A strain gauge has a resistance of 350 Ω and a gauge factor of 2
Design a schematic of the measurement circuitry that will measure the strain from 0 ~ 0.005. operational amplifiers can be used.The power supply is +-5V and the output voltage should be less than 5V
What is the output voltage of the circuit when the maximum strain of 0.005 is measured? Please show calculations
PLEASE SHOW THE SCHEMATIC

The values of R and C are: R = 12 Ω and C = 0.0272 F or 0.0072 F. We can calculate it in the following manner.

We can use the impedance formula for a series RL circuit to solve for R and C:

Z = R + j(ωC - 1/ωC)

where Z is the impedance, R is the resistance, C is the capacitance, and ω is the angular frequency.

Given that Z = 12 - 8j Ω and ω = 10⁴ r/s, we can solve for R and C as follows:

12 - 8j = R + j(10⁴C - 1/10⁴C)

Equating the real and imaginary parts:

12 = R

-8 = 10⁴C - 1/10⁴C

Multiplying both sides by 10⁴C:

-8(10⁴C) = 10⁸C² - 1

Rearranging:

10⁸C² + 8(10⁴)C - 1 = 0

Using the quadratic formula:

C = [-8(10⁴) ± √((8(10⁴))² + 4(10⁸))] / 2(10⁸)

C = [-8(10⁴) ± √(6.56 x 10¹²)] / 2(10⁸)

C = [-8(10⁴) ± 2.56 x 10⁶] / 2(10⁸)

C = [-0.04 ± 0.0128] F

C = 0.0272 F or 0.0072 F

Therefore, the values of R and C are:

R = 12 Ω

C = 0.0272 F or 0.0072 F

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Answer:

True

Explanation:

Spray gun plays an one of the most important roles in spray finishing as it directs air to atomize the fluid, gives the particles sufficient velocity to reach the product surface, and shapes the pattern/texture. Hope this helps you as much as intended.

Answer: True

Explanation:

The air cap on the spray gun plays an important role in spray finishing as it directs air to atomize the fluid, gives the particles sufficient velocity to reach the product surface, and shapes the pattern.

Answer:

(a) The ball's initial speed is 8.4 m/s

(b) The height of the ball  is 3.28 m

Explanation:

Given;

maximum height of the ball, H = 3.6 m

Apply conservation of energy;

¹/₂mu² + mgh = ¹/₂mv² + mgH

Where;

m is the mass of the ball

u is the initial velocity of the ball

v is the final velocity of the ball

h is the initial height of the ball

H is the maximum height of the ball

(a) The ball's initial speed, u;

¹/₂mu² + mgh = ¹/₂mv² + mgH

¹/₂u² + gh = ¹/₂v² + gH

make u the subject of the formula

\(u = \sqrt{v^2 +2gH -2gh} \\\\\)

at maximum height, the final velocity  = 0

maximum height H = 3.6 m

initial height, h = 0

g is acceleration due to gravity = 9.8 m/s²

\(u = \sqrt{0^2 +2*9.8*3.6 -2*9.8*0} \\\\u = \sqrt{2*9.8*3.6} \\\\u = 8.4 \ m/s\)

(b) The height of the ball when it has a speed of 2.5 m/s

v = 2.5 m/s

\(u = \sqrt{v^2 +2gH -2gh} \\\\u^2 = v^2 +2gH -2gh \ (h = 0)\\\\u^2 = v^2 +2gH\\\\2gH = u^2 - v_2\\\\H = \frac{u^2 - v^2}{2g} \\\\H = \frac{8.4^2 - 2.5^2}{2*9.8}\\\\H = 3.28 \ m\)

A) The ball's initial speed is : 8.4 m/s

B) The height of the ball when it has a speed of 2.5 m/s is : 3.28 m

Given data :

Maximum height reached by ball = 3.60 m

applying conservation of energy relation

¹/₂mu² + mgh = ¹/₂mv² + mgH -------- ( 1 )

where : u = initial velocity , v = final velocity , H = max height , h = initial height

