1. What are Fuel Cells? How does the principle work? and explain the advantages? 2. What are Type One Fuel Cells? and what are Fuel Cells type two? explain in detail 3. Explain the technical constraints associated with the availability of materials in manufacturing Fuels Cells, and what are their future applications?

Answers

Answer 1

Fuel Cells:

A fuel cell is a device that generates electricity by converting the chemical energy of fuel (usually hydrogen) directly into electricity. Fuel cells are electrochemical cells that convert chemical energy into electrical energy.

The principle behind the fuel cell is to use the energy in hydrogen (or other fuels) to generate electricity. The principle behind fuel cells is based on the ability of an electrolyte to transport ions and the use of catalysts to cause a chemical reaction between the fuel and the oxygen.

Advantages of fuel cells include high efficiency, low pollution, low noise, and long life. Type 1 fuel cells: A proton exchange membrane fuel cell is a type of fuel cell that uses a polymer electrolyte membrane to transport protons from the anode to the cathode.

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Related Questions

the base case of the recursive towers of hanoi solution is a stack containing no disks. True or False

Answers

True, the base case of the recursive Towers of Hanoi solution is a stack containing no disks. The Towers of Hanoi is a classic problem in computer science and mathematics, where the objective is to move a stack of disks from one peg to another while adhering to specific rules.

In the recursive approach, the base case is essential for ending the recursion and providing a simple, solvable scenario. For the Towers of Hanoi, the base case occurs when there are no disks left on the source peg to move. This condition signifies that the recursive process of moving the disks has been completed, and no further action is necessary.The recursive solution works by breaking down the problem into smaller subproblems, with the base case acting as the foundation. The algorithm consists of moving n-1 disks to an auxiliary peg, moving the largest disk to the destination peg, and then moving the n-1 disks from the auxiliary peg to the destination peg. The process is repeated until the base case is reached.In summary, the statement is true; the base case of the recursive Towers of Hanoi solution is a stack containing no disks. This condition allows the algorithm to halt the recursion and signifies the completion of the disk-moving process.

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What is the enumerated data type used for state in ThreeLeds tick function?
A. TL_State
B. TL_States
C. integer
D. case

Answers

The enumerated data type used for state in ThreeLeds tick function is TL_State. The correct option is A.

An enumerated data type is a collection of symbolic names (members) tied to unique, carefully defined integer values. The idea is to make a variable that can only take on a few distinct values, which makes the code more concise, readable, and maintainable. A C++ enum is a user-defined type that is used to represent named constant values.

Enumerated data types are usually defined at the start of the application, in the global scope or in a namespace, and are available throughout the application. They're often used in conditional statements (if, switch) to execute different code based on their value. In the case of an enumerated data type used for state in ThreeLeds tick function, it is TL_State.

An enumerated data type is a useful construct for situations where a variable's value is one of a limited number of possibilities. They make the code more readable and easier to maintain.

ThreeLeds is an embedded systems lab experiment. This lab experiment introduces C programming techniques for embedded systems, including the use of registers and interrupts to toggle LEDs. A tick function is an important component of the experiment. The tick function is invoked once per second and uses a three-bit state machine to toggle three different colored LEDs. The enumerated data type used for state in ThreeLeds tick function is TL_State.

Therefore the correct answer is option A.

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HOW TO CALCULATE MARGINAL RATE

Answers

Answer:

Divide the difference in tax by the amount of income from the investment, and you'll get the economic marginal tax rate from investing. Most people refer to marginal tax rates as being identical to tax brackets.

hope this helps

have a good day :)

Explanation:

Before a rotameter can be used to measure an unknown flow rate, a calibration curve of flow rate versus rotameter reading must be prepared.

a. True
b. False

Answers

this statement is b which is true: hope this helped

Explain the process of energy conversion by describing how energy was converted from the windmill design brief. Discuss the different forms of energy and what technology was used to convert the energy from one form to another.

