Let "g; A -> real;" and assume that "f" is a bounded function on "A subset real" . (i.e. there exists "0 < M" satisfying "abs(f(x) <= M)" for all "x in A" ). Show that if "limit(g(x), x = c) = 0" , then "limit(g(x)*f(x), x = c) = 0" as well.
Given an example to show that this does not necessarily hold if f is not bounded.
Answers
If "g(x)" tends to 0 as "x" approaches "c" and "f(x)" is a bounded function, then "g(x)*f(x)" tends to 0 as "x" approaches "c". However, this does not hold if "f(x)" is not bounded.
To prove that if "limit(g(x), x = c) = 0" then "limit(g(x)*f(x), x = c) = 0" for a bounded function f on A, we will use the definition of limit.
Given ε > 0, since "limit(g(x), x = c) = 0", there exists a δ > 0 such that for all x in A with 0 < |x - c| < δ, we have |g(x)| < ε/M (since M is a bound for f(x)).
Then, for the same δ, we have that |g(x)*f(x)| = |g(x)| * |f(x)| < (ε/M) * M = ε for all x in A with 0 < |x - c| < δ. Therefore, by definition, "limit(g(x)*f(x), x = c) = 0".
To provide an example where this does not hold if f is not bounded, let g(x) = 1/x and let f(x) = x². Then, "limit(g(x), x = 0) = ∞", but "limit(g(x)*f(x), x = 0) = 0". Therefore, the statement does not hold if f is not bounded.
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Related Questions
Tech A says that LED brake lights illuminate faster than incandescent bulbs. Tech B says that LED brake lights have
more visibility and last longer. Who is correct?
Answers
Answer:
Both
Explanation:
What is the process that a ceramist uses to knead and remove pockets of air from wet clay?
A. throwing
B. slabbing
C. coiling
D. wedging
Answers
The process that a ceramist uses to knead and remove pockets of air from wet clay is called wedging.
Wedging involves a technique of working the clay by hand to remove any air bubbles or inconsistencies in the clay's texture. The ceramist takes a lump of wet clay and repeatedly kneads, compresses, and folds it to ensure uniformity and eliminate air pockets. This process helps to improve the clay's plasticity, remove excess moisture, and create a more workable and consistent material for shaping and forming. Wedging is an essential step in the preparation of clay before it can be used for various ceramic techniques such as throwing, slabbing, or coiling. It ensures that the clay is free from air bubbles that could cause structural weaknesses or uneven drying during the firing process.
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drawing of twisted drill
Answers
5. (20 points) Identify and resolve (via forwarding) all the data hazards in the MIPS pipeline for the following sequence of MIPS instructions. Insert pipeline bubbles as necessary if forwarding cannot completely solve the data hazards. You may use multi-cycle pipeline representation to show the forwarding and bubbles. sub $4, $1, $3 sw $4, 0($2) lw $1, 0($2) add $1, $3, $4
Answers
Answer:
a
Explanation:
Why is formwork used in construction
Answers
Formwork is a temporary structure that is used in construction to provide support and shape to freshly poured concrete until it is strong enough to stand on its own.
It is a crucial component of any construction project as it ensures that the concrete is poured into the desired shape and size, and prevents any potential collapses or deformations. Additionally, formwork helps to create a smooth and uniform finish to the concrete surface, which is important for both aesthetic and functional purposes. Overall, formwork is an essential tool in modern construction, providing a safe and reliable method of shaping and supporting concrete structures.
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You must create a Low Pass Filter for an audio amplifier. You must pass 10khz and block
60khz. In designing this, you must choose a cutoff frequency exactly half way between
these two frequencies. In addition, you must use a 0.2uF capacitor in you LPF circuit.
