Propilot assist with navi-link's speed limit assist system works together to automatically adjust the vehicle's speed based on the posted speed limit and other traffic conditions.
When in auto mode, the system uses data from the navigation system to detect upcoming curves, exits, and interchanges, and adjusts the speed accordingly. Additionally, the speed limit assist system will provide an audible alert and display a visual warning on the instrument cluster if the vehicle exceeds the posted speed limit.
When the Speed Limit Assist system is engaged, the driver sets a desired speed, and the system will adjust the vehicle's speed to match the posted speed limit, up to the set speed. For example, if the driver sets the desired speed to 60 miles per hour and the posted speed limit is 55 miles per hour, the system will automatically adjust the vehicle's speed to 55 miles per hour.
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introduction to 80x86 assembly language and computer architecture 3rd edition answers
The book "Introduction to 80x86 Assembly Language and Computer Architecture 3rd Edition" provides answers and explanations related to assembly language programming and computer architecture concepts.
"Introduction to 80x86 Assembly Language and Computer Architecture" is a book that serves as a comprehensive resource for learning assembly language programming and understanding computer architecture. The third edition of this book offers answers to various questions and exercises related to these topics.
The book covers the fundamentals of assembly language programming for the 80x86 processor family, which includes popular architectures like Intel x86. It delves into the intricacies of low-level programming, instruction sets, memory management, and input/output operations. By providing answers to questions and exercises, the book helps readers solidify their understanding of the material and reinforce their knowledge through practical application.
Additionally, the third edition may include updates, enhancements, or revised content compared to previous editions, ensuring it remains relevant to the latest developments in assembly language programming and computer architecture.
For those interested in diving deeper into assembly language programming and computer architecture concepts, "Introduction to 80x86 Assembly Language and Computer Architecture 3rd Edition" can serve as a valuable resource.
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In the shop which of these indicates caution?
A: Red Light
B: Orange Light
C: Yellow Light
D: Green Light
Answer:
Yellow light
Explanation:
The flashing yellow light means: "proceed with caution." Traffic facing the yellow light has the right-of-way, but oncoming traffic usually also has a flashing yellow light, and cross-traffic will have a flashing red light.
YELLOW—A yellow signal light warns you that the red signal is about to appear. When you see the yellow light, you should stop, if you can do so safely. If you can't stop, look out for vehicles that may enter the intersection when the light changes. FLASHING YELLOW— What does a flashing yellow light mean?
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Which of the following would not be a good reason to use a linear model?
Thank
The disadvantage of using a linear model is that; It is sensitive to outliers and prone to multicollinearity.
What is the Linear Regression Model?Linear regression is defined as a regression technique whereby the independent variable has a linear relationship with the dependent variable.
Now, there are some advantages of this model in statistics such as;
Linear regression performs exceptionally well for linearly separable data.It is easy to implement and interpret.It carries out extrapolation beyond a specific data set.However, there are some disadvantages such as;
It is very sensitive to outliers.
It is prone to having multicollinearity.
It assumes linearity between dependent and independent variables.
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A section of land is 19.83ch x 19.09ch x 19.31ch x 20.14ch. The area of the lot is most nearly ...
A. 40ac
B. 38.39ac
C. unable to calculate
D. 37.38ac
When a section of land is 19.83ch x 19.09ch x 19.31ch x 20.14ch. The area of the lot is most nearly D. 37.38ac
How to calculate the areaIn order to calculate the area of the lot, we need to multiply the length and width of the lot. In this case, the length is 19.83ch and the width is 19.09ch.
Therefore, the area of the lot is 19.83ch x 19.09ch
= 373.8347 square chains.
To convert square chains to acres, we divide by 10. Therefore, the area of the lot in acres is:
= 373.8347 square chains / 10
= 37.38347 acres.
The answer is D.
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What accident theory divides an accident into three phases: pre-contact, contact, and post-contact?
The accident theory divides an accident into three phases: pre-contact, contact, and post-contact is the domino theory.
What is the domino theory?The domino theory is a geopolitical theory that holds that changes in democracy in one country have a domino impact on surrounding countries.