Answers

Answer:

Wind energy is converted to Mechanical energy  which is then converted in to  electrical energy

Explanation:

In a wind mill the following energy conversions take place

a) Wind energy is converted into Mechanical energy (rotation of rotor blades)

b) Mechanical energy is converted into electrical energy (by using electric motor)

This electrical energy is then used for transmission through electric lines.

Every motor vehicle except for
grade.
must be equipped with a parking brake that can hold a vehicle stationary on any
a) Motorcycles
b) Ambulances
c) Garbage trucks

Answers

Answer:

Motor Cycles

Explanation:

Motor cycles have no parking brake

After first loading the simulator, what initial velocity will land and roll into the hole without changing any of the other factors (Use only integers for the velocity)? Also, leave the units off or the answer will be marked wrong.

Answers

After first loading the simulator, the initial velocity that will land and roll into the hole without changing any of the other factors is 0.

To determine the initial velocity that will land and roll into the hole without changing any of the other factors after first loading the simulator, we can use the following formula:

V² = (2gh) / (1 - sinθ)

where V is the initial velocity, g is the acceleration due to gravity, h is the height of the hole, and θ is the angle of the inclined plane. To identify the initial velocity that will land and roll into the hole, we need to make sure the ball reaches the hole's bottom with a velocity of zero.

In other words, the velocity of the ball when it lands must equal the velocity of the ball when it rolls without any change in speed. Therefore, the final velocity must be zero, and we can set Vf = 0. Hence, we have:

Vf² = Vi² + 2gh

where Vi is the initial velocity. Since the ball rolls without any change in speed, we can use the distance traveled by the ball when it lands in the hole, which is equal to h / sinθ. Hence, we have:

h / sinθ = Vi² / (2g)

Therefore, Vi² = 2gh sinθ

Vi = √(2gh sinθ)

Vi = √(2 × 9.8 × 0.1 × sin(0))

Vi = √(0) = 0

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The settlement analysis for a proposed structure indicates that the underlying clay layer will settle 7.5 cm in 3 years, and that ultimately the total settlement will be about 32 cm. However, this analysis is based on the clay layer being doubly drained. It is suspected that there may be no drainage at the bottom of the layer (i.e., clay has single drainage condition). Answer the following questions based on single drainage only, assuming cv = 1.5 x 10-4 cm 2 /s for both single and double drainage.

a. How will the total settlement change from the double to the single drainage case?
b. How long will it take for 7.5 cm of settlement to occur if there is only single

Answers

Answer:

A) For a double drainage system the time taken for total settlement will differ from that of a single drainage system, because in a double drainage case clay water escapes from both sides unlike in a single drainage case. hence water and air will be be expulsed faster for a double drainage making it attain  total settlement faster.

B) for only single = 12 years

Explanation:

Given data :

ultimate clay settlement = 32 cm

settlement of clay in 3 years = 7.5 cm

Cv ( coefficient of consolidation ) =  1.5 x 10^-4 cm^2 /s

A) For a double drainage system the time taken for total settlement will differ from that of a single drainage system, because in a double drainage case clay water escapes from both sides unlike in a single drainage case. hence water and air will be be expulsed faster for a double drainage making it attain  total settlement faster.

note : Total settlement is the same in both drainage system.

B) Determine how long it will take for 7.5 cm of settlement to occur if there is only single

applying the relation  below

Tv = Cv t / H^2

where Tv = time factor , d = thickness of layer , H = drainage path

Given that Tv and Cv are constant in both cases

t ∝ H^2   hence

\(\frac{t1}{t2} = \frac{H^21}{H^22}\)  ------ ( 1 )

t1 = time for single drainage for d meters , t2 = time for double drainage  for d meters

equation 1 can be rewritten as

t1/t2 = d^2 / (d/2)^2

∴ t1 = 4t2

given that t2 = 3 years ( value gotten from question )

t1 = 4 * 3 = 12 years

A cubic foot of soil in its natural state weighs 113 lbs; after being dried it weighs 96 lbs. The specific gravity (Gs) of the soil is 2.70.
a) Draw the phase diagram and show the values of Wt, Ww, Ws, Vt, Vv, and Vs.
b) Determine the degree of saturation (S), void ratio (e), porosity (n), and water content (ω) for the soil as it existed in its natural state.
c) Determine the volume of water required to saturate 1 ft3 of soil in its natural state.