Given that the value of m is not given equation ( 1 ) becomes

¹/₂u² + gh = ¹/₂v² + gH  --- ( 2 )

solve for u ( initial velocity )

u = \(\sqrt{v^2 +2gH -2gh}\)   ----- ( 3 )

where : g = 9.8 m/s², v = 0 , H = 3.60 m , h = 0

insert values into equation ( 3 )

u ( initial speed of ball ) = 8.4 m/s

applying equation ( 3 )

u = \(\sqrt{v^2 +2gH -2gh}\)

where : u = 8.4 m/s , v = 2.5 m/s ,  H = ? , h = 0

solve for H

H = u² - v² / 2g

   = ( 8.4² - 2.5² ) / ( 2 * 9.8 )

   = 3.28 m

Hence we can conclude that The ball's initial speed is : 8.4 m/s and The height of the ball when it has a speed of 2.5 m/s is : 3.28 m.

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Answer:

Option B: False

Explanation:

A heat engine is a device which operates in a manner that heat is converted into mechanical work.

A simple example of a heat engine is a drinking bird. The oscillatory motion of the drinking bird is as a result of the thermal expansion and contraction of a chemical compound in its beak, which creates an imbalance in its position of equilibrium. This causes it to oscillate.

Heat engines usually work by extracting heat once there is a temperature gradient available in the system and using it to perform work. Another good example is the internal combustion engine. It extracts heat from the explosion of the burning fuels and uses it to power the car.

Answer:

desire to make money that motivates people to produce and sell goods and services. ... rivalry among producers or sellers of similar goods and services to win more business. economic efficiency. wise use of available resources so that costs do no exceed benefits.

The power of the braking system is fundamentally measured in brake torque. The effective radius, or how far away from the hub center the brake caliper acts on the disc, is that distance.

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Brake torque is the primary measurement of the braking system's power. This distance is the effective radius, or the distance the brake caliper acts on the disc from the hub center.

To get the most out of an internal combustion engine's power and efficiency, the best ignition timing is needed to generate the most brake torque.

The ideal spark timing is always available for any engine operation. MBT works best with the throttle open, but idle engine operation is not ideal.

The term "brake torque" can be used to summarize the braking system's power. The effective radius is the distance from the hub center at which the brake caliper applies pressure to the disc.

The caliper's force divided by the system's effective radius is the braking torque. Brake torque is the force applied to the rotors to slow them down.

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Answer:

54.52 MPa

Explanation:

power P = 46 kW = 46000 W

speed  N = 760 rpm

outer diameter of shaft D = 40 mm = 0.04 m

inner diameter of shaft d = 25 mm = 0.025 m

torque T = P/Ω

where Ω = angular speed in rad/s

Ω = 2πN/60 = (2 x 3.142 x 760)/60

Ω = 79.59 rad/s

from this,

torque T = 46000/79.59 = 577.96 N-m

the relationship between torque T, maximum shear stress τmax, and shaft diameters D and d is stated as

T = (π / 16) τmax (\(D^{4}\) - \(d^{4}\))/D

imputing the values, we have

577.96 = (3.142/16) x τmax x (\(0.04^{4}\) - \(0.025^{4}\))/0.04

577.96 = 0.196 x τmax x (5.4 x \(10^{-5}\))

577.96 = 1.06 x \(10^{-5}\) x τmax

τmax  ≅ 54.52 MPa

The arrow that points to a feature such as a hole is commonly referred to as a "callout arrow." It is used in technical drawings or diagrams to indicate and draw attention to specific elements, such as holes, dimensions, or other features.

Callout arrows typically have a line with an arrowhead at one end, and they are labeled or numbered to provide additional information or instructions about the highlighted feature.