Given these criteria, analyze this circuit, and determine the necessary resistor value in
Ohms. Find the output Voltage at both ends of the spectrum. Based on your results, is
this a good design? NOTE: You MUST show your work (when using MS Word, choose
“Insert”--- “Equation”).
a. Solve for fc
b. Solve for R
c. Solve for Vout at 10khz
d. Solve for Vout at 60khz
e. Good design> (yes or no with an explanation)
Answers
Answer:
) You must create a Low Pass Filter for an audio amplifier. You must pass 10khz and block
60khz. In designing this, you must choose a cutoff frequency exactly half way between
these two frequencies. In addition, you must use a 0.2uF capacitor in you LPF circuit.
Given these criteria, analyze this circuit, and determine the necessary resistor value in
Ohms. Find the output Voltage at both ends of the spectrum. Based on your results, is
this a good design? NOTE: You MUST show your work (when using MS Word, choose
“Insert”--- “Equation”). (6 marks)
a. Solve for fc
b. Solve for R
c. Solve for Vout at 10khz
d. Solve for Vout at 60khz
e. Good design> (yes or no with an explanation)
Explanation:
which of the following devices are used in networking? check all that apply?
switches, hubs,TCP or routers
Answers
Answer:
Hub , switch port , transmission media , hope I helped
Explanation:
Listen When using the range function, what effect does the specification of a third argument have? The third argument is simply included in the sequence, assuming it wasn't already in the range. The third argument specifies a step value to be used in the range. The third argument is used as the starting point for the range function. The third argument declares an exponential value the numbers will be raised to.
Answers
The third argument in the range function specifies a step value to be used in the range. The Option B.
How does the third argument affect the sequence?The third argument in the range function determines the step value for generating the sequence. By default, the step value is 1 which means the sequence increments by 1.
But by specifying a different value as the third argument which helps control the increment between each element in the sequence. For example, if the third argument is set to 2, the sequence will increment by 2 (e.g., 0, 2, 4, 6, ...).
Similarly, if third argument is set to -1, the sequence will decrement by 1 (e.g., 10, 9, 8, 7, ...). The third argument allows to customize the pattern and direction of the generated sequence based on your specific needs.
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If the two 304-stainless-steel carriage bolts of the clamp each have a diameter of 10 mmmm, and they hold the cylinder snug with negligible force against the rigid jaws, determine the temperature at which the average normal stress in either the magnesium or the steel first becomes 12.0 MPaMPa .
Answers
Answer: hello some data related to your question is missing attached below is the missing data
answer:
T2 = 265°C
Explanation:
First step : calculate sum of vertical forces
∑ y = 0
Fmg - 2(0.5 Fst ) = 0
∴Fmg = ( 12 * 10^6 ) ( 2 * π/4 (0.01)^2 )
= 1884.96 N
Also determine the Compatibility equation in order to determine the change in Temperature
ΔT = 250°C
therefore Temperature at which average normal stress becomes 12.0 MPa
ΔT = T2 - T1
250°C = T2 - 15°C
T2 = 250 + 15 = 265°C
attached below is the detailed solution
Consider a vólume of fluid for which the 3D Cartesian velocity components are given by: u
v
w
= 2
Hσ
e kz
cos(kx−σt)
=0
= 2
Hσ
e kz
sin(kx−σt)
where x is a horizontal coordinate, z is the vertical coordinate, and t is time. The parameters H,σ= T
2π
,k= L
2π
,T, and L are constants. 1. For the x-direction, find expressions for: (a) The local acceleration term in the equation of motion (LA). (b) The advective acceleration term in the equation of motion (AA).
Answers
(a) The local acceleration term in the equation of motion (LA) for the x-direction is given by -2Hσ²e^(kz)cos(kx - σt).
(b) The advective acceleration term in the equation of motion (AA) for the x-direction is zero.
The given fluid velocity components in Cartesian coordinates are u = 2Hσe^(kz)cos(kx - σt) and v = 0, w = 2Hσe^(kz)sin(kx - σt), where x represents the horizontal coordinate, z represents the vertical coordinate, and t represents time.
In order to find the expressions for the local acceleration term (LA) and the advective acceleration term (AA) in the equation of motion for the x-direction, we differentiate the x-component of velocity twice with respect to time.