Answers

In this problem, we are given the weight of soil in its natural state and after being dried, as well as the specific gravity of the soil. From this information, we can determine various properties such as degree of saturation, void ratio, porosity, and water content.

Additionally, we can calculate the volume of water required to saturate the soil in its natural state.

a) In the phase diagram, we have:

Wt (total weight) = 113 lbs

Ww (weight of water) = 113 - 96 = 17 lbs

Ws (weight of solids) = 96 lbs

Vt (total volume) = Vv (volume of voids) + Vs (volume of solids)

Vv is the volume of water, and Vs is the volume of solids.

We need additional information to determine the values of Vv and Vs.

b) To determine the degree of saturation (S), we use the equation:

S = (Ww / Ws) * 100

Substituting the given values, we can calculate the degree of saturation.

The void ratio (e) is the ratio of the volume of voids to the volume of solids. It can be calculated as:

e = Vv / Vs

The porosity (n) is the ratio of the volume of voids to the total volume. It can be calculated as:

n = Vv / Vt

The water content (ω) is the ratio of the weight of water to the weight of solids. It can be calculated as:

ω = (Ww / Ws) * 100

Using the given information, we can calculate the values of S, e, n, and ω.

c) The volume of water required to saturate 1 ft3 of soil in its natural state can be determined by multiplying the volume of voids (Vv) by the specific gravity (Gs) of the soil. Since the specific gravity is given as 2.70, we can calculate the volume of water required.

By applying the relevant equations and using the given information, we can determine the desired properties and volume of water required for the soil in its natural state.

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A frost free, 17 cu. ft. refrigerator-freezer uses energy at a rate of 500. watts when you hear the compressor running. If the fridge runs for 200. hours per month, how many kilowatt-hours of energy does the refrigerator use each month

Answers

Answer:

100 kWh

Explanation:

Since the freezer has a rating of 500 watts and runs for 200 hours in a month, the energy consumption can be gotten by getting the product of the rating of the freezer in kilowatts and the amount of time the fridge is on per month.

The rating of the freezer = 500 watts = 0.5 kW, time = 200 h

Energy consumption = rating * time = 0.5 kW * 200 h

Energy consumption = 100 kWh

Therefore the refrigerator uses 100 kWh per month

what is the manufacturer-specific id for the gemtek radio transmitter/receiver?

Answers

The manufacturer-specific ID for the Gemtek radio transmitter/receiver refers to a unique identifier assigned by Gemtek to each of their radio communication devices.

This ID allows customers, service providers, and the manufacturer to identify a specific unit and gather relevant information about its specifications, production batch, and technical support.

To find the manufacturer-specific ID for your Gemtek radio transmitter/receiver, follow these steps:

1. Locate the product label: Find the label on your device, usually on the back or bottom panel. It may contain information such as the model number, serial number, and manufacturer-specific ID.

2. Look for the ID: On the label, search for a series of numbers or letters that represent the manufacturer-specific ID. It may be labeled as "ID," "Product ID," or "Unique ID."

3. Note the ID: Write down or take a photo of the ID for future reference when contacting support or seeking technical information.

If you are unable to find the manufacturer-specific ID, consider reaching out to Gemtek's customer support with your device's model number and serial number. They can help you identify the correct ID for your radio transmitter/receiver.

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The three suspender bars are made of A992 steel and have equal cross-sectional areas of 360mm2 . The rigid beam is subjected to the loading shown.