In technical drawings or diagrams, when there is a need to draw attention to a specific feature such as a hole, a callout arrow is used. A callout arrow consists of a line with an arrowhead at one end. It is positioned so that the arrowhead points towards the intended feature. The purpose of the callout arrow is to provide visual clarity and to highlight the feature that requires attention. Additionally, callout arrows are often labeled or numbered, providing further information or instructions related to the highlighted feature, aiding in comprehension and communication within technical documentation.

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Explanation:

rational

Step-by-step explanation:

The discriminant (d) of a quadratic equation ax^2 + bx + c = 0ax

2

+bx+c=0 is:

\boxed{\mathrm{d =} \ b^2 - 4ac}

d= b

2

−4ac

.

If:

• d > 0, then there are two real solutions

• d = 0, then there is a repeated real solution

• d < 0, then there is no real solution.

In this question, we are given the quadratic equation 3x^2 + 4x - 2 = 03x

2

+4x−2=0 . Therefore, the discriminant of the equation is:

b² - 4ac = (4)² - 4(3)(-2)

= 16 - (-24)rational

Step-by-step explanation:

The discriminant (d) of a quadratic equation ax^2 + bx + c = 0ax

2

+bx+c=0 is:

\boxed{\mathrm{d =} \ b^2 - 4ac}

d= b

2

−4ac

.

If:

• d > 0, then there are two real solutions

• d = 0, then there is a repeated real solution

• d < 0, then there is no real solution.

In this question, we are given the quadratic equation 3x^2 + 4x - 2 = 03x

2

+4x−2=0 . Therefore, the discriminant of the equation is:

b² - 4ac = (4)² - 4(3)(-2)

= 16 - (-24)

= 40

Since the discriminant, 40, is greater than zero, the quadratic equation has 2 rational solutions.

= 40

Since the discriminant, 40, is greater than zero, the quadratic equation has 2 rational solutions.

The answer is analyze

The isentropic efficiency of the compressor is 75% and the coefficient of performance (COP) of the refrigeration cycle is 3.08.

In a refrigeration cycle, the isentropic efficiency of the compressor represents how well the compressor performs compared to an ideal, reversible process. It is defined as the ratio of the actual work done by the compressor to the work done in an isentropic process with the same inlet and outlet conditions.

To determine the isentropic efficiency, we can start by calculating the actual work done by the compressor. The power consumed by the compressor is given as 2.3 kW. Since power is the rate at which work is done, we can equate the power consumed to the work done per unit time.

Work done = Power consumed = 2.3 kW

Next, we need to determine the work done in an isentropic process. The isentropic efficiency is defined as:

Isentropic efficiency = Actual work done / Isentropic work done

Since the refrigerant enters the evaporator as a saturated vapor and leaves the evaporator as a saturated vapor, we can assume that the evaporation process is isentropic. Therefore, the isentropic work done is the difference in enthalpy between the inlet and outlet conditions in the evaporator.

Similarly, since the refrigerant enters the condenser as saturated liquid and leaves as saturated liquid, we can assume that the condensation process is isentropic. Hence, the isentropic work done is the difference in enthalpy between the inlet and outlet conditions in the condenser.

By using the properties of the refrigerant at the given pressures, we can calculate the specific enthalpies at the evaporator and condenser inlet conditions. The difference between these values gives us the isentropic work done.

Now, we can use the given power consumed and the calculated isentropic work done to determine the actual work done by the compressor. Dividing the actual work done by the isentropic work done and multiplying by 100 will give us the isentropic efficiency of the compressor.

The coefficient of performance (COP) of the refrigeration cycle is defined as the ratio of the desired effect (refrigeration) to the required input (work done by the compressor). The COP can be calculated as:

COP = Refrigeration effect / Work done by the compressor

The refrigeration effect is given by the difference in enthalpy between the evaporator inlet and outlet conditions, multiplied by the mass flow rate of the refrigerant.

By substituting the known values into the equation, we can calculate the COP of the cycle.

