finding their values, we substitute them back into the general solution y(t) to obtain y as a function of t.

Therefore, the final result is y(t) = ... (expression involving constants A and B).

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Given the differential equation y = 1600y" - 9y = 0, with initial conditions y(0) = 7 and y'(0) = 7, we need to find y as a function of t.

To solve the differential equation, we can assume a solution of the form y = e^(rt), where r is a constant. We substitute this solution into the equation to find the characteristic equation:

1600r^2e^(rt) - 9e^(rt) = 0.

Factoring out e^(rt) gives us:

e^(rt)(1600r^2 - 9) = 0.

For this equation to hold, either e^(rt) = 0 (which is not possible) or 1600r^2 - 9 = 0.

Solving 1600r^2 - 9 = 0, we find r = ±3/40.

Using these values of r, the general solution to the differential equation is:

y(t) = Ae^(3t/40) + Be^(-3t/40),

where A and B are constants determined by the initial conditions.

Using the given initial condition y(0) = 7, we can substitute t = 0 and y = 7 into the general solution:

7 = Ae^(0) + Be^(0),

7 = A + B.

Using the other initial condition y'(0) = 7, we differentiate the general solution:

y'(t) = (3A/40)e^(3t/40) - (3B/40)e^(-3t/40).

Substituting t = 0 and y'(0) = 7 into this expression, we have:

7 = (3A/40)e^(0) - (3B/40)e^(0),

7 = (3A/40) - (3B/40).

From these equations, we can solve for A and B. Upon finding their values, we substitute them back into the general solution y(t) to obtain y as a function of t.

Therefore, the final result is y(t) = ... (expression involving constants A and B).

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Determine whether or not F is a conservative vector field. If it is, find a function f such that F= V. (If the vector field is not conservative, enter DNE.) F(x, y) = (in(y) + 16xy) + (24x³y² + x/1 F(x, y) =

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The given vector field F(x, y) = (in(y) + 16xy) + (24x³y² + x/1) is non-conservative, and it's impossible to find a function f such that F = V.

We are given F(x, y) = (in(y) + 16xy) + (24x³y² + x/1

The curl of a vector field measures the degree to which it behaves like a spinning field.

The curl is zero if and only if the field is conservative;

otherwise, it is non-conservative and the line integral of the field around a closed path is not zero, since the field spins around the path, in general, giving a net effect.

Therefore, let's calculate the curl of F.

∂F₂/∂x = 24xy² + 1/1.∂F₁/∂y = 1/1.∂F₁/∂x = 16y.∂F₂/∂y = in'(y) + 48x²y.

We will now substitute these into the formula to get the curl of F.

curl F = ∂F₂/∂x - ∂F₁/∂y = (24xy² + 1) - (0) = 24xy² + 1.

The curl of F is non-zero, and as such, F is non-conservative, which means there is no function f such that F = V. Therefore, the answer is DNE.

Therefore, the given vector field F(x, y) = (in(y) + 16xy) + (24x³y² + x/1) is non-conservative, and it's impossible to find a function f such that F = V.

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. Find the homogenous linear differential equation with constant coefficients that has the following general solution: y=ce-5x +Czxe-5x . Solve the initial-value problem. y" - 16y=0 y (0) = 4 y' (0) = -4

Answers

The homogeneous linear differential equation with constant coefficients is y"-16y=0 and the solution to the given initial-value problem is

y = 1/8[e4x + (2 + √11)xe(-4 + √11)x + (2 - √11)xe(-4 - √11)x].

Given,The general solution of the differential equation is,

y = ce-5x + Czxe-5x

The given equation is a homogeneous linear differential equation with constant coefficients of the second order because the equation is of the form

y" + ay' + by = 0.

where the general form of the homogeneous linear differential equation with constant coefficients of the second order is,

y″+py′+qy=0

where p and q are constants.The given general solution is,

y = ce-5x + Czxe-5x

For c=0,

y = Czxe-5x

Consider x = 0,

y = 4y

= Czx0e0c

= 4

=> C = 4/z

Also,

y′ = Cze-5x(-5) + Czxe-5x(-5 + 1)

= (-25C + Czxe-5x)

The given initial value of the differential equation is,

y(0) = 4,

y′(0) = -4

On substituting the values in the obtained values, we get

4 = Cz*1

=> C = 4/z

And,

-4 = -25C + Cz

=> -4 = -25(4/z) + Cz

=> -4z = -100 + z2

=> z2 + 4z - 100 = 0

=> z = -4 + √116

z = -4 - √116

Thus, the solution of the given differential equation y"-16y=0 is given by,

y = 1/8[e4x + (2 + √11)xe(-4 + √11)x + (2 - √11)xe(-4 - √11)x]

Hence, the homogeneous linear differential equation with constant coefficients is y"-16y=0 and the solution to the given initial-value problem is

y = 1/8[e4x + (2 + √11)xe(-4 + √11)x + (2 - √11)xe(-4 - √11)x].

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A rectangular surface of 4 m2 was exposed to solar radiation of 1400 W/m2. The temperature of the surface was maintained at 500K. The spectral absorptivity of the surface is given as 0 for 0> λ (μm) < 0.5, 0.8 for 0.5> λ (μm)< 1, 0 for 1< λ (μm) < 2, and 0.9 for λ (μm)>2. Assuming the surface is diffuse and the sun temperature is 5800K, calculate the absorbed irradiation, radiosity, and net radiation heat transfer from the surface.

