To sketch the T-s diagram for the ideal Rankine cycle with water as the working fluid, we need to follow the cycle and plot the corresponding states on the diagram. Here are the steps and assumptions:
Assumptions:
1. The Rankine cycle is an ideal cycle, which means all processes are internally reversible.
2. There are no pressure drops in the condenser and pump.
3. The turbine and pump have isentropic efficiencies of 100%.
4. The specific heat of water is constant over the temperature range of the cycle.
Now let's determine the parameters of the Rankine cycle:
(i) Dry fraction of the steam leaving the turbine:
Since the steam leaves the turbine as a wet vapor, the dry fraction can be determined using steam tables or the quality (x) can be obtained from the given temperature and pressure conditions.
(ii) The net work per unit mass of steam flowing:
The net work per unit mass of steam flowing through the turbine can be determined using the equation:
Net Work = h1 - h2
(iii) The heat transfer to the steam passing through the boiler:
The heat transfer to the steam passing through the boiler can be determined using the equation:
Qin = h1 - h4
(iv) The thermal efficiency:
The thermal efficiency of the Rankine cycle can be determined using the equation:
Thermal Efficiency = (Net Work / Qin) * 100
(v) The heat transfer to cooling water passing through the condenser:
The heat transfer to the cooling water passing through the condenser can be determined using the equation:
Qout = h4 - h3
Using steam tables or appropriate software, the enthalpies (h) at the given states can be determined, and the values for the above parameters can be calculated.
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A wedge would be best described as
A wheel and axle used to cTeate a rotary motion
A lever arm fixed to a shaft
A triangle shaped tool that functions as an inclined plane
A rectangular shaped tool that functions as a pulley
Answer:
A rectangular shaped tool that functions as a pulley.
Explanation:
i beleive
How much does 1 gallon of water weigh in pound given that the density of water is 1gram/ cm3
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.
Per ASME Boiler and Pressure Code, what is the ruling regarding the requirement of a water column on all boilers?
According to ASME Boiler and Pressure Code, water columns are required on all steam boilers.
The purpose of a water column is to provide a visual indication of the water level in the boiler. This is important because if the water level in the boiler gets too low, it can cause damage to the boiler and be a safety hazard.
The ASME Boiler and Pressure Code sets safety standards for boilers and pressure vessels, and it requires water columns to be installed on all steam boilers. The water column typically consists of a vertical pipe with a valve at the bottom and a glass sight gauge at the top, which allows the operator to visually check the water level.
Additionally, some states and municipalities may have their own regulations regarding water columns and boiler safety, so it's important to be familiar with the relevant codes and standards in your area.
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PLEASE HURRY!!!!
Which of the following can be inferred about Bill in the following scenario?
Bill has graduated and obtained a job as a geographer. He develops environmental models to analyze soil and water issues for a chemical company.
A) Bill studied environmental geography.
B) Bill earned a bachelor’s degree.
C) Bill earned a graduate degree.
D) Bill earned a certification in GIS technology.
a step-up transformer is designed to have an output voltage of 2 200 v (rms) when the primary is connected across a 110-v (rms) source. (a) if the primary winding has exactly 84 turns, how many turns are required on the secondary? turns (b) if a load resistor across the secondary draws a current of 1.80 a, what is the current in the primary, assuming ideal conditions? a (c) if the transformer actually has an efficiency of 89.0%, what is the current in the primary when the secondary current is 1.20 a? a
The number of turns required on the secondary is 1,680. The current in the primary is 22.9 A.
What is step-up transformer?A step-up transformer is a device that increases the voltage of an AC power supply. It works by having more turns in the secondary coil than the primary coil, allowing it to convert low voltage to high voltage.
a) The ratio of the number of turns in the primary winding to the number of turns in the secondary winding of a transformer is equal to the ratio of the output voltage to the input voltage.