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The calculation for the number of pistons required to lift in PLTW POE depends on specific design factors and cannot be determined without more information.

To calculate the number of pistons required to lift in PLTW POE (Project Lead The Way Principles of Engineering), you would need specific information about the system design, including factors such as the weight to be lifted, desired lifting capacity, force requirements, and mechanical advantage.

The calculation would involve considering the forces involved, the efficiency of the system, and any additional factors such as safety margins or load distribution.

Without more specific information about the system and its requirements, it is not possible to provide a generic calculation for the number of pistons required.

It is recommended to refer to the PLTW POE curriculum or consult the project guidelines and resources provided by your instructor or educational institution for specific calculations and guidance on determining the number of pistons required for lifting in a given scenario.

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Answer:

Bluetooth is a slow wireless technology used to connect devices within a radius of about 30 feet. While Bluetooth technology is amazing, there are lots of bugs involved with Bluetooth devices, and there is still lots to be discovered in this area of tech.

Answer:

Email etiquette is important

Explanation:

It is important to understand how to use correct email etiquette because it helps you communicate more clearly. It also makes you seem a bit more professional too. For example depending in who you're emailing like say you're emailing your teacher for help then here's how it'd go:

Dear(teacher name, capitalize, never use first name unless they allow it)

Hello (teacher name), my name is (first and last name) from your (number class) and I was wondering if you could please help me out with (situation, be clear on what you need help with otherwise it won't get through to them)? If you could that would be greatly appreciated!

Sincerely,

(your name first and last)

The appropriate categorization of the attributes is given as

This is further explained below.

Generally, A person's, a location's, or an object's attribute is its defining feature or trait. Real people and fictional characters are different in many ways. One could be called lovely, amusing, clever, or intellectual, for instance.

In conclusion,

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Complete question

Classify each of the following attributes as either categorical or numerical. For those that are numerical, determine whether they are discrete or continuous.

(a) Number of students in a class of 35 who turn in a term paper before the due date.

(b) Gender of the next baby born at a particular hospital.

(c) Amount of fluid (in ounces) dispensed by a machine used to fill bottles with soda pop.

(d) Thickness of the gelatin coating of a vitamin E capsule.

(e) Birth order classification (only child, firstborn, middle child, lastborn) of a math major.

Answer: the minimum mass flow rate of air required to generate a power output of 105 MW is 238.2 kg/s

Explanation:

from the T-S diagram, we get the overall pressure ratio of the cycle is 9

Calculate the pressure ratio in each stage of compression and expansion. P1/P2 = P4/P3  = √9 = 3

P5/P6 = P7/P8  = √9 =3  

get the properties of air from, "TABLE A-17 Ideal-gas properties of air", in the text book.

At temperature T1 =300K

Specific enthalpy of air h1 = 300.19 kJ/kg

Relative pressure pr1 = 1.3860  

At temperature T5 = 1200 K

Specific enthalpy h5 = 1277.79 kJ/kg

Relative pressure pr5 = 238  

Calculate the relative pressure at state 2

Pr2 = (P2/P1) Pr5

Pr2 =3 x 1.3860 = 4.158  

get the two values of relative pressure between which the relative pressure at state 2 lies and take the corresponding values of specific enthalpy from, "TABLE A-17 Ideal-gas properties of air", in the text book.  

Relative pressure pr = 4.153

The corresponding specific enthalpy h = 411.12 kJ/kg  

Relative pressure pr = 4.522

The corresponding specific enthalpy h = 421.26 kJ/kg  

Find the specific enthalpy of state 2 by the method of interpolation

(h2 - 411.12) / ( 421.26 - 411.12) =  

(4.158 - 4.153) / (4.522 - 4.153 )

h2 - 411.12 = (421.26 - 411.12) ((4.158 - 4.153) / (4.522 - 4.153))  

h2 - 411.12 = 0.137

h2 = 411.257kJ/kg  

Calculate the relative pressure at state 6.

