The problem involves analyzing distribution costs, selecting initial feasible solutions using different methods, and adapting the model to accommodate transportation constraints. The quantities produced by each refinery, requirements of each storage facility, and associated distribution costs are provided.
The objective is to determine an initial feasible solution and calculate the total cost using two different approaches: the Northwest Corner Rule and the Minimum Cell Cost method. Additionally, the problem states that transportation from Takoradi to Bawku is prohibited, requiring the formulation of a mathematical model to incorporate this constraint. To solve the distribution problem, a network graph can be created to represent the costs and decision variables. The Northwest Corner Rule is a method used to find an initial feasible solution. It starts by allocating the maximum possible amount from the northwest corner and iteratively filling in the remaining cells until all requirements are met. This method provides an initial solution based on the corner cells and their associated costs.
Alternatively, the Minimum Cell Cost method can be employed to find the initial feasible solution. This approach selects the cell with the lowest cost and assigns the maximum possible quantity. It continues to assign quantities based on the minimum cost cells until all requirements are fulfilled. By comparing the results obtained from both methods, it is possible to evaluate the differences in the total cost. The two approaches may yield different initial feasible solutions and subsequently different total costs. These variations highlight the importance of selecting an appropriate method and the impact it can have on the overall distribution cost. Considering the prohibition of transportation from Takoradi to Bawku, the mathematical model needs to be modified to incorporate this constraint. The formulation should exclude any allocation of gasoline from Takoradi to Bawku in the initial feasible solution and subsequent iterations.
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As an input signal drives the base voltage in a positive direction, base current will_____ and collector current will _____.
Answer:
Base current increases and collector current decreases
Explanation:
Base current increases and collector current decreases
The collector current does reduces because electrons that moves from emitter to base and the electrons that moves from collector to base are both cancelled out. Some of these electrons enter from the emitter to the collector because, in a way, the emitter has been heavily döped
An increase in base current also means that there is more bias to the transistor
how to answer for computer science quora how do your interests directly connect with cornell engineering? if you have an intended major, what draws you to that department at cornell engineering? if you are unsure what specific engineering field you would like to study, describe how your general interest in engineering most directly connects with cornell engineering. it may be helpful to concentrate on one or two things that you are most excited about\.\* (250 words)
Focus primarily on highly precise specifics of what Cornell offers and how it matches with your interests and values. You can regard this as a "Why us?" essay with some optional "Why major" spice.
How to write essay ?Cornell is fundamentally a research institution, and I am fundamentally a researcher. The Collective Embodied Intelligence Lab would be the ideal place for me to put what I have learned from my own work in that area to use while learning from Dr. Petersen and her ground-breaking research in termite-inspired construction robots. The lab focuses on the control of multi-agent robotic systems, especially drawing inspiration from insect swarm mechanics. Cornell is known for its research, but what truly stood out to me was its distinct dedication to project teams. I discovered I wanted to join every team after doing my homework on them. Consider Baja; the idea of creating an off-road car from scratch is comparable to FTC competitions. Even though I have a strong foundation in CAD, wiring, and chassis construction, I'm eager to tackle more complex issues with even more room for creativity.To learn more about essay refer :
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Discuss the exciton roles in silicon solar cell
Excitons play a crucial role in silicon solar cells and are involved in several processes that contribute to the generation of electricity. Here are some key roles of excitons in silicon solar cells:
1. Absorption of Photons: When photons from sunlight strike the silicon material of a solar cell, they can be absorbed by silicon atoms, promoting an electron from the valence band to the conduction band. This process creates an exciton—a bound electron-hole pair.
2. Exciton Diffusion: After absorption, excitons can diffuse through the silicon material, moving towards the region of the solar cell where charge separation occurs. This diffusion process allows excitons to reach the vicinity of the p-n junction, where the separation of charges takes place.