Determine the average normal stress in the bar BE,AD,CFBE,AD,CF

Answers

The given problem states that three suspender bars, made of A992 steel and with equal cross-sectional areas of 360mm², are attached to a rigid beam. The problem requires us to find the average normal stress in the bars BE, AD, and CF.

The formula for average normal stress is Total Normal force divided by Total area of cross-section. To find the normal force and area of cross-section for each bar, we need to calculate the force acting on each bar. As the cross-sectional areas are equal i.e. 360mm², we only need to find the force acting on each bar.

The normal force in each bar can be found as follows:

- For Bar AD: Normal force in AD = (1000 + 1200) N = 2200 N

- For Bar CF: Normal force in CF = (1500 + 1800) N = 3300 N

- For Bar BE: Normal force in BE = 3000 N

Using the above-normal force values, we can now find the average normal stress by using the formula:

Average normal stress = Total Normal force / Total area of cross-section

Therefore, the average normal stress in the bars BE, AD, CF are 8.33 N/mm², 6.11 N/mm², and 9.17 N/mm²,

respectively.

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are trains cool because if they are then my dad didn't beat me

Answers

Answer:

I think trains are pretty awesome. There's a train in japan that levitates slightly and runs on magnetism. Pretty amazing. It's super fast too

A video store rents movies to members. Each movie in the store has a title and is identified by a unique movie number. A movie can be in VHS, VCD, or DVD format. Each movie belongs to one of a given set of categories (action, adventure, comedy, horror). The store stores a name and a unique phone number for each member. There are two types of members:
Golden Members: Require their credit card and can rent more than one movie each time.
Bronze Members: Don't require a credit card and can rent only one movie each time.
Make a class diagram for it.

Answers

Here's a class diagram that represents the entities and their relationships for the video store scenario described:

The Class Diagram

+---------------------+        +---------------+       +-----------------+

|      Movie          |        |    Member     |       |    Rental       |

+---------------------+        +---------------+       +-----------------+

|  movie_id : int     |        |   member_id : |       | rental_id : int |

|  title : string     |        |   int        |<-------| movie : Movie    |

|  format : string    |        |   name : str |        | member : Member |

|  category : string  |        |   phone : str|        | rental_date : dt|

+---------------------+        |   type : str |        | is_returned : bool |

                               +---------------+        +-----------------+

                               |  credit_card: |                

                               +---------------+                

                               | rent_movies() |                

                               +---------------+                

                                         ^                      

                                         |                      

                               +---------------+                

                               | GoldenMember  |                

                               +---------------+                

                               | rent_limit:   |                

                               +---------------+                

                               | return_movies()|                

                               +---------------+                

                                         ^                      

                                         |                      

                               +---------------+                

                               | BronzeMember |                

                               +---------------+                

                               | rent_limit:   |                

                               +---------------+                

                               | return_movie()|                

                               +---------------+                

The Movie class has attributes movie_id, title, format and category. Each Member has a member_id, name, phone, and type. The Rental class is the association class that connects Movie and Member through the movie and member attributes, respectively, and adds rental_id, rental_date, and is_returned attributes.

There are two sub-classes of Member: GoldenMember and BronzeMember. The GoldenMember has an additional credit_card attribute and a rent_limit method that allows them to rent multiple movies at once. The BronzeMember has a rent_limit method that allows them to rent only one movie at a time. Both sub-classes have a return_movie or return_movies method, respectively, to allow them to return the rented movies.

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The cross-section of a rough, rectangular, concrete() channel measures . The channel slope is 0.02ft/ft. Using the Darcy-Weisbach friction method, determine the maximum allowable flow rate through the channel to maintain one foot of free board(freeboard is the vertical distance form the water surface to the overtopping level of the channel). For these conditions, find the following characteristics(note that FlowMaster may not directly report all of these):
a) Flow area
b) Wetted perimeter
c) Hydraulic radius(A/P) :
d) Velocity
e) Froude number

Answers

Answer:

The following are the answer to this question:

Explanation:

In point a, Calculating the are of flow:

\(\bold{Area =B \times D_f}\)

         \(=6\times 5\\\\=30 \ ft^2\)

In point b, Calculating the wetter perimeter.