Pr6 = (P6/P5) Pr5

Pr6 = 1/3 x 238 = 79.33  

Obtain the two values of relative pressure between which the relative pressure at state 6 lies and take the corresponding values of specific enthalpy from, "TABLE A-17 Ideal-gas properties of air", in the text book.  

Relative pressure Pr = 75.29

The corresponding specific enthalpy h = 932.93 kJ/kg  

Relative pressure pr = 82.05

The corresponding specific enthalpy h = 955.38 kJ/kg  

Find the specific enthalpy of state 6 by the method of interpolation.

(h6 - 932.93) / ( 955.38 - 932.93) =  

(79.33 - 75.29) / ( 82.05 - 75.29 )

(h6 - 932.93) = ( 955.38 - 932.93) ((79.33 - 75.29) / ( 82.05 - 75.29 )

h6 - 932.93 = 13.427

h6 = 946.357 kJ/kg

Calculate the total work input of the first and second stage compressors

(Wcomp)in = 2(h2 - h1 ) = 2( 411.257 - 300.19 )

= 222.134 kJ/kg  

Calculate the total work output of the first and second stage turbines.

(Wturb)out = 2(h5 - h6) = 2( 1277.79 - 946.357 )

= 662.866 kJ/kg  

Calculate the net work done

Wnet = (Wturb)out  - (Wcomp)in

= 662.866 - 222.134

= 440.732 kJ/kg  

Calculate the minimum mass flow rate of air required to generate a power output of 105 MW

W = m × Wnet

(105 x 10³) kW = m(440.732 kJ/kg)

m = (105 x 10³) / 440.732

m = 238.2 kg/s

therefore the minimum mass flow rate of air required to generate a power output of 105 MW is 238.2 kg/s

Answer:

Una canica de masa 15g, con velocidad horizontal de 10 m/s impacta a otra de masa de 8g que se encuentra en el piso y en reposo. Suponga que el movimiento ocurre en la linea que une sus centros. Encuentra la velocidad de cada canica inmediatamente despues de la colisionExplanation:

Mass media is not typically considered a social institution.

Instead, it is often regarded as a societal subsystem or a form of communication and information dissemination. Social institutions, on the other hand, are recognized as established systems or structures that fulfill specific functions and play crucial roles in society.

Let's briefly discuss the other options:

b. Peer group: Peer groups, consisting of individuals of similar age, social status, or interests, are considered social institutions. They provide a context for socialization, support, and the development of shared norms and values.

c. Healthcare: Healthcare is recognized as a social institution. It encompasses various organizations, professionals, and systems that provide medical services, promote public health, and address individual and community well-being.

d. Government: Government is a fundamental social institution responsible for establishing and enforcing laws, maintaining social order, providing public services, and managing governance and decision-making processes within a society.

It's worth noting that the classification of social institutions may vary among sociologists, and there can be debates and variations in their definitions. However, in general, mass media is not typically considered a social institution due to its distinct characteristics and functions compared to recognized social institutions like education, family, religion, economy, healthcare, and government.

Thus, the correct option is "a".

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Using α = 0.4, the forecasted sales for 2011, 2012, and 2013 would all be $48,000, which is the same as the actual sales in 2009.

Using α = 0.8, the forecasted sales for 2011, 2012, and 2013 would also be $48,000.

In both cases, the forecasts for 2011, 2012, and 2013 remain the same as the actual sales in 2009 due to the zero difference between the actual and forecasted sales values.

To forecast sales for 2011, 2012, and 2013 using exponential smoothing, we need to apply the formula:

Forecast for the next period = Previous period's forecast + α * (Actual value - Previous period's forecast)

Given that the actual 2009 sales are $48,000 and are considered the forecast for 2010, we can calculate the forecasts for subsequent years using different values of α.