3. Exciton Dissociation: At the p-n junction of a silicon solar cell, excitons can undergo dissociation. The electric field created by the junction separates the electron and hole of the exciton, allowing them to move freely in opposite directions as charge carriers.
4. Electron and Hole Transport: Once the exciton is dissociated, the free electron and hole can move independently within the solar cell. They are transported through the silicon material to the respective electrodes, creating an electric current that can be harnessed for external use.
5. Recombination: Excitons can also undergo recombination, where the electron and hole recombine, releasing energy in the form of light or heat. Recombination is undesirable in solar cells as it reduces the overall efficiency of the device.
To enhance the efficiency of silicon solar cells, various strategies are employed to minimize exciton recombination and improve exciton dissociation and charge carrier transport. These include the use of anti-reflection coatings, surface passivation techniques, and optimization of the device structure.
Overall, excitons play a vital role in the absorption and conversion of sunlight into electrical energy in silicon solar cells. Understanding and controlling exciton dynamics are essential for improving the performance of solar cells and advancing the field of photovoltaics.
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What is the function of the microscope diaphragm?
a. source of light
b. condenses light from the light source into a narrow beam
c. regulates the amount of light passing through the specimen
d. used to focus the specimen
e. holds the objective lenses
The function of the microscope diaphragm is c. regulates the amount of light passing through the specimen.
The microscope diaphragm is a component located below the stage of a microscope. Its primary function is to control the amount of light that passes through the specimen being observed. It consists of an adjustable aperture with different settings that allow the user to regulate the size of the opening.
By adjusting the diaphragm, the amount of light reaching the specimen can be controlled. Opening the diaphragm wider allows more light to pass through, while closing it down reduces the amount of light. This feature is particularly important when observing specimens that require specific lighting conditions, such as those that are highly transparent or have low contrast.
The microscope diaphragm helps achieve optimal illumination by balancing the brightness and contrast of the specimen. By controlling the amount of light, it assists in enhancing the visibility of the specimen's details and structures.
To summarize, the function of the microscope diaphragm is to regulate the amount of light passing through the specimen, allowing for better control of illumination and optimizing the observation conditions.
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How many grains are on the surface of the head of a pin? assume that the head of a pin is spherical with a 1-mm diameter and has an astm grain size of 10
Answer:
Given, diameter of pin head d = 1 mm = 1/25.4 = 0.0394 in Surface area of a pinhead, A = 4pr^2 =
Explanation:
eesh
To avoid becoming drowsy on an expressway, you should: Keep your windows closed Call a friend to engage you in conversation Stop driving every couple hours
To avoid becoming drowsy on an expressway, there are several steps you can take. Firstly, it is important to keep your windows closed while driving. This helps to reduce noise and distractions from outside, creating a more conducive environment for alertness. Additionally, opening the windows can create a draft that may make you feel drowsier. Secondly, engaging in conversation with a friend or passenger can help keep your mind active and focused. Talking about various topics and sharing stories can help you stay mentally engaged and prevent drowsiness. Lastly, it is advisable to take regular breaks and stop driving every couple of hours. Pulling over at a rest area or gas station allows you to stretch your legs, get some fresh air, and give your mind a break from the monotony of driving. Taking short breaks can help you stay alert and maintain your energy levels throughout the journey. Remember, ensuring your safety and the safety of others on the road is of utmost importance, so it is crucial to take proactive measures to prevent drowsiness while driving on the expressway.
What are the indications that Cece is having problems
with her computer hardware? Check all that apply
-losing the Internet connection
-waiting for five minutes
-computer going blank
-mouse pointer freezing
-keyboard getting stuck
Answer:
-Computer going blank .
-Mouse pointer freezing.
-Keyboard getting stuck.
Explanation:
Any problems with the computer related to its hardware will consist of issues directly related to the physical components of the PC or computer. So any problem involving the physical component of the computer, then it can be termed as a hardware problem.
Based on the problems given in the option, the hardware issues will be problems with the computer, mouse, and keyboard. These form the physical parts of the computer so they will be a hardware issue.