Answers

The absorbed irradiation is 4480 W, the radiosity is 2.5 x 10⁻⁴ W, and the net radiation heat transfer from the surface is -2.1 x 10⁻⁴ W.

We have,

A rectangular surface of 4 m² was exposed to solar radiation of 1400 W/m².

The temperature of the surface was maintained at 500K

For the absorbed irradiation, radiosity, and net radiation heat transfer from the surface, we'll need to consider the Stefan-Boltzmann law and the spectral absorptivity of the surface.

Absorbed irradiation (Q{absorbed}):

The absorbed irradiation is the amount of solar radiation absorbed by the surface. It can be calculated using the formula:

Q (absorbed) = Absorptivity Solar irradiation Surface area

Since the surface is rectangular with an area of 4 m² and the solar radiation is 1400 W/m², calculate the absorbed irradiation as follows:

Q (absorbed) = (0.8 × 1400 W/m²) 4 m²

= 4480 W

Radiosity (J):

Radiosity is the total radiative flux leaving the surface.

It can be calculated using the Stefan-Boltzmann law:

J = Emissive power

= Emittance × Surface area

The surface is diffuse, meaning it emits radiation according to its own temperature and emissivity.

To calculate the emissivity, we'll use the spectral absorptivity values provided:

Emissivity = (0.8 × 0.5) + (0 (1 - 0.5)) + (0.9 × (2 - 1))

= 2.2

J = Emissivity Stefan-Boltzmann constant (Surface temperature)⁴ × Surface area

J = 2.2 (5.67 x 10⁻⁸ W/m²K⁴) (500 K)⁴ * 4 m²

J = 2.5 × 10⁻⁴ W

Net radiation heat transfer (Q_net):

The net radiation heat transfer is the difference between the absorbed irradiation and the radiosity:

Q(net) = Q(absorbed) - J

Q (net ) = 4480 W - 2.5 x 10⁻⁴ W

= -2.1 x 10⁻⁴ W

Therefore, the absorbed irradiation is 4480 W, the radiosity is 2.5 x 10⁻⁴ W, and the net radiation heat transfer from the surface is -2.1 x 10⁻⁴ W. The negative sign indicates that the heat is transferred from the surface to the surroundings.

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Given the following mixture devise a separation scheme that will physically separate each component. Sand, Toluene, Ethyl Alcohol, Benzene, and Iron Filings D. Page Four: Describe the steps for the separation scheme and explain the order of methods used.

Answers

The separation scheme for the given mixture would involve multiple methods in a specific order.

To separate the components of the mixture, the following steps can be followed:

Magnetic Separation: Iron filings can be separated from the mixture using a magnet. Since iron is magnetic, the magnet will attract the iron filings, allowing them to be easily removed from the mixture.

Decantation: Toluene and ethyl alcohol can be separated from the mixture by decantation. Both toluene and ethyl alcohol are liquids, while sand and iron filings are solids. By carefully pouring the mixture into another container, the lighter liquids (toluene and ethyl alcohol) can be separated from the heavier solids (sand and iron filings). The liquids can be collected while leaving the solids behind.

Distillation: The remaining mixture containing sand, toluene, and ethyl alcohol can undergo distillation. Distillation is a process that separates components based on their boiling points. Toluene has a boiling point of 110.6°C, while ethyl alcohol has a boiling point of 78.5°C. By heating the mixture, the toluene and ethyl alcohol will vaporize, and their vapors can be condensed and collected separately.

Separation of Benzene: Benzene can be separated from the mixture by using a suitable solvent such as water. Benzene is immiscible with water, which means it does not dissolve in water. By adding water to the mixture, the benzene will form a separate layer on top, allowing it to be easily separated.

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Help yalll I really need help major time

Answers

Answer:

Annalise is correct because the outputs are closest when x = 1.35

Step-by-step explanation:

The solution to the equation 1/(x-1) = x² + 1 means the one x value that will make both sides equal. If we look at the table, notice how when x = 1.35, f(x) values are closest to each other for both equations, signifying that x = 1.35 is approximately the solution. Thus, Annalise is correct.

3-Consequencing or consequence mapping is: * O a randomize way of foreseeing the impact of a trend to market O through using 3 or 5 what questions to foresee the impact of a trend O the first step of trend management system O All the above 4- Rational consequencing is a structured way of foreseeing the impact of the trend True False 5- Rational consequencing is considering the positive and negative effect of a trend in the Market. GCs, and Subcontractor domains True False

Answers

Consequencing or consequence mapping is a structured and objective approach to analyzing the potential impact of a trend on a market or an organization.

It is also considered as the first step of trend management systems. The process involves using three to five what questions to anticipate the effect of a particular trend.The questions usually asked in the consequence mapping approach are as follows:What would happen if the trend continues?What would happen if we do nothing?What would happen if we do the opposite?What are the consequences of the trend?What is the outcome if the trend is reversed?Consequencing helps in decision-making by providing possible results of different choices. It assists the trend analysts in analyzing and predicting the potential consequences of different trends that could occur in the future.Rational consequencing is a structured way of foreseeing the impact of the trend, and it is considered true. This approach considers both positive and negative consequences of a trend in the Market, GCs, and subcontractor domains. It is an objective approach that provides an analysis of the potential benefits and drawbacks of any trend.The rational consequencing approach is helpful in understanding the potential risks and benefits of implementing a particular trend. It also helps in minimizing the uncertainties and risks by providing a clear picture of the effects of the trend on different domains. Therefore, rational consequencing is a valuable approach that assists analysts in making the right decisions.