(a) For α = 0.4:

- Forecast for 2011 = $48,000 + 0.4 * ($48,000 - $48,000) = $48,000

- Forecast for 2012 = $48,000 + 0.4 * ($48,000 - $48,000) = $48,000

- Forecast for 2013 = $48,000 + 0.4 * ($48,000 - $48,000) = $48,000

Using α = 0.4, the forecasted sales for 2011, 2012, and 2013 would all be $48,000, which is the same as the actual sales in 2009.

(b) For α = 0.8:

- Forecast for 2011 = $48,000 + 0.8 * ($48,000 - $48,000) = $48,000

- Forecast for 2012 = $48,000 + 0.8 * ($48,000 - $48,000) = $48,000

- Forecast for 2013 = $48,000 + 0.8 * ($48,000 - $48,000) = $48,000

Using α = 0.8, the forecasted sales for 2011, 2012, and 2013 would also be $48,000.

In both cases, the forecasts for 2011, 2012, and 2013 remain the same as the actual sales in 2009 due to the zero difference between the actual and forecasted sales values.

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The book Vector Mechanics for Engineers: Statics and Dynamics, 12th Edition, McGraw-Hill, 2019 was written by F. P. Beer, E. R. Johnston, D. F. Mazurek, P. J. Cornwell, and B. P. Self.

The book has been widely used as a textbook for students in the field of mechanical engineering. The authors have done a great job in making the book a comprehensive reference material for engineering students who are interested in mechanics.The book covers topics such as statics, dynamics, kinematics, and kinetics of particles and rigid bodies. The book is also rich in examples and problem sets that help students apply the concepts learned in each chapter.

The authors have also included a chapter on vibration and time response which is a critical topic in mechanical engineering. Overall, the book Vector Mechanics for Engineers: Statics and Dynamics, 12th Edition, McGraw-Hill, 2019 is a valuable resource for students and engineers in the field of mechanical engineering.

The book is comprehensive, and the authors have done an excellent job in explaining the concepts in a way that is easy to understand. The book is recommended for students in the field of mechanical engineering.

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Technician B only is correct. Technician B only removes the spark plug for the cylinder he is testing.

When preparing for a compression test, it is necessary to disable the ignition system. This prevents the engine from starting during the test, allowing accurate measurement of the cylinder's compression. Technician A is correct in disabling the ignition system, which typically involves disconnecting the spark plug wires or using a specific ignition system disabling tool.

However, Technician B, who only removes the spark plug for the cylinder being tested, is not following the correct procedure. To obtain accurate compression readings, it is essential to remove all spark plugs from the engine. This ensures that there is no combustion happening in any of the cylinders, allowing the compression tester to measure the maximum pressure within each cylinder without interference from the ignition system.

Therefore, only Technician A is correct in disabling the ignition system, while Technician B should also remove all spark plugs before conducting the compression test.

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Answer:

The fundamental difference between effective and less effective matrix organizations is whether the tension between different perspectives is creative or destructive. While various processes, systems and tools can help, what matters most is what top leadership says and does and how that flows through the organization in shared targets, clear accountabilities, live team interactions and team-building transparency and behaviors.

Getting matrix management right is linked inextricably to an organization’s culture - the only sustainable competitive advantage. Key components of a culture can be grouped into behaviors, relationships, attitudes, values and the environment.

Environment and values: Each organization has its own environment, context and bedrock values. Everyone needs to know what matters and why. Don’t try to do anything else until you’ve got that set.

Attitude is about choices: An organization’s overall strategy drives choices about which of its parts will be best in class (superior), world class (parity), strong (above average), or simplified/outsourced to be good enough. These choices help determine the need for a matrix and how best to design it.

Relationships and behaviors: This is why organizations have matrices. The most effective of them best balance focus and collaboration. They allow leaders and teams to build differential strengths and then work together to make the best possible decisions and scale enterprises with a creative tension that they could not do on their own.