The local acceleration term (LA) represents the acceleration of fluid particles due to the changing velocity field within the fluid. To calculate LA in the x-direction, we differentiate the x-component of velocity with respect to time twice. The first derivative with respect to time gives us the partial derivative of u with respect to time, which is -2Hσ²e^(kz)sin(kx - σt). Taking the second derivative with respect to time gives us the local acceleration term in the x-direction: -2Hσ²e^(kz)cos(kx - σt).The advective acceleration term (AA) represents the acceleration of fluid particles due to the change in velocity as they move through the fluid. In this case, the x-component of velocity does not vary with time, i.e., ∂u/∂t = 0. Therefore, the advective acceleration term in the x-direction (AA) is zero.In summary, the local acceleration term (LA) in the x-direction is given by -2Hσ²e^(kz)cos(kx - σt), while the advective acceleration term (AA) in the x-direction is zero.
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write a program which calls a function relprime3(a, b, c) which returns true if all pairs of the three nimbers passed to it are relatively prime. the function relPrime3 should call your function relPrime from problem #1 of this assigment yhree times. here is some sample input and output of your program (run twice). your function should not call the print or input functions ; that should be done in your main program
Answers
Here's a Python program that defines the relprime3 function and uses it to check if all pairs of three numbers passed to it are relatively prime. It also calls the relPrime function from Problem #1 to check if two numbers are relatively prime.
python
Copy code
def gcd(a, b):
if a == 0:
return b
return gcd(b % a, a)
def relPrime(a, b):
return gcd(a, b) == 1
def relprime3(a, b, c):
if not relPrime(a, b):
return False
if not relPrime(a, c):
return False
if not relPrime(b, c):
return False
return True
# Sample input
a = 3
b = 5
c = 7
# Call relprime3 function
result = relprime3(a, b, c)
# Print output
print(f"Are {a}, {b}, and {c} relatively prime? {result}")
In this program, gcd is a function that calculates the greatest common divisor of two numbers. relPrime is a function that returns True if two numbers are relatively prime (i.e. their greatest common divisor is 1).
The relprime3 function takes three arguments a, b, and c, and checks if all pairs of the three numbers are relatively prime by calling relPrime three times. If any pair of numbers is not relatively prime, it returns False. Otherwise, it returns True.
In the sample input, the program checks if 3, 5, and 7 are relatively prime by calling relprime3(3, 5, 7). The output should be:
sql
Copy code
Are 3, 5, and 7 relatively prime? True
You can run the program multiple times with different inputs to check if the relprime3 function is working correctly.
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True or False the loope instruction jumps to a label under only one condition: when zf is clear
Answers
False. The loop instruction jumps to a label based on the ECX register.
What is loop instruction?A loop instruction is a type of programming instruction that allows a set of instructions to be repeated until a certain condition is met. This type of instruction is useful when performing a set of instructions repeatedly, such as counting from one to ten, or generating a report with multiple data points. Loops can also be used to execute a set of instructions multiple times, making it more efficient to perform a task. Loop instructions are used in a variety of programming languages, including C, Java, Python, and JavaScript.
This register is decremented by one each time a loop instruction is executed. When the ECX register reaches 0, the loop instruction will jump to the label.
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21. It doesn't really matter whether your adapters are clean as long as they're not worn.
Answers
It doesn't really matter whether your adapters are clean as long as they're not worn is a true statement.
What is an adapter?An adapter is said to be a kind of a physical device that gives room for a single hardware or electronic interface to be plugged in(accommodated without loss of function) to another hardware or electronic interface.
An adapter is known to be an electronic device tht is often used in regards to electrical connections.
Note that an adapter can work even if they are dirty. Hence, It doesn't really matter whether your adapters are clean as long as they're not worn is a true statement.
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the major components of stockholders' equity are ________.
Answers
The major components of stockholders' equity are contributed capital and earned capital.