Thus, the correct answers are the third, fourth, and fifth options.
Answer:
c d e
Explanation:
Thread, formed by spinning and twisting tibers together to hold the garment together. 'Therefore, the thread
the quality.
The thread is crucial for ensuring the quality and durability of the garment. It is formed by spinning and twisting fibers together, creating a continuous strand that is used to hold the various components of the garment together.
The quality of the thread directly affects the overall quality of the garment. A strong and well-constructed thread is essential for providing structural integrity and preventing the garment from unraveling or falling apart over time. It must be able to withstand the stresses and strains that occur during regular use, including stretching, pulling, and washing.
When choosing the appropriate thread for a garment, several factors are considered, including the type of fabric, the intended use of the garment, and the desired aesthetic. Different threads have varying levels of strength, elasticity, and resistance to abrasion. For example, a heavier fabric might require a thicker and more robust thread, while a delicate fabric may require a finer and more delicate thread to prevent damage.
The quality of the thread also relates to its consistency and uniformity. Irregularities in the thread's thickness or tension can result in uneven stitches, which may compromise the appearance and functionality of the garment. In addition, the thread's color and texture should be chosen carefully to complement the fabric and enhance the overall aesthetic appeal.
In the manufacturing process, quality control measures are implemented to ensure that the thread meets the required standards. This involves testing the thread for strength, colorfastness, and resistance to abrasion. By using high-quality thread and maintaining strict quality control, garment manufacturers can ensure that the final product meets or exceeds the expectations of customers in terms of both appearance and durability.
In summary, the thread plays a vital role in holding a garment together and contributes significantly to its quality and longevity. Choosing the right thread and ensuring its consistent quality throughout the manufacturing process are essential for creating garments that are durable, aesthetically pleasing, and able to withstand regular use.
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in mining auxiliary operations are the supplementry steps that support the production cycle . elucidate the auxiliary operations of underground mining?
Answer:
The answer is below
Explanation:
The mining auxiliary operations in underground mining involve various activities that are important for a successful mining operation particularly in the areas of productive operating conditions.
The activities involved in the auxiliary operations in underground mining include the following: ventilation, haulage, drainage, power supply, lighting, delivery of compressed air, water, supplies to the working sections, and communications.
the voltage valve at which a zirconia O2S switches from rich to lean and lean to rich is
A) 0.5v (500mv)
B) 0.45v (450mv)
C) 0.25v (250mv)
D) 0.90v (900)
Drag each tile to the correct box. Not all tiles will be used.
Adam wants to become a certified professional engineer. What are the steps that he will have to follow?
Answer:
I think it is the 2,3,5 and 1 ones
2..Three formations, each 25 m thick, overlie one another. If a constant-velocity vertical flow field is set up across the set of formations with h = 120 m at the top and h = 100 m at the bottom, calculate h at the two internal boundaries. The hydraulic conductivity of the top formation is 0.0001 m/s, the middle formation 0.0005 m/s, and the bottom formation 0.0010 m/s.
The values of h at the two internal boundaries are :
h₁ = 104.625 m h₂ = 101.55 mGiven data :
Z₁ = Z₂ = Z₃ = 25 m
h top = 120 m
h bottom = 100 m
K₁ = 0.0001 m/s
K₂ = 0.0005 m/s
K₃ = 0.0010 m/s
First step : Calculate the value of Keqwe will apply the formula below since flow is perpendicular to the bedding plane
Keq = \(\frac{Z1 + Z2 + Z3 }{\frac{Z1}{K1}+\frac{Z2}{K2} + \frac{Z3}{K3} }\) ----- ( 1 )
Insert values given above into equation 1
Therefore ; Keq = 2.307 * 10⁻⁴ m/s
Next step : determine the hydraulic gradientHydraulic gradient ( Ieq ) = head loss / length
= ( 120 - 100 ) / 3 * 25
Ieq = 0.266
Given that the flow is perpendicular to bedding plane
q1 = q2 = q3
V₁ = V₂ = V₃ = V
K₁i₁ = K₂i₂ = K₃i₃ = Keq * ieq
Hence :
V = Keq* Ieq
= 2.307 * 10⁻⁴ * 0.266
= 6.15 * 10⁻⁵ m/s .