The multiple-factor theory examines not just the three domino theory phases—precontact, contact, and post-contact—but also additional elements that influence an accident, such as management, machine, media, and man.
Therefore, the domino theory separates an accident into three phases: pre-contact, contact, and post-contact.
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answer my question I will mark brainliest
The answer is 150cm
Answer:
150
Explanation:
Mark me Brainliest
Answer:
you have told the answer already as 150 cm
Explanation:
here is your answer hope you will enjoy mark me as brain list
thank you
Engine coolant is typically made up of what?
OA. 25% Antifreeze/75% water
OB. 50% Antifreeze/50% water
OC. 75% Antifreeze/25% water
OD. 33% Antifreeze/67% water
which one of these reduce fraction?
In the first problem, there were 9 processes, many of which were listed as pairs under the precedence relation. Suppose we are dealing with a system of only 5 processes named P1 through P5. You are given a set of constraints that are expressed by the following precedence relation: → = {(P1,P3), (P1, P5), (P2,P4), (P3, P4), (P4, P5)} Provide pseudocode to show how you can use semaphores to enforce these constraints (i.e., the precedence relation →).
This pseudocode ensures that the processes are executed in the correct order according to the precedence relation →
To enforce the precedence relation → using semaphores in a system of 5 processes named P1 through P5, we can use the following pseudocode:
// Initialize semaphores
Semaphore P1, P2, P3, P4, P5;
P1 = 1;
P2 = 0;
P3 = 0;
P4 = 0;
P5 = 0;
// Process P1
P(P1);
// Critical section for P1
V(P3);
V(P5);
// Process P2
P(P2);
// Critical section for P2
V(P4);
// Process P3
P(P3);
// Critical section for P3
V(P4);
// Process P4
P(P4);
// Critical section for P4
V(P5);
// Process P5
P(P5);
// Critical section for P5
In this pseudocode, we initialize semaphores for each process and set the initial values to allow P1 to execute first. We then use the P and V operations to control access to the critical sections for each process.
Process P1 has a critical section that must be executed before processes P3 and P5. Therefore, we use the V operation to signal that P3 and P5 can proceed after P1 has finished its critical section.
Process P2 has a critical section that must be executed before process P4. Therefore, we use the V operation to signal that P4 can proceed after P2 has finished its critical section.
Process P3 has a critical section that must be executed before process P4. Therefore, we use the V operation to signal that P4 can proceed after P3 has finished its critical section.
Process P4 has a critical section that must be executed before process P5. Therefore, we use the V operation to signal that P5 can proceed after P4 has finished its critical section.
Process P5 has a critical section that must be executed last. Therefore, we do not need to use any V operations to signal other processes to proceed.
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If determine the gradient of ø at the point P(1,3,2) 2. If and determine the expression grad(A.B) at the point C(1,2,1)
Gradient of ø at the point P(1,3,2):The gradient of the scalar field ø at a point P in space is a vector that points in the direction of maximum increase of ø at P and whose magnitude equals the rate of increase of ø in that direction.
It is denoted by grad ø. The formula for the gradient of ø at the point P(1,3,2) is given by;grad ø (1,3,2) = (∂ø/∂x)i + (∂ø/∂y)j + (∂ø/∂z)kThe partial derivatives are:∂ø/∂x = 6xy - 2z∂ø/∂y = 3x² + 2y∂ø/∂z = -2xSubstituting the values of x,y and z we have:∂ø/∂x = 6(1)(3) - 2(2) = 16∂ø/∂y = 3(1)² + 2(3) = 9∂ø/∂z = -2(1) = -2
Therefore, grad ø (1,3,2) = 16i + 9j - 2k2. Expression grad(A.B) at the point C(1,2,1)Let A and B be vectors in space. The expression grad(A.B) at a point C in space is given by the formula: grad(A.B) = A x (grad B) + B x (grad A)where x denotes the cross product of two vectors
Therefore, the expression grad(A.B) at the point C(1,2,1) is 10i - 6j + k.