Stockholders' equity (SE) is a corporation's residual interest in assets after deducting liabilities. The stockholders' equity of a company represents the ownership interest of its owners. It is also known as net assets or shareholders' equity.
The stockholders' equity of a corporation is calculated by subtracting the total liabilities from the total assets. The remaining amount is the stockholders' equity.
The stockholders' equity is divided into two primary components: Contributed capital: This represents the funds obtained by a corporation in exchange for its equity securities.
Earned capital: This represents the corporation's accumulated profits and losses that have not been distributed as dividends.
The following are the major components of stockholders' equity: Contributed capital: This includes common stock, preferred stock, and additional paid-in capital.
Earned capital: This includes retained earnings, accumulated other comprehensive income, and treasury stock.
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Lydia is the CEO for a large pharmaceutical manufacturer. Her company is in the final stages of FDA
approval for a new drug for diabetics. The new drug is expected to bring in billions of dollars for the company. Lydia is acquainted with Bradley,
the CSHO on rotation for OSHA inspections. Lydia is concerned that a surprise inspection may turn up violations, which could affect the launch of
the drug. Lydia reaches out to Bradley and casually mentions that it would be helpful if he could tell her when the next OSHA inspection will be
Should Bradley give Lydia advance notice about an upcoming inspection?
No, because he could receive fines and a jail term.
No, because this situation does not meet the criteria for advance notice.
Yes, because employers may request an OSHA inspection at any time.
Yes, because the inspection will be conducted during regular business hours.
Answers
It is a criminal offense for any person to give unauthorized advance notice of an OSHA inspection.
Write an Essay describing in your own words, the two-way Communication Cycle naming all the stages and explaining what goes on at each stage. Illustrate any two barriers that may occur at each of the stages. A correctly labelled diagram is essential for your essay.
Answers
n
e
g
r
o
means black in spanish!
1 Define the following technical terms: A) Sewage Factor B) Connection Factor C) Infiltration Coe. D) Design Period E) Drop Manhole F) Self Cleansing velocity 2 Which factors do affect on water demand
Answers
A) Sewage Factor: It represents the proportion of water inflow that is expected to be discharged as sewage. It is used in the design of sewer systems to estimate the quantity of sewage flow that will be generated.
B) Connection Factor: It represents the percentage of buildings or properties that are expected to connect to a sewer system. It is used in the design of sewer systems to estimate the total number of connections that will be made to the system.
C) Infiltration Coefficient: It represents the rate at which water enters a sewer system through cracks, joints, and other defects in pipes. It is used in the design of sewer systems to estimate the volume of infiltration that will occur during wet weather conditions.
D) Design Period: It is the length of time for which a particular engineering project is designed to function effectively. For example, in the case of water supply systems, the design period may be 20-30 years, during which the system is expected to meet the water demand requirements of the users.
E) Drop Manhole: It is a type of manhole that is constructed at a location where the sewer pipe changes direction from a horizontal to a vertical alignment. The purpose of a drop manhole is to reduce the velocity of the sewage flow and prevent damage to the downstream sewer structures.
F) Self Cleansing Velocity: It is the minimum velocity required in a sewer pipe to prevent the deposition of solids and ensure the self-cleansing of the pipe. A value of twice the average velocity is commonly used as the self-cleansing velocity.
The factors that affect water demand include population size, economic activity, climate, lifestyle, and water pricing policies. Changes in any of these factors can influence the level of water demand in a given area. For example, an increase in population size or economic activity can lead to a higher demand for water, while the implementation of water conservation measures can reduce water demand.
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Drag each tile to the correct box. Not all tiles will be used.
Adam wants to become a certified professional engineer. What are the steps that he will have to follow?