Also;
K₁i₁ = Keq * ieq = K₂i₂ = K₃i₃
therefore :
i₁ = 0.615
i₂ = 0.123
i₃ = 0.0615
Final step : determine the value of h at the two internal boundariesPressure at point 1 ( i.e. pressure between first two formations )
h₁ = h top - i₁L₁
= 120 - 0.615 * 25
= 104.625 m
Pressure at point 2 ( i.e. pressure between the 2nd and 3rd formation )
h₂ = h₁ - i₂L₂
= 104.625 - 0.123 * 25
= 101.55 m
Therefore we can conclude that The values of h at the two internal boundaries are : h₁ = 104.625 m , h₂ = 101.55 m
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2. In a certain Village in eastern Uganda, residents use on average 1.5 Kg per inhabitant of
wood per day in a traditional stove of 12% efficiency. If the village has 200 in habitants,
Find,
i.
The
total mass of wood consumed daily.
ii.
The Energy demand of the village in KWh.
iii.
The actual energy consumption of the village in KWh.
iv.
If an investor would like to provide this village with a new energy converter of 30%
efficiency, how many Kilograms of wood will be required per day
probably alot lol
Explanation:
it probably is
Assignment: Explain any three
ways that research can facilitate
the work of building technicians.
The three ways that research can facilitate the work of building technicians is that:
They will know the timeframe to start and complete the buildingThey will know the type and right materials to use.It will help them in the area of budgeting of equipment, tools and building materials needed.What do building technicians do?Building technicians are known to be people who help with some tasks around construction projects and building works.
Note that building technician overseeing a scope of tasks such as monitoring build progress and as such The three ways that research can facilitate the work of building technicians is that:
They will know the timeframe to start and complete the buildingThey will know the type and right materials to use.It will help them in the area of budgeting of equipment, tools and building materials needed.Learn more about technicians from
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In relation to mine planning and design define scheduling
Answer:
Scheduling is a process of create a structure that shows the way a schedule is organized before developing a complete and final schedule of a project.
Explanation:
This is the initial step in of developing a project schedule for a capital cost project. At this stage, the estimates for the project are done involving the various actions in the project. A lot of details are included in this schedule showing the activities that are to be performed and the constraints involved.
A transmitter has an output power of 0.1mW while the fiber has coupling loss of 12dB, attenuation of
6dB/km for the length of 500m. The link contains two connectors of 2dB average loss. The receiver has a
minimum acceptable power ( sensitivity) of -35dBm. The designer has allowed a 4dB margin. Based on
the given information,
a) Calculate total link loss
b) Determine the receiver's sensitivity
c) Identify this system is good practice or not
A 19,400-N weight is raised using a jackscrew having a pitch of 5.00 mm and a handle length of 255 mm. What force must be applied?
To calculate the force required to lift a weight, we need to determine the mechanical advantage provided by the jackscrew. The mechanical advantage can be calculated as the ratio of the handle length to the pitch of the screw.
How to calculate the force required to lift a weight?
In this case, the mechanical advantage is:
255 mm / 5.00 mm = 51
This means that for every 51 turns of the handle, the screw will raise the load by a distance equal to the pitch of the screw, or 5.00 mm.
Now that we have the mechanical advantage, we can calculate the required force as follows:
Force = Weight / Mechanical Advantage
Force = 19,400 N / 51
Force = 380 N
So, a force of 380 N must be applied to the handle of the jackscrew to lift the 19,400 N weight.
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What are the important subassemblies and subsystems?