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Water that has evaporated returns to earth as
Answer:
rain
Explanation:
evaoration causes clouds
clouds condense and rain
Answer:
rain
Explanation:
Question # 3
Multiple Choice
Which events significant to the United States transportation industry occurred in the 1970s and 1980s?
A.The FCC was created.
B.Laws to begin regulating pipeline transportation were enacted.
C.Many transportation industries were deregulated.
D.The regulation of transportation industries began.
Answer:
c Many transportation industries were deregulated.
Explanation:
correct on edge 2022
a commercial refrigerator with r-134a as the working fluid is used to keep the refrigerated space at -35 c by rejecting waste heat to cooling water that enters the condenser at 18 c at a rate of 0.25 kg/s and leaves at 26 c. the refrigerant enters the condenser at 1.2 mpa and 50 c and leaves at the same pressure subcooled by 6 c. if the compressor consumes 3.3 kw of power , determine (a) the mass flow rate of the refrigerant, b) the refrigerant load, c) the cop, and d) the minimum power input to the compressor for the same refrigeration load.
At 1.2mpa pressure and 50c
What is pressure?
By pressing a knife against some fruit, one can see a straightforward illustration of pressure. The surface won't be cut if you press the flat part of the knife against the fruit. The force is dispersed over a wide area (low pressure).
a)Mass flow rate of the refrigerant
Therefore h1= condenser inlet enthalpy =278.28KJ/Kg
saturation temperature at 1.2mpa is 46.29C
Therefore the temperature of the condenser
T2 = 46.29C - 5
T2 = 41.29C
Now,
d)power consumed by compressor W = 3.3KW
Q4 = QL + w = Q4
QL = mR(h1-h2)-W
= 0.0498 x (278.26 - 110.19)-3.3
=5.074KW
Hence refrigerator load is 5.74Kg
(COP)r = 238/53
(Cop) = 4.490
Therefore the above values are the (a) mass flow rate of the refrigerant, b) the refrigerant load, c) the cop, and d) the minimum power input to the compressor for the same refrigeration load.
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the distribution of ground shaking around the fault
Ground shaking is a term used to describe the vibration of the ground during an earthquake. Ground shaking is caused by body waves and surface waves. As a generalization, the severity of ground shaking increases as magnitude increases and decreases as distance from the causative fault increases.
Greek engineers had the unenviable task of moving largecolumns from the quarries to the city.One engineer,Chersiphron, tried several different techniques to do this. Onemethodwas to cut pivot holes into the ends of the stone andthen use oxen to pull the column. The 5-ft diameter columnweighs 14,000 lbs, andthe team of oxen generates a constantpull force of 2,000 lbs on the center of the cylinder,G. Knowingthat the column starts from rest and rolls without slipping,determine:(a) the velocity of its center,G,after it has moved7ft,and (b) the minimum static coefficient of friction that will keepit from slipping.
Answer:
yea
Explanation:
okkudjeheud email and delete the electronic version of this communication
The section 5(a)(1) of the osh act is commonly known as
Answer:
general duty clause
Explanation:
đạo hàm hàm boole là gì
Answer:
đạo hàm hàm boole là gì
Explanation:
Định nghĩa: Ký hiệu B = {0, 1} và Bn = {(x1, x2, …, xn) | xiB, 1≤ i ≤ n}, ở đây
B và Bn là các đại số Boole (xem 2) và 3) của Thí dụ 1). Biến x được gọi là một biến Boole nếu nó nhận các giá trị chỉ từ B. Một hàm từ Bn vào B được gọi là một hàm Boole (hay hàm đại số lôgic) bậc n.
Các hàm Boole cũng có thể được biểu diễn bằng cách dùng các biểu thức được
tạo bởi các biến và các phép toán Boole (xem Bảng 1 trong Thí dụ 1). Các biểu thức
Boole với các biến x1, x2, …, xn được định nghĩa bằng đệ quy như sau:
- 0, 1, x1, x2, …, xn là các biểu thức Boole.
- Nếu P và Q là các biểu thức Boole thì P, PQ và P+Q cũng là các biểu thức Boole.