N₂/N₁ = V₂/V₁
Plugging in the given values, we get:
N₂/84 = 2,200/110
N₂ = 84 x 2,200/110
N₂ = 1,680 tu
b) In an ideal transformer, the power is conserved, so the product of the primary current and the primary voltage is equal to the product of the secondary current and the secondary voltage. That is:
I₁V₁ = I₂V₂
We can rearrange this equation to solve for the primary current:
I₁ = (I₂V₂)/V₁
Plugging in the given values, we get:
I₁ = (1.80 A x 2,200 V)/110 V
I₁ = 36 A
The current in the primary is 36 A.
c) The efficiency of a transformer is given by the ratio of the output power to the input power. That is:
efficiency = output power / input power
P₁ = V₁I₁
We can use the efficiency formula to calculate the output power:
efficiency = output power / (output power + power loss)
output power + power loss = output power / efficiency
= (V₂I₂)² / V₁I₁ / 0.89
power loss = output power - (output power / efficiency)
= (V₂I₂)² / V₁I₁ / 0.89 - (V₂I₂)² / V₁I₁
Now we can use the power formulas to solve for the primary current:
P₁ = P₂ / efficiency
V₁I₁ = (V₂I₂) / 0.89
I₁ = (V₂I₂ / 0.89) / V₁
Plugging in the given values, we get:
I₁ = (2,200 V x 1.20 A / 0.89) / 110 V
I₁ = 22.9 A
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need urgent help!!
Determine the point(s) P on the line e with equation x−6 = ( y−3)/4 = ( 1−z)/3
for which the line connecting P with Q(2, −6, 5) is perpendicular to e.
The quartiles divide a set of observations into four portions, each representing 25% of the observations, together with the minimum and maximum values of the data set. The interquartile range, a measurement of variation around the median, is calculated using quartiles.
How are quartiles determined?In order to quartile a set of data with n items (numbers), we choose the n/4th, n/2nd, and n/4th items. Interpolation between the adjacent items is used if indexes n/4, n/2, or 3n/4 are not integers.For instance, the first quartile Q1 of ordered data is the 25th item, the second quartile Q2 is the 50th item, and the third quartile Q3 is the 75th item. The fourth quartile Q4 would be the highest item of data, and the zeroth quartile Q0 would be the minimum item; however, these extreme quartiles are referred to as the minimum and maximum of a set, respectively.Calculation:Statistical file: {2, -6, 5}
Quartile Q1: -6
Quartile Q2: 2
Quartile Q3: 5.
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PLZ HELP I GIVE BRAINLIEST!!
Determine the gauge of the wire needed in circuits that specify power source, wire length, amps, and maximum volt drop.
Part I
Locate the wire-size engineering reference table (Chart 44-2) of your textbook to determine wire gauge when the diameter of the wire is known.
Use the table to determine the wire gauge for each wire diameter shown below. You may need to round the numbers to obtain the correct answer.
d = 2576 inch
d = 0.03196 inch
d = 0.0100 inch
d = 0.1285 inch
d = 0.0508 inch
Using the answers you just obtained, place the wire sizes in order from the smallest gauge to the largest.
Remember: The smaller the wire gauge, the larger the diameter of the wire.
Part II
Using what you’ve learned in Part I and the directions below, determine the recommended wire gauge for the following circuits:
Circuit A. Starter circuit using 5 feet of wire, with a 12 V power supply, and a current of 200 Amps.
Circuit B. Dome light circuit using 14 feet of wire, with a 12 V power supply, and a current of 10 Amps.
Circuit C. A/C blower circuit using 24 feet of wire, with a 14.6 V power supply, and a current of 18 Amps.
Use Ohm’s law (E = IR) to determine the resistance in the wire for each circuit. Remember, Volts = E, and the given current = I. (You can refer back to page 433 in your textbook to find the exact formula you’ll need to use.)
Circuit A: R =
Circuit B: R =
Circuit C: R =
The relationship between the resistance and the circuit’s wire is shown in this formula:
R=4ρπ(Id2)
To determine the diameter of the wire needed for each circuit when you know the resistance and wire length, you would use this formula:
R=4ρπ(Id2) d=IR√×π4ρ
R = resistance
r = 250 ohm/inch
l = length of the wire (inches)
d = cross-sectional area of the wire (in2)
You should substitute the calculated value for R and the given values for r and l and find the value of d for each circuit. (Use π = 3.1416.)