Answer:
Subsystem denotes to the installation of some subassemblies, which can be very small or gigantic in size, that serve this subsystem and the overall system. ... In addition, availability importance measures are employed to rank various subsystems with regards to their impact on the overall system availability.
Explanation:
Subsystem refers to the installation of a few subassemblies that support this subsystem and the entire system.
What are subassemblies?An assembly is a template for a corridor's cross section at a certain station.
A set of interconnected subassemblies that are each connected to a center point or to other subassemblies makes up an assembly. An assortment of shapes, linkages, and points make up a subassembly.
The installation of a few subassemblies that support this subsystem and the overall system is referred to as a subsystem.
These subassemblies can range in size from little to huge. In addition, subsystems are ranked according to their impact on the overall system's availability using availability importance criteria.
The primary memory, the input/output subsystem, and the central processor unit (CPU) are the three basic categories or subsystems that make up a computer. Data processes are carried out by the central processing unit (CPU).
A subassembly could be:
Semiconductor.Amplifier.Transistor.Impedance.Oscillators.Thus, these are important subassemblies and subsystems.
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personal watercraft are considered what type of vessel?
Personal watercraft, also known as water scooters or Jet Skis, are considered a type of recreational vessel.
What is recreational vessel?
A recreational vessel is any type of watercraft that is used for leisure and recreational activities, rather than for commercial or military purposes. Some examples of recreational vessels include sailboats, powerboats, personal watercraft, houseboats, and recreational fishing boats.
Recreational vessels come in a wide range of sizes, from small inflatable rafts to large luxury yachts, and can be powered by different means, such as sail, human power, internal combustion engines, or electric motors.
Personal watercraft, also known as water scooters or Jet Skis, are considered a type of recreational vessel. They are small, lightweight watercraft that are powered by an internal combustion engine or an electric motor and are designed for one or two people.
They are called personal watercraft because of their small size and the fact that they are intended for personal use, typically for recreation and leisure activities such as water skiing, wakeboarding, and leisure cruising. They are operated by standing or sitting on the watercraft, and steering and accelerating are typically done with handlebars, similar to a motorcycle.
Personal watercraft are subject to different regulations compared to other types of vessels, such as larger boats and ships, due to their size, speed, and maneuverability. For example, they may have specific rules regarding minimum age of the operator, required safety equipment, and speed limits in certain areas.
In summary, personal watercraft are considered a type of recreational vessel designed for personal use, with specific regulations and rules due to their unique characteristics.
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A 32x10^-6 F capacitor is connected to a 60V AC supply in series with a 56 ohm resistor. The current flowing in the circuit is 0.16 A.
Calculate the frequency of the AC supply.
The frequency of the AC supply is 0.036 Hz.
What is the frequency?We know that an alternating current circuit is the kind of circuit in which we do have the resistor in addition to the to the capacitor or the inductor or both as the case may be.
Here we are told that; A 32x10^-6 F capacitor is connected to a 60V AC supply in series with a 56 ohm resistor. The current flowing in the circuit is 0.16 A.
We can tell that the impedance of the circuit can be obtained by the use of the formula;
V = IZ
V = voltage
I = current
Z = impedance
Z = V/I
Z = 60 V/0.16 A
Z = 375 ohms
Then we have;
Z = √R^2 - XC^2
375 = √(56)^2 - (1/2 * 3.142 * f * 32x10^-6)^ 2
140625 = 3136 - (1/2 * 3.142 * f * 32x10^-6)^ 2
140625 - 3136 = (1/2 * 3.142 * f * 32x10^-6)^ 2
137489 = 1/2 * 10^-4 f
137489 * 2 * 10^-4 f = 1
f = 1/137489 * 2 * 10^-4
f = 0.036 Hz
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An ideal vapor-compression refrigeration cycle that uses refrigerant-134a as its working fluid maintains a condenser at 800 kPa and the evaporator at −20°C. Determine this system’s COP and the amount of power required to service a 150 kW cooling load. Answers: 3.83, 39.2 kW
The COP of the refrigeration cycle is 3.83, and the power required to service a 150 kW cooling load is 39.2 kW.