Mỗi một biểu thức Boole biểu diễn một hàm Boole. Các giá trị của hàm này nhận
được bằng cách thay 0 và 1 cho các biến trong biểu thức đó.
Hai hàm n biến F và G được gọi là bằng nhau nếu F(a1, a2, …, an)=G(a1, a2, …,an)
với mọi a1, a2, …, anB. Hai biểu thức Boole khác nhau biểu diễn cùng một hàm Boole
được gọi là tương đương. Phần bù của hàm Boole F là hàm F với F (x1, x2, …, xn) =
),...,,( 1 2 nxxxF . Giả sử F và G là các hàm Boole bậc n. Tổng Boole F+G và tích Boole
FG được định nghĩa bởi:
(F+G)(x1, x2, …, xn) = F(x1, x2, …, xn)+G(x1, x2, …, xn),
(FG)(x1, x2, …, xn) = F(x1, x2, …, xn)G(x1, x2, …, xn).
Guided by the papers of Ferdowsi, Ahmad, and Paschedag? solve the following tasks for two cascaded buck converters with the parameter values given in Table 1. 1. Derive the closed-loop transfer function for each converter individually, using the small-signal model with voltage controlled feedback loop.
To solve this task for two cascaded buck converters, we'll use the small-signal model with a voltage-controlled feedback loop as described in the papers of Ferdowsi, Ahmad, and Paschedag.
1. For each converter individually, we need to derive the closed-loop transfer function. To do this, we start by examining the small-signal model for a buck converter. The small-signal model consists of the input voltage (Vin), output voltage (Vout), duty cycle (D), and the small-signal perturbations (ΔVin, ΔVout, ΔD).
According to the papers, the open-loop transfer function (OLTF) of a buck converter can be expressed as:
OLTF = ΔVout/ΔD = (Vout/Vin) * (1/(s*L*C)) / (s²L*C + (1-D)R*C)
To derive the closed-loop transfer function (CLTF) for each converter, we use the following formula:
CLTF = OLTF / (1 + OLTF * Feedback)
Here, "Feedback" refers to the voltage-controlled feedback loop gain. Since the parameter values for each converter are given in Table 1, you can plug them into the OLTF formula and then use the CLTF formula to derive the closed-loop transfer function for each converter individually.
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Which type of engineer finds his or her skills needed in the electronics, architectural, medical, and aerospace industries?
nuclear engineer
chemical engineer
biomedical engineer
mechanical engineer
Answer:
mechanical engineer
Explanation:
1) a field is bounded by an irregular hedge running between points e and f and three straight fences fg, gh and he. the following measurements are taken: ef = 167.76 m, fg = 105.03 m, gh = 110.52 m, he = 97.65 m and eg = 155.07 m offsets are taken to the irregular hedge from the line ef as follows. the hedge is situated entirely outside the quadrilateral efgh. e (0 m) 25 m 50 m 75 m 100 m 125 m 150 m f(167.76 m) 0 m 2.13 m 4.67 m 9.54 m 9.28 m 6.39 m 3.21 m 0 m calculate the area of the field to the nearest m2 .
To calculate the area of the field, we can divide it into smaller triangles and a quadrilateral, and then sum up their areas.
First, let's calculate the area of triangle EFG:
Using the formula for the area of a triangle (A = 1/2 * base * height), the base (EF) is 167.76 m and the height (offset from the irregular hedge to EF) is 25 m. So, the area of triangle EFG is A1 = 1/2 * 167.76 m * 25 m.
Next, we calculate the area of triangle FGH:
The base (FG) is 105.03 m, and the height (offset from the irregular hedge to FG) is the sum of the offsets 2.13 m, 4.67 m, 9.54 m, 9.28 m, 6.39 m, 3.21 m, and 0 m, which totals to 35.22 m. So, the area of triangle FGH is A2 = 1/2 * 105.03 m * 35.22 m.