For example, here’s an example for Circuit A:
d=IR√×π4ρ=5.24494×3.14161000=.064
Circuit A: d =
Circuit B: d =
Circuit C: d =
Now, look in the engineering reference table for standard American wire or metric gauges (on page 468 of your textbook) to determine the gauge of wire needed for the circuit.
Circuit A:
Circuit B:
Circuit C:
Answer:
See below.
Explanation:
Part I
Using Chart 44-2 in the textbook, we can determine the wire gauge for each given diameter
For d = 0.2576 inch, the wire gauge is 2 AWG.
For d = 0.03196 inch, the wire gauge is 20 AWG.
For d = 0.0100 inch, the wire gauge is 30 AWG.
For d = 0.1285 inch, the wire gauge is 8 AWG.
For d = 0.0508 inch, the wire gauge is 16 AWG.
Ordering the wire sizes from smallest to largest gauge, we have:
30 AWG < 20 AWG < 16 AWG < 8 AWG < 2 AWG
Part IICircuit A
Using Ohm's law, we can calculate the resistance in the wire:
R = E/I = 12/200 = 0.06 ohms
Substituting into the formula R = 4ρπ(Id^2), we can solve for the diameter of the wire:
d = sqrt(R/(4ρπI)) = sqrt(0.06/(42503.1416*200)) = 0.064 inches
Using the engineering reference table, we can see that the wire gauge needed for Circuit A is 2 AWG.
Circuit B
Using Ohm's law, we can calculate the resistance in the wire:
R = E/I = 12/10 = 1.2 ohms
Substituting into the formula R = 4ρπ(Id^2), we can solve for the diameter of the wire:
d = sqrt(R/(4ρπI)) = sqrt(1.2/(42503.1416*10)) = 0.023 inches
Using the engineering reference table, we can see that the wire gauge needed for Circuit B is 14 AWG.
Circuit C
Using Ohm's law, we can calculate the resistance in the wire:
R = E/I = 14.6/18 = 0.811 ohms
Substituting into the formula R = 4ρπ(Id^2), we can solve for the diameter of the wire:
d = sqrt(R/(4ρπI)) = sqrt(0.811/(42503.1416*18)) = 0.060 inches
Using the engineering reference table, we can see that the wire gauge needed for Circuit C is 4 AWG.
technician A says that a power balance test is a good way to narrow a misfire down to a particular cylinder(s). technician B says that a cylinder power balance test measures the volumetric efficiency of the cylinder being tested
Answer: Technician B.
Explanation: Please vote brainliest.
which of the following is true for the depletion region capacitance of a pn junction? select one: a. all of these b. the capacitance depends on the square root of the reverse bias for an abrupt step junction c. the capacitance depends on the cube root of the reverse bias for a linearly graded junction d. the capacitance decreases as the reverse bias increases e. the amount of charge stored increases as the reverse bias increases
All of these statements are true.
The depletion region functions as an insulating or dielectric substance. P-n junction diodes can therefore be compared to parallel plate capacitors.
What is PN junction?A P-N junction is the boundary or interface between the p-type and n-type semiconductor material types inside of a semiconductor.The process of doping produces the P-N junction in a semiconductor.In an electrical circuit, a diode (PN junction) makes it easier for current to flow in one way than the other.While reverse biasing is applying a voltage across a diode in the opposite direction, forward biasing refers to applying a voltage across a diode that facilitates easy current passage. High resistance is present in the p-n junction diode's depletion zone.As a result, the depletion region functions as an insulating or dielectric substance.P-n junction diodes can therefore be compared to parallel plate capacitors.Transition capacitance is the measurement of how much capacitance changes as voltage increases.
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One option for protecting a motor-compressor from overloads and failure to start is to use a time-delay fuse or inverse- time circuit breaker rated at not more than ______ percent of the rated load current.
One option for protecting a motor compressor from overloads and failure to start is to use a time-delay fuse or inverse-time circuit breaker rated at not more than 125% percent of the rated load current.