The given problem involves an ideal vapor-compression refrigeration cycle that uses refrigerant-134a as its working fluid. The condenser is maintained at 800 kPa, and the evaporator is at -20°C.
We need to determine the COP (Coefficient of Performance) and the power required to service a 150 kW cooling load. Firstly, we can determine the enthalpy change of the refrigerant during the cycle by using the saturation tables.
The enthalpy at the evaporator inlet is -129.2 kJ/kg, and at the condenser outlet is 214.5 kJ/kg. The COP can be calculated as the ratio of cooling effect to the work input, which is equal to the enthalpy change divided by the work input.
Thus, COP = (-129.2 - 214.5) / -129.2 = 3.83.
The power required to service the cooling load can be determined as the product of cooling load and COP.
Therefore, power = 150 kW / 3.83 = 39.2 kW.
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When my animal is to old to physically carry her baby what process can I use to still produce her young from her
Find the volume of the rectangular prism
9 cm
10 cm
Answer:
V= 90h cm³ where h is the height of the rectangular prism.
Explanation:
The formula for volume of a rectangular prism is ;
V=l*w*h where;
V=volume in cm³
l= length of prism=10cm
w =width of the prism = 9 cm
Assume the height of the prism as h cm then the volume will be;
V= 10* 9*h
V= 90h cm³
when the value of height of the prism is given, substitute that value with h to get the actual volume of the prism.
The ACH (air changes per hour) of a house is a measure of its air-tightness. The formula for ACH is
ACH=60L/V,
where L is the air leakage in cubic feet per minute (cfm), and V is the volume of the house in cubic feet. If a house has a volume of 25,700 cu ft, what is the maximum amount of air leakage that would result in an ACH of no more than 2.25?
Answer: The maximum amount of air leakage that would result in an ACH of no more than 2.25 is approximately _______ cfm.
Answer: I believe the answer is 963.75 if I am reading the question right.
Explanation:
ACH=60L/V
ACH=2.25
V=25,700
25,700*2.25=57,825
57,825/60=963.75
L=963.75
60(963.75)/25,700=2.25
The maximum amount of air leakage that would result in an ACH of no more than 2.25 would be approximately 956.25 cfm (cubic feet per minute).
Given that ACH of a house is a measure of its air-tightness and the formula for ACH is ACH = 60L/V. It means that ACH is inversely proportional to air-tightness or leakage. Therefore, the lower the air leakage the higher the ACH and vice versa.Mathematically, it is represented as:ACH ∝ 1/L or L ∝ 1/ACH
We can solve the question as follows:ACH = 2.25 (since the maximum ACH is 2.25)The volume of the house, V = 25,700 cubic feet.Substituting in the formula,2.25 = 60L/25,700Dividing both sides by 2.25 gives us,L = (2.25 * 25,700)/60L = 956.25 cubic feet per minute (cfm)
Therefore, the maximum amount of air leakage that would result in an ACH of no more than 2.25 is approximately 956.25 cfm (cubic feet per minute).
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Come up with a topic that can be put on research project/topic
proposal concerning applications of hydrographic surveying. include
research and review of related literature.
The research project/topic proposal focuses on the applications of hydrographic surveying. It involves conducting research and reviewing related literature to explore the various uses and advancements in hydrographic surveying techniques and technologies.
Hydrographic surveying plays a crucial role in various fields such as marine navigation, coastal engineering, offshore resource exploration, and environmental monitoring. This research project aims to investigate the applications of hydrographic surveying and analyze its impact on these industries.
The proposal will begin with a comprehensive literature review to gather existing knowledge and understanding of hydrographic surveying techniques, equipment, and methodologies. This review will encompass both academic research papers and industry reports to gain insights into the current state of the field and identify any gaps or areas that require further investigation.