Answers
Answer:
I think it is the 2,3,5 and 1 ones
analog to digital conversion in digital electronics
Answers
The purification of hydrogen gas is possible by diffusion through a thin palladium sheet. Calculate the number of kilograms of hydrogen that pass per hour (in kg/h) through a 4.0-mm thick sheet of palladium having an area of 0.25 m^2 at 500°C. Assume a diffusion coefficient of 6.0 x 10^-8 m^2/s, that the concentrations at the high- and low-pressure sides of the plate are 3.5 and 0.25 kg/m^3 (kilogram of hydrogen per cubic meter of palladium), and that steady-state conditions have been attained. (clearly show your solution step by step, pay attention to units otherwise you will lose points!)
Answers
Computer Science question
Answers
Answer: а в г
Explanation:
Single plantwide factory overhead rate The total factory overhead for Cypress Marine Company is budgeted for the year at $900,000. Cypress Marine manufactures two types of boats: speedboats and bass boats. The speedboat and bass boat each require 10 direct labor hours for manufacture. Each product is budgeted for 400 units of production for the year. a. Determine the total mumber of budgeted direct labor hours for the year, direct labor hours b. Determine the single plantwide factory overhead rate. Round your answer to two decimal places. per dih c. Determine the factory overhead allocated per unit for each product using the single plantwide factory overhead rate. 5peedboats 4 per unit Bass boats 4 per unit
Answers
Factory overhead allocated per unit for speedboats is $1,125 per unit and that for bass boats is $1,125 per unit.
a. To determine the total number of budgeted direct labor hours for the year: Direct labor hours Speedboat = Direct labor hours Bass boat = Total direct labor hours Speedboat = Number of units × Direct labor hours per unit SpeedboatTotal direct labor hours Speedboat = 400 × 10Total direct labor hours Speedboat = 4,000Direct labor hours Bass boat = Number of units × Direct labor hours per unit Bass boatTotal direct labor hours Bass boat = 400 × 10Total direct labor hours Bass boat = 4,000Total budgeted direct labor hours = Total direct labor hours Speedboat + Total direct labor hours Bass boatTotal budgeted direct labor hours = 4,000 + 4,000Total budgeted direct labor hours = 8,000Answer: Total number of budgeted direct labor hours for the year is 8,000 direct labor hours.b. The single plantwide factory overhead rate is calculated as follows:Single plantwide factory overhead rate = Total factory overhead / Total budgeted direct labor hoursSingle plantwide factory overhead rate = $900,000 / 8,000Single plantwide factory overhead rate = $112.50Answer: The single plantwide factory overhead rate is $112.50 per direct labor hour.c. Factory overhead allocated per unit for each product using the single plantwide factory overhead rateSpeedboatsFactory overhead allocated per unit = Single plantwide factory overhead rate × Direct labor hours per unitSpeedboatsFactory overhead allocated per unit = $112.50 × 10SpeedboatsFactory overhead allocated per unit = $1,125Bass boatsFactory overhead allocated per unit = Single plantwide factory overhead rate × Direct labor hours per unitBass boatsFactory overhead allocated per unit = $112.50 × 10Bass boatsFactory overhead allocated per unit = $1,125.
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Drag and heat transfer on a falling sphere) A hot copper sphere of diameter D = 20 mm is initially at T = 200°C and falling through a bath of glycerin at 20°C. Initially, the sphere is falling at a velocity u = 0.5 m/s. Assume that the properties of copper are pcu = 8876 kg/m³, ccu = 374.4 J/kg-K, kcu = 389.1 W/m-K, and the properties of glycerin are pg = 1200 kg/m³, g = 0.01228 Pa-s, kg = 0.3 W/m-K, Prg = 117. (a) Assume that the LCM is valid and calculate the initial cooling rate of the sphere. Use the Ranz and Marshall correlation to calculate the heat transfer coefficient. Was the LCM assumption valid? (b) Determine the initial acceleration of the sphere. In order to do this, use the balance of forces on the submerged sphere is given by m du/dt = mg - Fb - FD where m is the mass of the sphere, u is the sphere's velocity, g is the acceleration of gravity, F is the buoyancy force (weight of the fluid displaced by the copper sphere), and Fp is the drag force given by: C_D = 8FD / rhou²πD² and C_D = 0.4 + 24 / Re_D + 6 / 1+ReD¹/²
(c) Assume that one second has past At = 1 s, recalculate the velocity and temperature of the sphere and repeat (a) and (b). Hint: use the acceleration previously calculated as Au/At to estimate the new velocity after 1 s. Extra: plot the variation of the temperature and velocity of the sphere with time. No partial credit will be given for any work done unless the answer is the correct one. Go after this extra credit only if you can afford to put in the extra work.