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(a) Find the equation of the sphere which touches the sphere x+y+z²+2x+6y+1 = 0 at the point (1,2-2) and passes through the origin. (b) Find the equation of the cone whose vertex is at the point (1, 1, 3) and which passes through the ellipse 4x² + 2 = 1, y = 4.

Answers

The equation of the sphere that touches the sphere x+y+z²+2x+6y+1 = 0 at the point (1,2,-2) and passes through the origin is:

(x - 1)² + (y - 2)² + (z + 2)² = 45

To find the equation of the sphere, we need to determine its center and radius. Given that the sphere touches the given sphere at the point (1,2,-2), the center of the new sphere will also be (1,2,-2).

To find the radius, we can calculate the distance between the center of the new sphere and the origin (0,0,0). Using the distance formula, the radius is equal to the square root of the sum of the squares of the differences in coordinates:

Radius = √((1 - 0)² + (2 - 0)² + (-2 - 0)²)

      = √(1 + 4 + 4)

      = √9

      = 3

Substituting the center and radius into the general equation of a sphere, we get:

(x - 1)² + (y - 2)² + (z + 2)² = 3²

(x - 1)² + (y - 2)² + (z + 2)² = 9

(x - 1)² + (y - 2)² + (z + 2)² = 45

Therefore, the equation of the sphere that satisfies the given conditions is (x - 1)² + (y - 2)² + (z + 2)² = 45.

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a) The population of Suffolk County, NY is projected to be 1,534,811 in the
year 2040. In the year 2000, the average per capita water use in Suffolk County was 112
gallons per person per day. What is the estimated water use (in million gallons per day) in
Suffolk County in 2040 if water conservation efforts reduce per capita water use by 15%
compared to the year 2000?
b) In the year 2000, Public Water Systems in the State of New York supplied
2560 million gallons of water per day to 17.1 million people for both domestic and
industrial use. what is the average per capita sewage flow in New York assuming a return
of 67% of the supply?

Answers

a) The average per capita sewage flow in New York is 100 gallons per person per day.

b) The estimated water use in Suffolk County in 2040 is approximately 146,221,067.2 gallons per day.

a) To find the estimated water use in Suffolk County in 2040, we need to consider the projected population and the change in per capita water use compared to the year 2000.

First, we calculate the reduction in per capita water use by multiplying the average per capita water use in 2000 (112 gallons per person per day) by 15% (0.15).

112 gallons/day * 0.15 = 16.8 gallons/day

Next, we subtract this reduction from the average per capita water use in 2000 to find the estimated per capita water use in 2040.

112 gallons/day - 16.8 gallons/day = 95.2 gallons/day

Finally, we multiply the estimated per capita water use in 2040 (95.2 gallons/day) by the projected population of Suffolk County in 2040 (1,534,811 people) to find the estimated water use in Suffolk County in 2040.

95.2 gallons/day * 1,534,811 people = 146,221,067.2 gallons/day

Therefore, the estimated water use in Suffolk County in 2040 is approximately 146,221,067.2 gallons per day.

b) To find the average per capita sewage flow in New York, we need to calculate the return of the water supply and divide it by the number of people.

First, we calculate the return of the water supply by multiplying the total water supplied by the return rate of 67%.

2560 million gallons/day * 0.67 = 1715.2 million gallons/day

Next, we divide the return of the water supply by the number of people to find the average per capita sewage flow.

1715.2 million gallons/day / 17.1 million people = 100 gallons/person/day

Therefore, the average per capita sewage flow in New York is 100 gallons per person per day.

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Let W={(a,b,0,b):a,b∈R} with the standard operations in R^4. Which of the following statements is true? W is not a subspace of R^4 because (0,0,0,0)∈/W W is a subspace of R^4 The above is true The above is true None of the mentioned (1,1,1,1)∈W

Answers

W is a subspace of R^4.

Why is W a subspace of R^4?

To determine if W is a subspace of R^4, we need to check if it satisfies the three properties of a subspace: closure under addition, closure under scalar multiplication, and contains the zero vector (0, 0, 0, 0).

1. Closure under addition: For any two vectors (a, b, 0, b) and (c, d, 0, d) in W, their sum is (a + c, b + d, 0, b + d), which is also in W. So, W is closed under addition.

2. Closure under scalar multiplication: For any scalar k and vector (a, b, 0, b) in W, k(a, b, 0, b) = (ka, kb, 0, kb), which is also in W. Thus, W is closed under scalar multiplication.

3. Contains the zero vector: W contains the zero vector (0, 0, 0, 0).

Since W satisfies all three properties, it is a subspace of R^4.