For the high torque demands of air compressors, compressor duty motors are specially created. Both single-phase and three-phase motors with open drip-proof frames made of rolled steel and ball bearings to manage belt load and tension are used.
An air compressor is a pneumatic device that transforms power (from an electric motor, diesel engine, or other engine, for example) into potential energy stored in pressurised air (also known as compressed air). A storage tank's pressure rises when an air compressor adds air using one of several techniques.
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1. It's very kind _______ you to help us. Thanks a lot. A. for B. to C. with D. of
A series RL circuit with 150 resistance and 0. 05 H inductance is energized by 200 V dc supply. Determine the rate of change of the current when t=0. 02s. 6. A current wave is represented by the equation i = 10e^(- 200x) amperes. Find the average and rms value of the wave if its period is 0. 05 seconds
A series RL circuit with 150 resistance and 0.05 H inductance is energized by a 200 V dc supply.This means that the current is increasing at a rate of 4000 amperes per second at \( t = 0.02 \) s.
In a series RL circuit, the rate of change of current is given by the formula
\( \frac{{di}}{{dt}} = \frac{{V}}{{L}} \),
where
\( \frac{{di}}{{dt}} \)
is the rate of change of current,
\( V \)
s the voltage applied, and
\( L \) is the inductance of the circuit.
In this question, we are given the resistance \( R \) as 150 ohms,
the inductance \( L \) as 0.05 H,
and the voltage \( V \) as 200 V.
We can substitute these values into the formula to find the rate of change of the current at \( t = 0.02 \) s.
By simplifying the expression, we find that the rate of change of the current is 4000 A/s. This means that the current is increasing at a rate of 4000 amperes per second at \( t = 0.02 \) s.
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Choose the correct rewritten sentence for “Scientists have discovered that the climate of our planet is becoming warmer every year.
What is the maximum rating of the motor branch-circuit short-circuit and ground-fault protective device for a 7 1/2-horsepower, 208-volt, 3-phase squirrel-cage induction motor using time-delay fuses?.
The maximum rating of the motor branch-circuit short-circuit and ground-fault protective device for a 7 1/2-horsepower, 208-volt, 3-phase squirrel-cage induction motor using time-delay fuses is approximately 45 A.
To determine the maximum rating of the motor branch-circuit short-circuit and ground-fault protective device for a 7 1/2-horsepower, 208-volt, 3-phase squirrel-cage induction motor, we can use the National Electrical Code (NEC) guidelines.
Step 1: Calculate Full Load Current (FLA)
The full load current (FLA) of a motor can be calculated using the formula:
\(\mathrm{FLA = \frac{Horsepower \times 746}{\sqrt{3}\times voltages \times efficiency \times power factor } }\)
Since efficiency and power factor are not given, we will assume typical values of 0.85 for efficiency and 0.85 for power factor.
Given:
Horsepower (HP) = 7.5 HP
Voltage = 208 V
Efficiency = 0.85
Power Factor = 0.85
Substitute these values into the formula:
\(\mathrm{FLA = \frac{7.5 \times 746}{\sqrt{3}\times 208 \times 0.85 \times 0.85 } }\)
Step 2: Determine the Maximum Rating:-
According to NEC guidelines, the maximum rating of the protective device can be calculated by multiplying the FLA by a percentage that corresponds to the type of motor and the type of protective device.
For a squirrel-cage induction motor with time-delay fuses, the percentage is typically around 175%.
Maximum Rating = FLA × 175%
Maximum Rating = 25.76A × 1.75 ≈ 45.12A
Rounded to the nearest standard fuse size, the maximum rating of the protective device is 45 A.
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I need help with these 2 questions, I am not sure what the answer is and would like to know the solution to them.
Based on the code given , the Step 1 is done by enforcing maximum() and min() in ARM7 assembly while Step 2 is done by enforcing the main while circle in ARM7 assembly.
What is the code about?To apply the maximum() and min() functions in ARM7 assembly, we can use some instructions to optimize the law and code speed. There is one possible way to do it based on the image attached.
Therefore, To apply the main while loop, we need to check if the left over of the division between result and d isn't zero, and if so, add c to affect. We can use the SWI 0x6 instruction to gain the balance of the division.