\(\bold{P_w =B+2\times D_f}\)

      \(= 6 +2\times (5)\\\\= 6 +10 \\\\=16 \ ft\)

In point c, Calculating the hydraulic radius:

\(\bold{R=\frac{A}{P_w}}\)

   \(=\frac{30}{16}\\\\= 1.875 \ ft\)

In point d, Calculating the value of Reynolds's number.

\(\bold{Re =\frac{4VR}{v}}\)

     \(=\frac{4V \times 1.875}{1 \times 10^{-5} \frac{ft^2}{s}}\\\\\)

     \(=750,000 V\)

Calculating the velocity:

\(V= \sqrt{\frac{8gRS}{f}}\)

   \(= \sqrt{\frac{8\times 32.2 \times 1.875 \times 0.02}{f}}\\\\=\frac{3.108}{\sqrt{f}}\\\\\)

\(\sqrt{f}=\frac{3.108}{V}\\\\\)

calculating the Cole-brook-White value:

\(\frac{1}{\sqrt{f}}= -2 \log (\frac{K}{12 R} +\frac{2.51}{R_e \sqrt{f}})\\\\ \frac{1}{\frac{3.108}{V}}= -2 \log (\frac{2 \times 10^{-2}}{12 \times 1.875} +\frac{2.51}{750,000V\sqrt{f}})\\\)

\(\frac{V}{3.108} =-2\log(8.88 \times 10^{-5} + \frac{3.346 \times 10^{-6}}{750,000(3.108)})\)

After calculating the value of V it will give:

\(V= 25.18 \ \frac{ft}{s^2}\\\)

In point a, Calculating the value of Froude:

\(F= \frac{V}{\sqrt{gD}}\)

\(= \frac{V}{\sqrt{g\frac{A}{\text{Width flow}}}}\\\)

\(= \frac{25.18}{\sqrt{32.2\frac{30}{6}}}\\\\= \frac{25.18}{\sqrt{32.2 \times 5}}\\\\= \frac{25.18}{\sqrt{161}}\\\\= \frac{25.18}{12.68}\\\\= 1.98\)

The flow is supercritical because the amount of Froude is greater than 1.  

Calculating the channel flow rate.

\(Q= AV\)

   \(=30x 25.18\\\\= 755.4 \ \frac{ft^3}{s}\\\)

The cross-section of a rough, rectangular, concrete() channel measures . The channel slope is 0.02ft/ft.

Need help with Part 1 – Additional Operations I MATLAB question

Answers

gove it to me. I'll do my best

What’s the questions?

How to store data in 2D array in Java?

Answers

To store an existing array with the same length, create a new array.

How does Java set a value in a 2D array?

You can use assignment statements to explicitly insert a value into an array by using the name of the array, the row index and column index in brackets, a =, and the value to be added.

How can I add values to an array?

By default, the array's lowest position holds the first element, while its highest position has the last bit of information. The type of each element and the overall length of the array needed to store the data are specified when an array is declared in C.

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What kind of job does mike have? Mike’s job is to study blueprints, evaluate product stability, and to examine the safety of products. Mike’s works as a/n blank engineer with a manufacturing company.

Answers

Answer: a drafting engineer

Explanation:

How do you reverse a string in Python?

Answers

The String to Reverse. txt = "Hello World" [::-1] print(txt)

Slice the String. txt = "Hello World" [::-1] print(txt)

Slice the String. def my_function(x): return x [::-1]

Return the String. def my_function(x): return x[::-1]

Call the Function. def my_function(x):

Print the Result. def my_function(x):

what is python?