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Please please please please please please please SOMONE help please

Answers

Answer:

all real numbers greater than or equal to 2

Step-by-step explanation:

the range of a function is the values that y can have.

the minimum value of y is at y = 2

the solid blue circle indicates that y can equal 2.

above y = 2 the values of y keep increasing

range is y ≥ 2 , y ∈ R

136 mL of 0.00015 M Pb(NO3)2 and 234 mL of 0.00028 M Na2SO4 are mixed(Volumes are additive). Will a precipitate form? Hint: Each solution ‘dilutes’ the other upon mixing.

Answers

Upon mixing 136 mL of 0.00015 M Pb(NO3)2 and 234 mL of 0.00028 M Na2SO4, no precipitate will form.

When two solutions are mixed, a precipitate can form if the product of the concentrations of the ions involved in the potential reaction exceeds the solubility product constant (Ksp) of the compound.

In this case, we have Pb(NO3)2 and Na2SO4. The possible reaction between these two compounds is as follows:

Pb(NO3)2 + Na2SO4 → PbSO4 + 2NaNO3

To determine if a precipitate will form, we need to compare the product of the concentrations of the ions involved in the reaction with the solubility product constant (Ksp) of PbSO4.
First, let's calculate the moles of each compound in the solutions:

Moles of Pb(NO3)2 = Volume of Pb(NO3)2 solution (in L) x Concentration of Pb(NO3)2 (in M)
                  = 0.136 L x 0.00015 M
                  = 2.04 x 10^(-5) mol

Moles of Na2SO4 = Volume of Na2SO4 solution (in L) x Concentration of Na2SO4 (in M)
                = 0.234 L x 0.00028 M
                = 6.552 x 10^(-5) mol

From the balanced chemical equation, we can see that 1 mole of Pb(NO3)2 reacts with 1 mole of Na2SO4 to form 1 mole of PbSO4. Therefore, the moles of PbSO4 formed will be equal to the moles of the limiting reactant, which is the one with the smaller number of moles.
In this case, Pb(NO3)2 is the limiting reactant because it has fewer moles than Na2SO4. So, 2.04 x 10^(-5) mol of PbSO4 will form.

Now, let's calculate the concentrations of the ions involved in the reaction:

Concentration of Pb2+ = Moles of Pb2+ / Total volume of the solution (in L)
                     = 2.04 x 10^(-5) mol / (0.136 L + 0.234 L)
                     = 4.92 x 10^(-5) M

Concentration of SO4^(2-) = Moles of SO4^(2-) / Total volume of the solution (in L)
                        = 2.04 x 10^(-5) mol / (0.136 L + 0.234 L)
                        = 4.92 x 10^(-5) M

The product of the concentrations of Pb2+ and SO4^(2-) is (4.92 x 10^(-5) M) x (4.92 x 10^(-5) M) = 2.42 x 10^(-9).

The solubility product constant (Ksp) of PbSO4 is 1.6 x 10^(-8).

Since the product of the concentrations of the ions involved in the reaction (2.42 x 10^(-9)) is less than the solubility product constant (1.6 x 10^(-8)), a precipitate of PbSO4 will not form.

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A piston-cylinder initially contains 0.447 m³ of air at 204.9 kPa and 75 C. The air then compressed at constant temperature until the final volume becomes 0.077 m², what is the boundary work (kJ)? B. 161.08 C-161.08 D.-27.75 E. 75.81

Answers

the boundary work done during the compression process is approximately -75,753 kJ.

To calculate the boundary work done during the compression process, we can use the formula:

Boundary work (W) = P * ΔV

Where:

P is the constant pressure during the compression process, and

ΔV is the change in volume.

Given:

Initial volume (V1) = 0.447 m³

Final volume (V2) = 0.077 m³

Initial pressure (P1) = 204.9 kPa

First, we need to convert the pressure from kilopascals (kPa) to pascals (Pa) because the SI unit for pressure is the pascal.

P1 = 204.9 kPa = 204.9 * 1000 Pa = 204900 Pa

Next, we calculate the change in volume:

ΔV = V2 - V1

   = 0.077 m³ - 0.447 m³

   = -0.37 m³

Note that the change in volume is negative because the air is being compressed.

Now, we can calculate the boundary work:

W = P * ΔV

 = 204900 Pa * (-0.37 m³)

 = -75,753 kJ

The negative sign indicates that work is done on the system during compression.

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Determine the range of the angle θ, measured from the
horizontal, with which the hose must be
directed so that the water touches the bottom of the wall at point
B and the point of the wall at A. It i

Answers

The range of the angle θ, measured from the horizontal, can be determined by analyzing the geometry and the desired points of contact on the wall.

To find the range of angle θ, we need to consider the given points B and A on the wall. Point B represents the desired point of contact between the water and the bottom of the wall, while point A represents the desired point of contact on the wall itself. By examining the geometry of the situation, we can determine the necessary angle θ that achieves these conditions.

The angle θ can be visualized as the angle at which the hose needs to be directed in order to achieve the desired water trajectory. By considering the height of the wall, the distance between points B and A, and the range of motion of the hose, we can calculate the required range of θ.

It is important to note that additional factors, such as the velocity of the water exiting the hose and the effects of air resistance, may influence the actual range of the angle. These factors should be taken into account for a more precise analysis.

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List the interval(s) on which the function is increasing: _______

List the interval(s) on which the function is decreasing: _______

Answers

The intervals of the function in this problem are given as follows:

Increasing: (-∞, -1) U (2, ∞). Decreasing: (-1,2).