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See text below
We will translate the following C function, which calculates the Lowest Common Multiple (1cm) between two positive numbers, into ARM7 assembly:
unsigned int lcm(unsigned int a, unsigned int b)
{
(unsigned int c, d, result; // cannot be translated)
c = max(a, b); // i.e. c-a if a >= b, otherwise c=b d = min(a, b); // same, but vice-versa
result = c;
while ((result % d) != 0) {
}
result = result + c;
}
(return(result);
// cannot be translated)
In doing so, you are asked to optimize the assembly code for execution speed. i.e., a) fewest number of cycles, taking into account pipeline emptying/refilling on branch instructions for example, and b) fewest number of instructions.
Disregard the first/last lines of the lcm() function, which cannot be translated into assembly. This exercise is broken into these two steps:
1. First, implement the two successive lines min() and max() in ARM7 assembly:
c = max(a, b); // i.e. c-a if a>=b, otherwise c=b
d = min(a, b); // same, but vice-versa
[Hint 1]: Remember that the function's arguments, a and b, will be found in registers r0 and rl respectively. Every other register is free for you to use in your code. Remember to use conditional instructions whenever possible, to optimize code density and execution speed.
2. Implement the main while loop in ARM7 assembly.
[Hint 2]: The remainder of a division (i.e., the “modulo” operation %) can be obtained by relying on the BIOS, using the ARM7 instruction: SWI 0x6 (which cannot be conditional) after placing the input in the appropriate, predefined registers (see lecture notes), which cannot be selected/changed, and reading the output from the appropriate register.
Remember to comment each line of your program to explain what your code does.
Describe the changes to the memory and the registers, after the execution of each of the following five load/store instructions in the (five-lined) program below (i.e.. these five instructions are run as a sequence from the initial memory state shown below).
We assume big endian formatting.
Initial Memory State 0x420014 DE OC 63 20 0x420010 FF AE 10 00 0x42000c 13 46
FA 08
0x420008 0x420004 0x420000
24 AB
A0
22
00 00 CO
FF
00 1C OE 3B
Initial Registers
State
r0=0x00000000, r1=0x00000000, r2=0x00420008, 13=0x00000007,
r4=0x00000001
# Start of the program
LDR
r0, [r2, #-4]
LDRB
r1, [r2, r3]
STR
r1, [2], r4 LSL #2
SWP
STMDA
r4, r0, [r2]
# End of the program
r2!, (r4, r3, r0}
CODE
PUZZLE 92
B
C
M
H
K
1
M
Fiil the square with numbers with albhabets
Answer:
Explanation:
I'm not 100% this is what you want, but here it is:
2
3
13
8
11
A
13
AWi-Fi router has a MTB of 10 month. What is the Availability, if th hours and the number of days in a month is 307 99. 8316 100% $98. 80 $76. 20
The question is asking for the availability of a Wi-Fi router with an MTB (Mean Time Between) failure of 10 months. However, the provided numbers and information seem to be unrelated to the calculation of availability. To calculate availability, we need the uptime and the total time.
To calculate the availability of the Wi-Fi router, we need to know the uptime and downtime values. However, the given information does not provide these values. Without the uptime and downtime, it is not possible to calculate the availability accurately.
Availability is typically calculated using the following formula:
Availability = Uptime / (Uptime + Downtime)
It is important to note that availability is a measure of how reliably a system or service is accessible to users. It is usually expressed as a percentage, where higher percentages indicate better availability.
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"Transportation is the way of expanding business activies" justify this statement with long answer
Answer:
Transportation methods ensure deliveries to and from your facility flow smoothly and arrive at their designated destinations on time. Because of the importance of transportation to your business's success, it's vital to include this factor in your supply chain management strategy.
So,transportation is the way of expanding business activities.
Steam with specific enthalpy of 3278kj/kg goes through nozzle at station A velocity of 20m\s. If the exit area of the nozzle are adiabatic, find enthalpy per kg of steam leaving nozzle of steam is incompressible
If the steam is incompressible, it means that its specific volume remains constant throughout the process. In this case, the enthalpy per kilogram of steam leaving the nozzle will also remain constant.