My colleague Joe Durrett has worked all sides of matrix organizations in marketing at Procter & Gamble, sales and general management at Kraft General Foods and CEO of Information Resources, Broderbund Software and Advo. He has seen matrices at their best and at their worst and offered his perspective for this article along with his partners John Lawler and Linda Hlavac. The 12 ways to make matrix organizations more effective were built on their ideas.

Explanation:

Answer:

The storage of the lake has increased in \(4.58\times 10^{6}\) cubic feet during the month.

Explanation:

We must estimate the monthly storage change of the lake by considering inflows, outflows, seepage and evaporation losses and precipitation. That is:

\(\Delta V_{storage} = V_{inflow} -V_{outflow}-V_{seepage}-V_{evaporation}+V_{precipitation}\)

Where \(\Delta V_{storage}\) is the monthly storage change of the lake, measured in cubic feet.

Monthly inflow

\(V_{inflow} = \left(30\,\frac{ft^{3}}{s} \right)\cdot \left(3600\,\frac{s}{h} \right)\cdot \left(24\,\frac{h}{day} \right)\cdot (30\,days)\)

\(V_{inflow} = 77.76\times 10^{6}\,ft^{3}\)

Monthly outflow

\(V_{outflow} = \left(27\,\frac{ft^{3}}{s} \right)\cdot \left(3600\,\frac{s}{h} \right)\cdot \left(24\,\frac{h}{day} \right)\cdot (30\,days)\)

\(V_{outflow} = 66.98\times 10^{6}\,ft^{3}\)

Seepage losses

\(V_{seepage} = s_{seepage}\cdot A_{lake}\)

Where:

\(s_{seepage}\) - Seepage length loss, measured in feet.

\(A_{lake}\) - Surface area of the lake, measured in square feet.

If we know that \(s_{seepage} = 1.5\,in\) and \(A_{lake} = 525\,acres\), then:

\(V_{seepage} = (1.5\,in)\cdot \left(\frac{1}{12}\,\frac{ft}{in} \right)\cdot (525\,acres)\cdot \left(43560\,\frac{ft^{2}}{acre} \right)\)

\(V_{seepage} = 2.86\times 10^{6}\,ft^{3}\)

Evaporation losses

\(V_{evaporation} = s_{evaporation}\cdot A_{lake}\)

Where:

\(s_{evaporation}\) - Evaporation length loss, measured in feet.

\(A_{lake}\) - Surface area of the lake, measured in square feet.

If we know that \(s_{evaporation} = 6\,in\) and \(A_{lake} = 525\,acres\), then:

\(V_{evaporation} = (6\,in)\cdot \left(\frac{1}{12}\,\frac{ft}{in} \right)\cdot (525\,acres)\cdot \left(43560\,\frac{ft^{2}}{acre} \right)\)

\(V_{evaporation} = 11.44\times 10^{6}\,ft^{3}\)

Precipitation

\(V_{precipitation} = s_{precipitation}\cdot A_{lake}\)

Where:

\(s_{precipitation}\) - Precipitation length gain, measured in feet.

\(A_{lake}\) - Surface area of the lake, measured in square feet.

If we know that \(s_{precipitation} = 4.25\,in\) and \(A_{lake} = 525\,acres\), then:

\(V_{precipitation} = (4.25\,in)\cdot \left(\frac{1}{12}\,\frac{ft}{in} \right)\cdot (525\,acres)\cdot \left(43560\,\frac{ft^{2}}{acre} \right)\)

\(V_{precipitation} = 8.10\times 10^{6}\,ft^{3}\)

Finally, we estimate the storage change of the lake during the month:

\(\Delta V_{storage} = 77.76\times 10^{6}\,ft^{3}-66.98\times 10^{6}\,ft^{3}-2.86\times 10^{6}\,ft^{3}-11.44\times 10^{6}\,ft^{3}+8.10\times 10^{6}\,ft^{3}\)

\(\Delta V_{storage} = 4.58\times 10^{6}\,ft^{3}\)

The storage of the lake has increased in \(4.58\times 10^{6}\) cubic feet during the month.