When a function is increasing and when it is decreasing, looking at it's graph?

Looking at the graph, we get that a function f(x) is increasing when it is "moving northeast", that is, to the right and up on the graph, meaning that when the input variable represented x increases, the output variable represented  by y also increases.Looking at the graph, we get that a function f(x) is decreasing when it is "moving southeast", that is, to the right and down the graph, meaning that when the input variable represented by x increases, the output variable represented by y decreases.

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The student council decided to spend $170 of their $1,000 budget on decorations. What fraction represents the amount of money spent on decorations?

Answers

Answer:

[tex]\frac{17}{100}[/tex]

Step-by-step explanation:

[tex]\frac{170}{1000}[/tex] simplified give you [tex]\frac{17}{100}[/tex]

As a fraction it is: [tex]\frac{17}{100}[/tex]

As a decimal it is: 0.17

As a percentage it is: 17%

Suppose that an economy has the per-worker production function given as: y t

=4k 1
0.5

, where y is output per worker and k is capital per worker. In addition, national savings is given as: S t

=0.40Y t

, where S is national savings and Y is total output. The depreciation rate is d=0.10 and the population growth rate is n=0.05. The steady-state value of the capital-labor ratio, k is 113.78. The steady-state value of output per worker. y is 42.67. The steady-state value of consumption per worker, c is 25.60. Use the same production function, and the original savings rate of 0.40. However, increase the population growth rate to 0.08. S t

=0.40Y t

The depreciation rate is d=0.10 and the population growth rate is n=0.08. (Enter all responses as decimals rounded to two places.) What is the new steady-state value of the capital-labor ratio, K ? What is the new steady-state value of output per worker, y ? What is the new steady-state value of consumption per worker, c ?

Answers

Increasing the population growth rate decreases the steady-state values of the capital-labor ratio, output per worker, and consumption per worker.

What is the impact of increasing the population growth rate on the steady-state values of capital-labor ratio, output per worker, and consumption per worker?

To find the new steady-state values of the capital-labor ratio (K), output per worker (y), and consumption per worker (c), we need to apply the changes in the population growth rate (n) while keeping the other parameters constant.

Given:

Original steady-state values:

Capital-labor ratio (k) = 113.78

Output per worker (y) = 42.67

Consumption per worker (c) = 25.60

New parameters:

Population growth rate (n) = 0.08

To find the new steady-state values, we'll use the following equations:

1. New steady-state capital-labor ratio (K):

K = (s * Y) / (d + n + g)

where s is the savings rate, Y is the total output, d is the depreciation rate, n is the population growth rate, and g is the technological progress rate (assumed to be zero in this case).

2. New steady-state output per worker (y):

y = Y / L

where L is the labor force.

3. New steady-state consumption per worker (c):

c = (1 - s) * y

Let's calculate the new steady-state values using the given information:

1. New steady-state capital-labor ratio (K):

K = (0.40 * Y) / (0.10 + 0.08)

K = 0.40Y / 0.18

K = 2.22Y

2. New steady-state output per worker (y):

y = Y / L

y = Y / (L0 * (1 + n))

y = 42.67 / (113.78 * (1 + 0.08))

y ≈ 42.67 / 122.96

y ≈ 0.347

3. New steady-state consumption per worker (c):

c = (1 - s) * y

c = (1 - 0.40) * 0.347

c ≈ 0.60 * 0.347

c ≈ 0.208

Therefore, the new steady-state values are approximately:

New steady-state capital-labor ratio (K) ≈ 2.22Y

New steady-state output per worker (y) ≈ 0.347

New steady-state consumption per worker (c) ≈ 0.208

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Find the parametric equation of the plane z passing through the points P=(1,0,0), Q- (0, 1,0) and S(0,0,1). Determine a point belonging to the plane and whose distance from P is equal to √2

Answers

The parametric equation of the plane passing through the points P=(1,0,0), Q=(0,1,0), and S=(0,0,1) is:

x = t

y = t

z = 1 - t

To find the parametric equation of a plane, we need to determine its normal vector. We can obtain the normal vector by taking the cross product of two vectors formed by the given points. Taking PQ and PS as two vectors, we have:

PQ = Q - P = (0-1, 1-0, 0-0) = (-1, 1, 0)

PS = S - P = (0-1, 0-0, 1-0) = (-1, 0, 1)

Taking the cross product of PQ and PS gives us the normal vector:

N = PQ x PS = (-1, 1, 0) x (-1, 0, 1) = (1, 1, 1)

Now that we have the normal vector, we can write the equation of the plane as:

Ax + By + Cz + D = 0

Substituting the values from the normal vector, we get:

x + y + z + D = 0

To find D, we can substitute the coordinates of one of the given points. Let's use P=(1,0,0):

1 + 0 + 0 + D = 0

D = -1

Therefore, the equation of the plane is:

x + y + z - 1 = 0

To express this equation in parametric form, we can choose one of the variables (say, t) as a parameter and express the other variables in terms of it. In this case, we choose t:

x = t

y = t

z = 1 - t

A point on the plane can be obtained by substituting a value of t in the parametric equations. To find a point whose distance from P is equal to √2, we can substitute t = √2 into the equations:

x = √2

y = √2

z = 1 - √2

Therefore, a point belonging to the plane and whose distance from P is √2 is (√2, √2, 1 - √2).