Given that the specific enthalpy of the steam at station A is 3278 kJ/kg and the velocity at station A is 20 m/s, we can calculate the enthalpy per kilogram of steam leaving the nozzle.
The enthalpy per kilogram of steam leaving the nozzle can be determined using the specific enthalpy equation:
h2 = h1 + (V1^2 - V2^2)/2
Where:
h1 = specific enthalpy at station A
h2 = specific enthalpy at the exit of the nozzle
V1 = velocity at station A
V2 = velocity at the exit of the nozzle
Since the steam is incompressible, the specific volume remains constant. Therefore, the velocity at the exit of the nozzle, V2, can be calculated using the equation:
V2 = V1 * (A1/A2)^0.5
Where:
A1 = cross-sectional area at station A
A2 = cross-sectional area at the exit of the nozzle
Since the exit area of the nozzle is adiabatic, the cross-sectional area at the exit remains the same as the cross-sectional area at station A (A1 = A2).
Substituting the given values into the equations, we can calculate the enthalpy per kilogram of steam leaving the nozzle:
V2 = V1 * (A1/A2)^0.5
V2 = 20 m/s * (1/1)^0.5
V2 = 20 m/s
h2 = h1 + (V1^2 - V2^2)/2
h2 = 3278 kJ/kg + (20^2 - 20^2)/2
h2 = 3278 kJ/kg
Therefore, the enthalpy per kilogram of steam leaving the nozzle is 3278 kJ/kg, assuming the steam is incompressible.
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What is the output? for num in range(3): print (num + 5)
Answer: 5 6 7
Explanation:
you can run this in python and get this result
The output for the given program is: 5 6 7
What is Python Programming Language?This refers to the high-level language that was created and is used for data structures due to its OOP (object-oriented programming).
Hence, this python code asks for an array of numbers in the range of 3 and when that is found, it should make a display of the number and increment it.
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What is the hardest part of engineering?
ANSWER:
Aerospace Engineering. ...
Chemical Engineering. ...
Biomedical Engineering.
EXPLANATION:
This is all i know but ... I hope this helps~
how to create a bash script that unzip several zipped
files in a folder and sort them alphabetical and remove white
spaces from their names ?
To create a bash script that unzips several zipped files in a folder and sorts them alphabetically while removing whitespaces from their names, the following steps should be taken.
Step 1: Navigate to the folder containing the zipped files you want to unzip
Step 2: Create a new bash script file using the touch command, for example, touch unzip_sort.sh
Step 3: Open the script file in a text editor of your choice. For example, nano unzip_sort.sh
Step 4: Add the following code to the file:#/bin/bashfor i in `ls *.zip | sort`; dounzip "$i" && rm "$i"donefor file in *; do mv "$file" `echo $file | tr ' ' '_'` 2>/dev/null; done
Step 5: Save and close the file
Step 6: Make the script executable using the chmod command. For example, chmod +x unzip_sort.sh
Step 7: Run the script using the following command: ./unzip_sort.sh
The first paragraph of the answer explains the steps to create a bash script that unzips several zipped files in a folder and sorts them alphabetically while removing whitespaces from their names. It includes a step by step guide on how to navigate to the folder, create a new bash script file, open the script file in a text editor, add the code to the file, save and close the file, make the script executable and run the script using a command.
The second paragraph explains each of the steps in detail. It explains what each of the commands used in the steps does and provides examples of how to use them. This will help readers who are not familiar with bash scripting to understand what the script does and how it works.
The third paragraph highlights the benefits of using a bash script to unzip several zipped files in a folder and sort them alphabetically while removing whitespaces from their names. It explains that using a script makes the process faster and more efficient, especially when dealing with a large number of files. It also makes it easier to perform the same operation multiple times, as all that is required is to run the script again.
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Anyone got a pc that can run 240 fps? Around like 1,300 dollars that can run 240 fps on fortnite whoever answers and gives me a good pc I will give brainliest
Answer:
What do u need it for just gaming or for streaming and other things
a pipe discharges wine into a 1.5m diameter tank. Another pipe (15cm diameter), located near the base of the, is used to discharge wine out of the tank. Calculate the volumetric flow rate into the tank if the wine level remains constant at 2.5m.