The research project will then delve into specific applications of hydrographic surveying, such as the use of multibeam sonar for seafloor mapping, the application of LiDAR technology for coastal zone management, the role of hydrographic surveys in the installation and maintenance of underwater infrastructure, and the use of remote sensing techniques for monitoring and assessing coastal erosion and sediment transport.
By conducting thorough research and reviewing relevant literature, this project aims to contribute to the understanding of the applications of hydrographic surveying and highlight its importance in various industries. It will also identify potential areas for further research and advancements in hydrographic surveying technologies and methodologies.
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1. What are some pendulum wave characteristics?
2. What are waves characteristics?
3. List characteristics that they both share
Answer:
Explanation:
locate the centroid of the shaded area between the two curves
9514 1404 393
Answer:
(x, y) = (5.76, 1 5/7)
Explanation:
The location of the centroid in the x-direction is the ratio of the first moment of area about the y-axis to the total area. Similarly, the y-coordinate of the centroid is the first moment of area about the x-axis, divided by the area.
For the moment about the y-axis, we can define a differential of area as ...
dA = (y2 -y1)dx
where y2 = √(x/k2) and y1 = k1·x^3
The distance of that area from the y-axis is simply x.
So, the x-coordinate of the centroid is ...
\(\displaystyle c_x=\frac{a_x}{a}=\frac{\int{x\cdot dA}}{\int{dA}}\\\\a_x=\int_0^{12}{x(k_2^{-1/2}\cdot x^{1/2}-k_1x^3)}\,dx=\frac{2}{5k_2^{1/2}}\cdot12^{5/2}-\frac{k_1}{5}12^5\\\\a=\int_0^{12}{(k_2^{-1/2}\cdot x^{1/2}-k_1x^3)}\,dx=\frac{2}{3k_2^{1/2}}\cdot12^{3/2}-\frac{k_1}{4}12^4\\\)
For k1 = 4/12^3 and k2=12/4^2, these evaluate to ...
\(a_x=115.2\\a=20\\c_x=5.76\)
The y-coordinate of the centroid requires we find the distance of the differential of area from the x-axis. We can use (y2 +y1)/2 for that purpose. Then the y-coordinate is ...
\(\displaystyle c_y=\frac{a_y}{a}\\\\a_y=\int_0^{12}{(\frac{y_2+y_1}{2}(y_2-y_1))}\,dx=\frac{1}{2}\int_0^{12}{(\frac{x}{k_2}-(k_1x^3)^2)}\,dx\\\\a_y=\frac{12^2}{4k_2}-\frac{k_1^212^7}{14}=\frac{240}{7}\\\\c_y=\frac{12}{7}\approx1.7143\)
The centroid of the shaded area is ...
(x, y) = (5.76, 1 5/7)
A lake with a surface area of 525 acres was monitored over a period of time. During onemonth period the inflow was 30 cfs (ie. ft3 /sec), the outflow was 27 cfs, and a 1.5 in seepage loss was measured. During the same month, the total precipitation was 4.25 inches. Evaporation loss was estimated as 6 inches. Estimate the storage change for this lake during the month.
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:
The storage change for the lake in a month is 1,582,823.123 ft.³How can the given information be used to calculate the storage change?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
\(Storage \, change \, \Delta V = \mathbf{V_{fl} - V_s + V_p - V_e}\)Which gives;
ΔV = 7776000 - 2858625 + 8099445.123 - 11434500 = 1582823.123
The storage change, ΔV = 1,582,823.123 ft.³Learn more about water resources and hydrology here:
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A capacitor is connected into a 1250v 1000hz circuit. The current is 80A. What is the capacitance of the capacitor
Explain why Complements are used in the digital computer
Answer:
Explanation:
Complements are used in digital circuits, because it is faster to subtract by adding complements than by performing true subtraction. The binary complement of a number is created by reversing all bits and adding 1. The carry from the high-order position is eliminated.