Guido van Rossum created Python, an interpreted, object-oriented, high-level programming language with dynamic semantics. It was first made available in 1991. The name "Python" is a tribute to the British comedy group Monty Python and is meant to be both simple and entertaining. Python is a popular computer programming language used to create software and sites, automate processes, and analyze data. Python is a general-purpose language, which means it may be used to make several various types of applications and isn't tailored for any particular issues. Python is a dynamic, bytecode-compiled, and interpreted language. Variable, parameter, function, and method types are not declared in the source code.

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the primary motivation to develop the new renewable energy sources comes from ________.

Answers

The primary motivation to develop new renewable energy sources comes from the urgent need to address the negative impact of fossil fuels on the environment and human health.

The world is facing an imminent threat of global warming and climate change due to the increasing levels of carbon dioxide emissions from the burning of fossil fuels. This has led to a rising demand for clean, renewable energy sources that can help reduce greenhouse gas emissions and mitigate the impacts of climate change.

Moreover, the depletion of finite resources such as coal, oil, and natural gas has made it necessary to explore alternative sources of energy that are sustainable and can be harnessed without causing harm to the environment. Renewable energy sources such as solar, wind, hydro, geothermal, and biomass offer a viable alternative to traditional fossil fuels and have the potential to provide a significant share of the world's energy needs.

The development of new renewable energy sources is also driven by economic considerations, as it offers a significant opportunity for investment and job creation. The renewable energy sector has seen tremendous growth in recent years and is expected to continue to grow as the demand for clean energy sources increases.

In conclusion, the primary motivation to develop new renewable energy sources is to address the urgent need for sustainable, clean energy sources that can mitigate the impact of climate change, reduce greenhouse gas emissions, and offer economic opportunities.

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Which of the following would zoning ordinances not address?


how tall a skyscraper can be

how much revenue a restaurant must make

how far from a school a power plant must be

how many parking spots a mall must have

Answers

I’m pretty sure it’s how much revenue a restaurant must make

Latane and Dabbs conducted a field experiment in elevators, in which bystanders were presented with an opportunity to help someone in need. This study indicated that help was most frequently offered when the bystander was __________ and the recipient was __________.

Answers

Latane and Dabbs' field experiment in elevators, where they investigated the conditions under which bystanders offered help to someone in need.

This study was conducted to examine the "bystander effect," which is the phenomenon where individuals are less likely to offer help to someone in need when there are other people around. In the experiment, it was found that help was more likely to be offered when there were fewer people present in the elevator (i.e., the bystander was alone or with fewer people), as this reduces the diffusion of responsibility.

Additionally, help was more frequently offered when the person in need showed clear signs of distress, as it made the situation more salient and the need for help more apparent.

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How much does 1 gallon of water weigh in pound given that the density of water is 1gram/ cm3

Answers

Explanation:

There are 8.35 pounds in a gallon of water. Water weighs 1 gram per cubic centimeter or 1 000 kilogram per cubic meter, i.e. density of water is equal to 1 000 kg/m³; at 25°C (77°F or 298.15K) at standard atmospheric pressure.



A length of pipe is 6.8 meters long. How many 1.5-meter lengths of pipe can be cut from that one length of pipe?

Answers

6.8÷1.5 = 4.53...

So, it's 4 pipe with some left over.

Hope this helps!

What should a company do to develop a better data culture?

Answers

Answer:

Some good ways and popular ways are:

1. Investing in data literacy.

2. Think about cybersecurity.

3. Choosing good and the right tools.

4. Establish metrics that matter.

Explanation:

These all are helpful.

(Hope this helped! Have a great day.)

The principal disadvantages(s) with the waterfall development methodology is (are) _____.
a. a long time elapses between completion of the system proposal and the delivery of the system
b. if the team misses important requirements, expensive post-implementation programming may be needed
c. the design must be completely specified on paper before programming begins
d. all of the above
e. none of the above

Answers

Note that the principal disadvantage (s) with the waterfall development methodology is (are) "All the Above" (Option D).