The volumetric flow rate into the tank if the wine level remains constant at 2.5m is; 0.1232 m³/s
How to Calculate Volumetric Flow Rate?The formula for volumetric flow rate is;
V' = area * velocity
We are given;
Diameter; d = 15 cm = 0.15 m
Thus;
Area; A = (π/4)d²
A = (π/4)(0.15)²
A = 0.0176 m²
Velocity is; v = √(2gh)
v = √(2 * 9.8 * 2.5)
v = 7 m/s
Thus volumetric flow rate is;
V' = 0.0176 * 7
V' = 0.1232 m³/s
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Which of these things is a good thing to do when steering to avoid a crash?
One cloud-delivered security service that provides security for branches and mobile users is Zscaler.
This service offers a cloud-native platform that provides secure access to applications and data for remote workers, as well as secure connectivity for branch offices. Zscaler's security solution includes web security, cloud sandboxing, threat prevention, data protection, and secure access service edge (SASE) capabilities, all delivered from a single platform. This ensures that all traffic, whether from branch offices or mobile users, is secured with the same level of protection. Additionally, Zscaler provides a zero trust security model that verifies identity and device posture before granting access to corporate resources, making it an ideal solution for today's distributed workforce.
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The acceleration of a particle is defined by the relation a= -k/x. It has been experimentally determined that v=15 ft/s when x=0.6 ft and that v=9 ft/s when x=1.2 ft. Determine (a) velocity of particle when x=1.5 ft.(b)Position of particle at which velocity is zero.
Answer:
(a) 5.89 ft/s
(b) x= 1.77 ft
Explanation:
Given that the acceleration of the particle, a=-k/x
As \(a=v\frac{dv}{dx}\) , so
\(v\frac{dv}{dx}=-\frac{k}{x} \\\\\Rightarrow vdv=-k\frac{dx}{x} \\\\\)
On integrating both sides, we have
\(\frac{v^2}{2}=-k\ln(x) + C\cdots(i)\)
where C is a constant.
At x=0.6 ft, v=15 ft/s
From equation (i)
\(\frac{15^2}{2}=-k\ln(0.6) + C \\\\\Rightarrow C=\frac{225}{2} + k\ln(0.6) \cdots(ii)\)
Similarly, at x=1.2 ft, v=9 ft/s
\(\frac{9^2}{2}=-k\ln(1.2) + C \\\\\Rightarrow \frac{81}{2} = -k\ln(1.2) + \frac{225}{2} + k\ln(0.6) \\\\\Rightarrow k(\ln(1.2) - \ln(0.6))= \frac{225}{2}-\frac{81}{2} \\\\\Rightarrow k\ln(1.2/0.6)= 72 \\\\\Rightarrow k = 72 / ln(2)=103.87\)
From equation (ii),
\(C=\frac{225}{2} + 103.87 \times \ln(0.6) \\\\\Rightarrow C=112.5-53.06=59.44\)
Putting the value of k and C in the equation (i), we have
\(\frac{v^2}{2}=-103.87\ln(x) + 59.44 \\\\\Rightarrow v^2=-207.74\ln(x) + 118.88 \\\\\Rightarrow v = \sqrt{-207.74\ln(x) + 118.88}\)
(a) At x=1.5 ft, the velocity of the particle is
\(\Rightarrow v = \sqrt{-207.74\ln(1.5) + 118.88} \\\\\)
\(\Rightarrow v = 5.89\) ft/s
At x=1.5 ft, the velocity of the particle is 5.89 ft/s.
(b) For v=0, we have
\(\Rightarrow 0 = \sqrt{-207.74\ln(x) + 118.88} \\\\\Rightarrow \ln(x) = -118.88/-207.74=0.572 \\\\\Rightarrow x= e^{0.572} \\\\\)
\(\Rightarrow x= 1.77\) ft
At x= 1.77 ft the velocity of the particle is zero.
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