Now, let's calculate the area of triangle GEH:
The base (HE) is 97.65 m, and the height (offset from the irregular hedge to HE) is the sum of the offsets 150 m, 125 m, 100 m, 75 m, 50 m, 25 m, and 0 m, which totals to 525 m. So, the area of triangle GEH is A3 = 1/2 * 97.65 m * 525 m.
Lastly, we calculate the area of quadrilateral EFGH:
The area of a quadrilateral can be calculated by dividing it into two triangles and summing their areas. We can divide EFGH into triangles EFG and GEH. Therefore, the area of quadrilateral EFGH is A4 = A1 + A3.
Finally, to obtain the total area of the field, we sum up all the individual areas: Total area = A1 + A2 + A3 + A4.
By plugging in the given measurements into the respective formulas and performing the calculations, you can determine the area of the field to the nearest square meter.
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An electrical engineer at GRIDCO is given two separate toolboxes to keep his working tools. The first toolbox has 4 white fuses and 3 black fuses and the second toolbox has 3 white fuses and 5 black fuses. Suppose the engineer select a fuse from the first toolbox and placed unseen in the second toolbox. What is the probability that: (a) the fuse drawn from the second toolbox is black? (B) the fuse drawn from the second toolbox is white? (8) ane is white?
(a) The probability of drawing a black fuse from the second toolbox is 4/7.
(b) The probability of drawing a white fuse from the second toolbox is 3/7.
(c) The probability that one fuse is white is 27/49.
To calculate the probabilities, we need to consider the number of white and black fuses in each toolbox.
First, let's determine the total number of fuses in each toolbox:
First Toolbox:
Total fuses = 4 white fuses + 3 black fuses = 7 fuses
Second Toolbox:
Total fuses = 3 white fuses + 5 black fuses = 8 fuses
(a) The probability that the fuse drawn from the second toolbox is black:
The probability of drawing a black fuse from the second toolbox depends on the fuse selected from the first toolbox. There are two scenarios to consider:
Scenario 1: The fuse selected from the first toolbox is black.
In this case, the second toolbox will have 3 black fuses remaining out of the total 7 fuses.
Probability = (Number of black fuses in the second toolbox)/(Total number of fuses in the second toolbox)
Probability = 3/7
Scenario 2: The fuse selected from the first toolbox is white.
In this case, the second toolbox will have 5 black fuses out of the total 7 fuses.
Probability = (Number of black fuses in the second toolbox)/(Total number of fuses in the second toolbox)
Probability = 5/7
To calculate the overall probability, we need to consider the probability of each scenario and weigh it by the probability of selecting a fuse of that color from the first toolbox. Since the fuse from the first toolbox has an equal chance of being white or black, we need to take an average of the probabilities in both scenarios.
Probability of drawing a black fuse from the second toolbox = (Probability of scenario 1 + Probability of scenario 2)/2
Probability of drawing a black fuse from the second toolbox = (3/7 + 5/7)/2
Probability of drawing a black fuse from the second toolbox = 8/14
Probability of drawing a black fuse from the second toolbox = 4/7
Therefore, the probability of drawing a black fuse from the second toolbox is 4/7.
(b) The probability that the fuse drawn from the second toolbox is white:
Similarly, we can calculate the probability of drawing a white fuse from the second toolbox. It will be the complement of the probability of drawing a black fuse.
Probability of drawing a white fuse from the second toolbox = 1 - Probability of drawing a black fuse from the second toolbox
Probability of drawing a white fuse from the second toolbox = 1 - 4/7
Probability of drawing a white fuse from the second toolbox = 3/7
Therefore, the probability of drawing a white fuse from the second toolbox is 3/7.
(c) The probability that one is white:
To calculate the probability that one fuse is white, we need to consider both scenarios: either the fuse drawn from the first toolbox is white and the fuse drawn from the second toolbox is black, or the fuse drawn from the first toolbox is black and the fuse drawn from the second toolbox is white.