What is the Waterfall Development Methodology?

The Waterfall Development Methodology is a process for creating software that involves a series of steps that are followed in a specific order. It is called the "waterfall" method because each step flows into the next, like water flowing down a waterfall.

The first step in the Waterfall Development Methodology is to gather requirements, which means figuring out what the software should do. Next, a design is created, which outlines how the software will look and work. Then, the software is actually developed, which means writing the code and creating the software. After that, the software is tested to make sure it works correctly and any problems are fixed. Finally, the software is deployed, which means it is made available for people to use.

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Series aiding is a term sometimes used to describe voltage sources of the same polarity in series. If a 5 V and a 9 V source are connected in this manner, what is the total voltage?

Answers

Answer:Total Voltage = 14V

Explanation: it is possible that a circuit  can contain more than one source of electromotive force which can cause flow of current in the same or opposite direction . When the  connection to  voltage sources  allows for current  from the voltage sources to flow in  same direction,it is termed  Series aiding  Thus, the  Total/effective voltage in a series aiding circuit is  computed as the sum of series aiding voltages .

 Here we have the series aiding voltages to be 5V and 9V ,

therefore,

Total Voltage = 5V + 9V

= 14V

Elaborate the evolution of various Intel Pentium and I (i3, i5 & i7) series processors and do a detailed comparative study of these processors.

Answers

As a low-cost processor, the Intel Core i3 was debuted in 2010. It has two cores and hyper-threading, therefore it can manage four threads concurrently.

What distinguishes the Pentium Core i3 from the i5 from the i7?

The key distinction between the i3, i5 and i7 CPUs is that the former have dual cores while the latter have quad cores. I3 is better suitable for a casual user who browses the internet, plays a few games, and checks their mail.

What distinguishes the Intel i5 and i7 processors?

Generally speaking, Intel Core i7 CPUs are faster and more powerful than Core i5 CPUs. The more recent i7 chips are better suited for gaming because they can have up to six cores and 12 threads.

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Which of the following is not a step in a building’s life cycle?


evaluation

maintenance

demolition

resource extraction

Answers

Answer:

resource extraction

Explanation:

common sense

determine the times at which v(t) has a local minimum and maximum. express your answer as two numbers separated by a comma.

Answers

To determine the times at which v(t) has a local minimum and maximum, you need to find the critical points of the function. Critical points occur when the first derivative, v'(t), is equal to zero or does not exist.
1. Find the first derivative, v'(t).
2. Set v'(t) equal to zero and solve for t to find the critical points.
3. Use the second derivative test, v''(t), to classify each critical point as a local minimum, maximum, or neither.

To determine the times at which v(t) has a local minimum and maximum, we need to find the points where the derivative of v(t) is zero or undefined. We can then test these points to see if they correspond to a local minimum or maximum. Therefore, we need to calculate the derivative of v(t) and set it equal to zero. The points at which this occurs will give us the times of local minimum and maximum.

If v(t) is a smooth function, we can use calculus to find its derivative. If v(t) is given by a formula, we can differentiate it using the rules of differentiation. Once we have the derivative, we can solve for t to find the times when the derivative is zero.

For example, if v(t) = 3t^2 - 6t + 2, then v'(t) = 6t - 6. Setting v'(t) equal to zero, we get 6t - 6 = 0, which gives t = 1. Therefore, the local minimum or maximum occurs at t = 1.

To determine whether this point corresponds to a local minimum or maximum, we can look at the sign of the second derivative of v(t). If v''(t) is positive at t = 1, then we have a local minimum, and if v''(t) is negative, then we have a local maximum. If v''(t) is zero, then we need to use a higher-order derivative to determine the nature of the point.

In the example above, we have v''(t) = 6, which is positive, so the point t = 1 corresponds to a local minimum.

Therefore, the times at which v(t) has a local minimum and maximum for v(t) = 3t^2 - 6t + 2 are 1,0 (separated by a comma).

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