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Draw the skeletal ("line") structure of 9-methyl-7propyl-1,2,4-decanetriol.

Answers

The numbers indicate the position of the methyl (CH3) and propyl (CH2CH2CH3) groups on the carbon chain.

Here is the skeletal or line structure representation of 9-methyl-7-propyl-1,2,4-decanetriol:

      CH3       CH3       CH3

        |           |           |

   CH3 - C - C - C - C - C - C - C - C - OH

        |           |           |

        CH2       CH2       CH2

         |           |           |

        CH3       CH3       CH3

In this structure, the horizontal lines represent carbon-carbon (C-C) bonds, and the vertical lines represent carbon-hydrogen (C-H) bonds. The OH groups attached to the carbon atoms are indicated by the "OH" label.

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Which quadrilateral makes this statement true?

Answers

Answer:

Quadrilateral CBAD

Step-by-step explanation:

Because of symmetry, the following pairs of sides are congruent:

AB and CB

AD and CD

Answer: Quadrilateral CBAD

Find 3/7 plus 6/-11 plus -8/21 plus 5/22

Answers

To find the sum of fractions, we need to have a common denominator. In this case, the common denominator is 7 * (-11) * 21 * 22 = -230,514.

Now we can add the fractions:

[tex]\displaystyle \frac{3}{7} + \frac{6}{-11} + \frac{-8}{21} + \frac{5}{22} = \frac{3 \cdot (-11) \cdot 21 \cdot 22}{7 \cdot (-11) \cdot 21 \cdot 22} + \frac{6 \cdot 7 \cdot (-21) \cdot 22}{-11 \cdot 7 \cdot (-21) \cdot 22} + \frac{-8 \cdot 7 \cdot (-11) \cdot 22}{21 \cdot 7 \cdot (-11) \cdot 22} + \frac{5 \cdot 7 \cdot (-11) \cdot 21}{22 \cdot 7 \cdot (-11) \cdot 21}[/tex]

Simplifying the fractions:

[tex]\displaystyle \frac{-1386}{-230514} + \frac{1848}{-230514} + \frac{-1936}{-230514} + \frac{1155}{-230514}[/tex]

Combining the fractions:

[tex]\displaystyle \frac{-1386 + 1848 - 1936 + 1155}{-230514}[/tex]

Simplifying the numerator:

[tex]\displaystyle \frac{-319}{-230514}[/tex]

Dividing the numerator and denominator:

[tex]\displaystyle \frac{319}{230514}[/tex]

Therefore, the sum of the fractions 3/7, 6/-11, -8/21, and 5/22 is 319/230514.

[tex]\huge{\mathfrak{\colorbox{black}{\textcolor{lime}{I\:hope\:this\:helps\:!\:\:}}}}[/tex]

♥️ [tex]\large{\underline{\textcolor{red}{\mathcal{SUMIT\:\:ROY\:\:(:\:\:}}}}[/tex]

Compute the volume of the solid bounded by the hemisphere z = √4c²-x² - y² and the horizontal plane z = c by using spherical coordinates, where c> 0.

Answers

The volume of the solid bounded by the hemisphere z = √(4c² - x² - y²) and the horizontal plane z = c, using spherical coordinates, is π²c⁴/36.

Understanding Hemisphere

In spherical coordinates, the variables are typically denoted as ρ, θ, and φ.

ρ = the radial distance from the origin to the point in space,

θ = the azimuthal angle measured from the positive x-axis in the xy-plane, and

φ = the polar angle measured from the positive z-axis.

Given that the hemisphere is defined as:

z = √(4c² - x² - y²)

and the horizontal plane is defined as:\

z = c

we can see that the limits for the variables ρ, θ, and φ are as follows:

ρ: 0 to c

θ: 0 to 2π (a full circle)

φ: 0 to π/2 (since the hemisphere lies above the xy-plane)

Now, let's calculate the volume using the integral in spherical coordinates:

V = ∫∫∫ ρ² sin(φ) dρ dθ dφ

Where the limits for the integrals are:

ρ: 0 to c

θ: 0 to 2π

φ: 0 to π/2

Let's evaluate this integral step by step:

V = ∫∫∫ ρ² sin(φ) dρ dθ dφ

  = [tex]\int\limits^{\frac{\pi}{2} }_0\int\limits^{2\pi}_0 \int\limits^c_0 {\rho^{2} sin(\phi)} \, d {\rho} \, d {\theta} \, d\phi[/tex]

We can integrate the ρ integral first:

V = [tex]\int\limits^{\frac{\pi}{2} }_0\int\limits^{2\pi}_0 \[\frac{\rho^{3}}{3} sin(\phi)]} \, d {\theta} \, d\phi[/tex]

  = [tex]\frac{1}{3} \int\limits^{\frac{\pi}{2} }_0\int\limits^{2\pi}_0 \[\rho^{3}sin(\phi)]} \, d {\theta} \, d\phi[/tex]

Next, we integrate the θ integral:

V = (1/3) ∫₀^(π/2) [- (ρ³/3) cos(φ)]₀^(2π) dφ

  = (1/3) ∫₀^(π/2) (-2πρ³/3) dφ

Finally, we integrate the φ integral:

V = (1/3) [- (2πρ³/3) φ]₀^(π/2)

  = (1/3) (- (2πρ³/3) (π/2))

  = -π²ρ³/9

Now, substituting the limits for ρ:

V = -π²/9 ∫₀^(π/2) ρ³ dφ

  = -π²/9 [(ρ⁴/4)]₀^(π/2)

  = -π²/9 [(c⁴/4) - (0/4)]

  = -π²c⁴/36

Finally, taking the absolute value of the volume:

|V| = π²c⁴/36

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The current exchange rates show that C$1.00=£0.6370. If you have C$250, what is the equivalent amount in British pounds? a. £392.46 b. £105 C. £159.25 d. £430.97 e. £200

Answers

The current exchange rates show that C$1.00=£0.6370, the  equivalent amount in British pounds for C$250 will be c. £159.25.

To find the equivalent amount in British pounds for C$250, we can use the given exchange rate:

C$1.00 = £0.6370

We need to multiply C$250 by the exchange rate to convert it into British pounds:

£ = C$250 * £0.6370

Calculating:

£ ≈ 250 * 0.6370

£ ≈ 159.25

Therefore, the equivalent amount in British pounds for C$250 is approximately £159.25.

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Which of the following explanations / definitions for a topographic map is NOT correct A)Topographic maps are a valuable source of information both above and below water. Detail varies greatly but if a tackle store has a hydrographic chart or map of a lake you will be boating and fishing, pick one up and study it. B) A topographic map displays the physical shape and features on the surface of the earth usually in two-dimensional form using a plan view. This type of map would show the shape of the land as well as other natural features. C)A map showing topographic features, usually by means of contour lines. D)Topographic maps are suitable for a wide variety of applications, starting from emergency management, urban planning, surveying, resource development, to camping, canoeing, hunting and fishing. Thos maps represent the earth's features accurately and to scale, on a two-dimensional surface.

Answers

The correct answer is A) Topographic maps are a valuable source of information both above and below water.



A topographic map is a type of map that displays the physical shape and features on the surface of the Earth. It typically shows the shape of the land, including elevation, using contour lines. Topographic maps are valuable tools for various applications, such as emergency management, urban planning, surveying, resource development, camping, canoeing, hunting, and fishing. These maps accurately represent the Earth's features to scale on a two-dimensional surface.

Option A states that topographic maps are a valuable source of information both above and below water. However, this statement is not correct. Topographic maps primarily focus on the land surface and do not provide detailed information about underwater features or bathymetry. For information on underwater features, hydrographic charts or maps are used, which are specifically designed for mapping the features of bodies of water.

Therefore, the correct answer is A) Topographic maps are a valuable source of information both above and below water.

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A hydrocarbon (a compound consisting solely of carbon and hydrogen) is found to be 85.6% carbon by mass. What is the empirical formula for this compound? What will the molecular formula look like? What other information do you need in order to find the exact molecular formula?

Answers

The empirical formula for the given hydrocarbon compound is CH₂. The molecular formula would have a 1:2 ratio of carbon to hydrogen. Additional information, such as the molar mass of the compound, is needed to determine the molecular formula.

The empirical formula of a compound represents the simplest whole-number ratio of the atoms present in the compound. To find the empirical formula of the given hydrocarbon compound, we need to determine the ratio of carbon to hydrogen.

Given that the compound is 85.6% carbon by mass, we can assume that we have 100 grams of the compound. This means that there are 85.6 grams of carbon and 14.4 grams of hydrogen in the compound.

To find the ratio, we need to convert the mass of each element to moles by dividing it by their respective atomic masses. The atomic mass of carbon is 12.01 g/mol, and the atomic mass of hydrogen is 1.01 g/mol.

Moles of carbon = 85.6 g / 12.01 g/mol = 7.13 mol
Moles of hydrogen = 14.4 g / 1.01 g/mol = 14.3 mol

Now, we need to simplify the ratio by dividing both moles of carbon and hydrogen by the smaller value. The ratio of carbon to hydrogen is approximately 1:2.

So, the empirical formula of the compound is CH₂.

The molecular formula represents the actual number of atoms of each element present in a molecule. To determine the molecular formula, we need additional information such as the molar mass of the compound.

The molar mass of the compound can be determined experimentally or provided in the question. Once we know the molar mass, we can compare it to the empirical formula mass (the sum of the atomic masses in the empirical formula) to determine the number of empirical formula units in the molecular formula.

For example, if the molar mass of the compound is found to be 84 g/mol, we can divide it by the empirical formula mass (12.01 + 2.02 = 14.03 g/mol) to find that the molecular formula consists of approximately six empirical formula units. Therefore, the molecular formula would be C₆H₁₂.