Scenario 1: Fuse drawn from the first toolbox is white, and the second toolbox has a black fuse:
Probability = (Probability of drawing a white fuse from the first toolbox) * (Probability of drawing a black fuse from the second toolbox)
Probability = (3/7) * (5/7)
Scenario 2: Fuse drawn from the first toolbox is black, and the second toolbox has a white fuse:
Probability = (Probability of drawing a black fuse from the first toolbox) * (Probability of drawing a white fuse from the second toolbox)
Probability = (4/7) * (3/7)
To calculate the overall probability, we need to sum up the probabilities of both scenarios:
Probability that one fuse is white = Probability
of scenario 1 + Probability of scenario 2
Probability that one fuse is white = (3/7) * (5/7) + (4/7) * (3/7)
Probability that one fuse is white = 15/49 + 12/49
Probability that one fuse is white = 27/49
Therefore, the probability that one fuse is white is 27/49.
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In unguided medium (free space), the electromagnetic (EM) signal wave spreads as it leaves the transmit antenna. Since the power of the EM signal resides at the surface area of the wave front, signal power is described as signal power density (i.e., watts per area).
a. True
b. False
Answer:
a. True
Explanation:
Fast fourier transforms (FFT) are algorithms that speed up the computation of fourier coefficients compared to the traditional direct form discuss how the speed up is achieved
Answer:
Fast Fourier ( FFT ) algorithms speed up computation of Fourier coefficients by simply reducing the the computing time of a traditional direct form Fourier series. it achieves this by breaking complex DFTS into smaller DFTS to reduce its complexity and in turn reduce its computing time
Explanation:
Fast Fourier ( FFT ) algorithms speed up computation of Fourier coefficients by simply reducing the the computing time of a traditional direct form Fourier series. it achieves this by breaking complex DFTS into smaller DFTS to reduce its complexity and in turn reduce its computing time. an example of such FFT is Cooley-Tukey algorithm
Refrigerant-134a enters an adiabatic compressor at -30oC as a saturated vapor at a rate of 0.45 m3 /min and leaves at 900 kPa and 55oC. Determine (a) the power input to the compressor, (b) the isentropic efficiency of the compressor, and (c) the rate of exergy destruction and the second-law efficiency of the compressor. Take T0
Answer:
a) 1.918 kw
b) 86.23%
c) 0.26 kw
Explanation:
Given data:
T1 = -30°C = 243 k , T0 = 27°C
using steam tables
h1 = 232.19 KJ/kg
s1 = 0.9559 Kj/Kgk
T2 = 55°C P2 = 900 kPa
Psat = 1492 kPa, h2 = 289.95 Kj/Kg, s2 = 0.9819 Kj/kgk , m = 0.0332 kg/s
a) Determine the power input to the compressor
power input = 1.918 kw
b) Determine isentropic efficiency of compressor
Isentropic efficiency = 86.23%
c) Determine rate of exergy destruction
rate = 0.26 kw
Attached below is the detailed solution of the given problems
Draw the ipo chart for a program that reads a number from the user and display the square of that number ???Anyone please
Answer:
See attachment for chart
Explanation:
The IPO chart implements he following algorithm
The expressions in bracket are typical examples
Input
Input Number (5, 4.2 or -1.2) --- This will be passed to the Processing module
Processing
Assign variable to the input number (x)
Calculate the square (x = 5 * 5)
Display the result (25) ----> This will be passed to the output module
Output
Display 25
Define hermetic compressor
Answer:
Hermetic compressors are ideal for small refrigeration systems, where continuous maintenance cannot be ensured.
reason fo I.EE regulations in electrical installations
Answer:
The IEE Wiring Regulations Explained and Illustrated, Second Edition discusses the recommendations of the IEE Regulations for the Electrical Equipment of Buildings for the safe selection or erection of wiring installations. The book emphasizes earthing, bonding, protection, and circuit design of electrical wirings.
Explanation:
i hope it help you please make me brainlist and answer my question
The tank of the air compressor is subjected to an internal pressure of 90 psi. If the internal diameter of the tank is 22 in., and the wall thickness is 0.25 in., determine the stress components acting at point A. Draw a volume element of the material at this point, and show the results on the element. What would be the maximum shear that this material would experience?