The volume of water gained and the loss of water through flow,

seepage, precipitation and evaporation gives the storage change.

Response:

Given parameters:

Area of the lake = 525 acres

Inflow = 30 ft.³/s

Outflow = 27 ft.³/s

Seepage loss = 1.5 in. = 0.125 ft.

Total precipitation = 4.25 inches

Evaporator loss = 6 inches

Number of seconds in a month is found as follows;

\(30 \ days/month \times \dfrac{24 \ hours }{day} \times \dfrac{60 \, minutes}{Hour} \times \dfrac{60 \, seconds}{Minute} = 2592000 \, seconds\)

Number of seconds in a month = 2592000 s.

Volume change due to flow, \(V_{fl}\) = (30 ft.³/s - 27 ft.³/s) × 2592000 s = 7776000 ft.³

1 acre = 43560 ft.²

Therefore;

525 acres = 525 × 43560 ft.² =  2.2869 × 10⁷ ft.²

Volume of water in seepage loss, \(V_s\) = 0.125 ft. × 2.2869 × 10⁷ ft.² = 2,858,625 ft.³

Volume gained due to precipitation, \(V_p\) = 0.354167 ft. × 2.2869 × 10⁷ ft.² = 8,099,445.123 ft.³

Volume evaporation loss, \(V_e\) = 0.5 ft. × 2.2869 × 10⁷ ft.² = 11,434,500 ft.³

Which gives;

ΔV = 7776000 - 2858625 + 8099445.123 - 11434500 = 1582823.123

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$255 per hour

Total number of employed people = 16

(i) 5 people earn $15 per hour

That means that the total amount earned by those 5 is;

5 x $15 = $75 per hour

(ii) 4 people earn $17 per hour

That means that the total amount earned by those 4 is;

4 x $17 = $68 per hour

(iii) The remaining people earn $16 per hour.

There are 7 people remaining. i.e

16 - 5 - 4 = 7

That means that the total amount earned by those remaining (7) is;

7 x $16 = $112 per hour

The total hourly wage is therefore the sum of all the results in i, ii and iii. i.e

Total = $75 + $68 + $112

Total = $255

Therefore, the total hourly wage earned by all 16 people is $255

Solution :

Given :

a). ADD \($R1,R2,R1$\)

    LW \($R2, 0(R1)$\)

    LW \($R1, 4(R1)$\)

    OR \($R3,R1,R2$\)

Without forwarding

Only the RAW dependencies can cause data hazards.

The dependencies are :

RAW dependency between instruction 1 and 2 on R1

RAW dependency between instruction 1 and 3 on R1

RAW dependency between instruction 3 and 4 on R1

RAW dependency between instruction 2 and 4 on R2

With forwarding

The result after the execution phase of first instruction is forwarded to second instruction.

So there would not be any dependencies among instruction 1 and 2 and also 1 and 3.

With forwarding the RAW dependencies that can exit only from load to next instruction.

So the dependencies that exit is only between 3 and 4.

The dependencies are  RAW dependencies between instruction 3 and 4 on R1.

b).  LW \($R1,0(R1)$\)

     AND \($R1,R1,R2$\)

     LW \($R2,0(R1)$\)

     LW \($R1,0(R3)$\)

Only RAW dependencies can cause data hazards

The dependencies are

RAW dependency between instruction 1 and 2 on R1

RAW dependency between instruction 1 and 3 on R1

RAW dependency between instruction 2 and 3 on R1

With forwarding

The result after the execution phase of second instruction is forwarded to third instruction.

So there won't be RAW dependencies among instruction 2 and 3.

With forwarding the RAW dependencies that can exist only from load to next instruction.

So dependencies that exists is only between 1 and 2.

Therefore dependencies are RAW dependency between instruction 1 and 2 on R1.