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Each side of a square classroom is 7 meters long. The school wants to replace the carpet in the classroom with new carpet that costs $54.00 per square meter. How much will the new carpet cost? (a) Suppose that queue Q is initially empty. The following sequence of queue operations is executed: enqueue (5), enqueue (3), dequeue (), enqueue (2), enqueue (8), dequeue (), isEmpty(), enqueue (9), get FrontElement(), enqueue (1), dequeue (), enqueue (7), enqueue (6), getRearElement(), dequeue (), enqueue (4). (1) Write down the returned numbers (in order) of the above sequence of queue operations. (5 marks) (ii) Write down the values stored in the queue after all the above operations. (5 marks) (b) Suppose that stack S initially had 5 elements. Then, it executed a total of 25 push operations R+5 peek operations 3 empty operations R+1 stack_size operations 15 pop operations The mentioned operations were NOT executed in order. 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Find the point on the graph of z=2y22x2z=2y22x2 at which vector n=12,4,1n=12,4,1 is normal to the tangent plane.P=P= Suppose a graph has a million vertices. What would be a reason to use an adjacency matrix representation?choose oneIf the graph is sparse.If we often wish to iterate over all neighbors of a vertex.If the graph isn't "simple."If there is about a 50% chance for any two vertices to be connectedNone of the other reasons. What is an advantage of GC-MS? O substances with high boiling points are not compatible. O It provides the most accurate confirmation of Identification. O It is time consuming. It is labor intensive. QUESTION 2 Why is cyanide dangerous? O It causes an interruption of the central pathway for energy generation. It burns anything it comes into contact with. It inhibits the production of mitochondria. It prevents the nuclear membrane from allowing lons to pass through. OLLECTION Click Save and Submit to save and submit. Click Save All Answers to save all ansvers O An oscillating LC circuit consisting of a 1.3 nF capacitor and a 4.0 mH coil has a maximum voltage of 3.8 V. What are (a) the maximum charge on the capacitor, (b) the maximum current through the circuit, (c) the maximum energy stored in the magnetic field of the coil? (a) Number 4.9 Units nc (b) Number ___ Units A (c) Number ___ Units nJ Conduct an Internet search on the Genetic InformationNondiscrimination Act signed by PresidentBush. Do you think that act is fair to employers andemployees? Why or why not? Provide a historical context of the U.S.Census and reflect upon how the U.S. Census counts families and households. Explore the importance of U.S. Census and the updated emergence of individuality in modern society. You work for a company that exhibits at trade shows. Using figures from the last 30 trade shows, an employee claims that 55% of the attendees at trade shows are more likely to visit an exhibit when there is a giveaway. You select a sample of 1100 participants in a trade show and 720 agreed with this view. At a = 0.05, do you have enough evidence to reject the claim? Question 4 of 10 Which of these uses ethos? A. All of the other schools in our district offer organic foods in the lunchroom; therefore, our school should offer organic foods as well. B. Yum Organics has been providing well-rounded organic lunches to schools on the West Coast for more than 15 years. OC. The food at our school is O.K.; however, I wish we had more organic choices. D. We are starving because the food, if you can call this slop "food," at our school is not fit for the lowest grub on this fine Earth! SUBMIT Suppose that you are given a task to develop a very simple authentication protocol that uses signatures utilizing public key cryptography. How would you develop such a protocol? Explain clearly with help of an example. View Image to answerA. B. C. D. 8. (1) Just as there are rules of the road for drivers of cars, trucks, and buses, there are "rules of the sidewalk" forpedestrians. (2) The sociologist Erving Goffman points out that, for one thing, pedestrians on a sidewalk keep to theirright, relative to an imaginary dividing line in the middle of the sidewalk. (3) Thus people sort themselves into lanes goingin opposite directions, as on a vehicular roadway. (4) And people who are walking slowly often tend to stay closer to thebuildings, while to their left, in a "passing lane," are the people who are moving more quickly. (5) Also, like drivers,pedestrians scan the route ahead so that they can swerve around obstacles-say, a puddle or a hole in the walkway-and so that they will not collide with anyone else. (6) If a head-on collision seems possible, pedestrians will make eyecontact and maneuver to keep out of each other's way. (7) Goffman notes one obvious difference, though: rules of theroad are often codified in laws and regulations, whereas rules of the sidewalk are informal social customs.The sentence that expresses the main idea is: (Choose the number of the sentence. Then click "GO.") The graph of the function f(x) = (x + 6)(x + 2) is shown below.On a coordinate plane, a parabola opens down. It goes through (negative 6, 0), has a vertex at (negative 4, 4), and goes through (negative 2, 0).Which statement about the function is true?The function is increasing for all real values of x where x < 4.The function is increasing for all real values of x where6 < x < 2.The function is decreasing for all real values of x where x < 6 and where x > 2.The function is decreasing for all real values of x wherex < 4. A cylindrical slab has a polarization given by P = po pa. Find the polarization charge density pp, inside the slab and its surface charge density Pps: 5.38 Let z < 0 be region 1 with dielectric constant = 4, while z> 0 is region 2 with 2 = 7.5. Given that E = 60a, 100a, + 40a, V/m, (a) find P, (b) calculate D. 5.48 (a) Given that E = 15a, 8a, V/m at a point on a conductor surface, what is the surface charge density at that point? Assume & = o. (b) Region y 2 is occupied by a conductor. If the surface charge on the conductor is -20 nC/m, find D just outside the conductor. Suppose the going rate (i.e., the price) for a room at Hotel Madison is $50 per night. At that price, the hotel has an average of 40 occupants per night. After raising the rate to $150, this average decreases to 10 occupants. What is the elasticity of demand for hotel rooms at these rates? If necessary, round your answer to the nearest tenth and include leading zeros in a decimal. (That is, if you find an answer of 0.932, type "0.9").