Given Data:
Internal pressure of tank = 90 psi
Internal diameter of tank = 22 in
Wall thickness = 0.25 in
Stress components are to be determined at point A and maximum shear is to be calculated.
Volume Element:
The volume element at point A has six faces and the stress components are acting on these faces. The stress components acting at point A need to be calculated.
Stress Components:
Consider the cylinder element shown below:
The stress acting on the horizontal and vertical faces is called longitudinal stress and the stress acting on the oblique faces is called shear stress.
Longitudinal Stress:
Longitudinal stress is given by the formula:
σL = (P x D) / (4t)
Where,
P is the internal pressure of the tank
D is the internal diameter of the tank
t is the thickness of the tank
Substituting the values in the formula, we get:
σL = (90 x 22) / (4 x 0.25)
σL = 1980 psi
Shear Stress:
The shear stress is given by the formula:
τ = σ / 2
Where,
σ is the longitudinal stress
Substituting the value of σ in the formula, we get:
τ = 1980 / 2
τ = 990 psi
The shear stress acting on the oblique faces is 990 psi and the maximum shear stress acting on the element is 990 psi. Hence, the maximum shear stress that this material would experience is 990 psi.
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An air conditioner operates exactly as a refrigerator; it removes heat from a cold place (a bedroom, for example) and conveys it to a warmer place (usually the outside). Quantities of practical importance in understanding the efficiency of air conditioners are the rate of heat removal and the electric power input to the unit (i.e., the electric energy consumed per unit time). Find an expression for the coefficient of performance KKK of an air conditioner that has a rate of heat removal HHH and a power consumption PPP .
The expression for coefficient of heat performance is; K = H/P
We are given the expressions;
Coefficient of performance = K
Rate of heat removal = H
Power consumption = P
Formula for coefficient of performance is usually;
K = Q/W
However, the rate of heat removal H can be further expressed as;
H = Q/T
Where;
Q is heat removed
T is time
Similarly, for power consumption, it can also be expressed as;
P = W/T
Where;
W is workdone
T is time taken
Thus, Q = HT and W = PT
Finally;
K = HT/PT
K = H/P
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(a) (6 points) Find the integer a in {0, 1,..., 26} such that a = -15 (mod 27). Explain. (b) (6 points) Which positive integers less than 12 are relatively prime to 12?
a. a = 12 is the solution to the given congruence relation. b. the positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.
(a) The main answer: The integer a that satisfies a ≡ -15 (mod 27) is 12.
To find the value of a, we need to consider the congruence relation a ≡ -15 (mod 27). This means that a and -15 have the same remainder when divided by 27.
To determine the value of a, we can add multiples of 27 to -15 until we find a number that falls within the range of {0, 1,..., 26}. By adding 27 to -15, we get 12. Therefore, a = 12 is the solution to the given congruence relation.
(b) The main answer: The positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.
Supporting explanation: Two integers are relatively prime if their greatest common divisor (GCD) is 1. In this case, we are looking for positive integers that have no common factors with 12 other than 1.
To determine which numbers satisfy this condition, we can examine each positive integer less than 12 and calculate its GCD with 12.
For 1, the GCD(1, 12) = 1, which means it is relatively prime to 12.
For 2, the GCD(2, 12) = 2, so it is not relatively prime to 12.
For 3, the GCD(3, 12) = 3, so it is not relatively prime to 12.
For 4, the GCD(4, 12) = 4, so it is not relatively prime to 12.
For 5, the GCD(5, 12) = 1, which means it is relatively prime to 12.
For 6, the GCD(6, 12) = 6, so it is not relatively prime to 12.
For 7, the GCD(7, 12) = 1, which means it is relatively prime to 12.
For 8, the GCD(8, 12) = 4, so it is not relatively prime to 12.
For 9, the GCD(9, 12) = 3, so it is not relatively prime to 12.
For 10, the GCD(10, 12) = 2, so it is not relatively prime to 12.
For 11, the GCD(11, 12) = 1, which means it is relatively prime to 12.
Therefore, the positive integers less than 12 that are relatively prime to 12 are 1, 5, 7, and 11.
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