Answers
This problem involves multiple stages of complex calculations, each dependent on the previous step.
Based on the given information and required calculations, the initial cooling rate of the sphere and its initial acceleration can be calculated, followed by recalculations of the sphere's velocity and temperature after one second.
The cooling rate of the sphere initially can be calculated using the Ranz and Marshall correlation to find the heat transfer coefficient. Then, the initial acceleration of the sphere can be determined using a balance of forces that includes gravity, buoyancy, and drag forces. After one second, the velocity and temperature of the sphere can be recalculated using the previously calculated acceleration and cooling rate. The entire problem is an application of the principles of fluid mechanics and heat transfer, involving equations for heat transfer, drag force, buoyancy, and acceleration. Without specific numerical calculations, it is not possible to verify the validity of the LCM assumption or provide the numerical results.
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You plan to take your hair blower to Europe, where the electrical outlets put out 240V instead of the 120 V seen in the United States. The blower puts out 1,660 W at 120 V. a. What current will your blower draw from a European outlet? b. What resistance will your blower appear to have when operated at 240 V?
Answers
The hair blower will draw approximately 6.92 Amperes of current drawn from the European outlet, and it will appear to have a resistance of approximately 34.68 Ohms when operated at 240 V.
What is the current drawn by the hair blower from a European outlet, and what resistance does it appear to have when operated at 240 V?The current drawn by the hair blower can be calculated using Ohm's Law, which states that current (I) is equal to the voltage (V) divided by the resistance (R).
In this case, the voltage is 240 V (European outlet) and the power output is 1,660 W. Using the formula P = IV, we can solve for the current:
a. Current (I) = Power (P) / Voltage (V) = 1,660 W / 240 V = 6.92 A
Therefore, the hair blower will draw approximately 6.92 Amperes of current from the European outlet.
b. To find the resistance (R) of the blower at 240 V, we can rearrange Ohm's Law to solve for resistance:
Resistance (R) = Voltage (V) / Current (I) = 240 V / 6.92 A = 34.68 Ω
So, when operated at 240 V, the hair blower will appear to have a resistance of approximately 34.68 Ohms.
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What basic principle do reciprocating engines operate off of?
Answers
Answer:
Reciprocating engines operate on the basis principle of converting fuel/chemical energy into mechanical energy.
Explanation:
These are piston engines that uses up and down motions of pistons to convert pressure into rotational motion. The common types of a reciprocating engines are :
internal combustion enginesteam enginestirling engineThe engine utilizes 4 processes to complete a cycle, which are;
Intake-where a fuel mixture is put into the through the intake portCompression-where the fuel mixture is pushed to the top by the piston to compress it and ignite it through the spark plugIgnition- where the ignition pushes the piston back down to produce useful workExhaust-the waste chemical are eliminated out via the exhaust port and the cycle repeats.These processes indicate that chemical energy in the fuel mixture is converted to mechanical energy causing motion.
A driver is traveling at 90 km/h down a 3% grade on good, wet pavement. An accident
investigation team noted that braking skid marks started 75m before a parked car was
hit at an estimated 45 km/h. Ignoring air resistance, calculate the theoretical friction
coefficient.
Answers
Answer:
0.35
Explanation:
We resolve the component of the weight of the car along and perpendicular to the grade. We have mgsinФ and mgcosФ where Ф = angle of grade.
Now, the frictional force f = μN = μmgcosФ where μ = coefficient of friction
So, the net force along the grade is F = mgsinФ - μmgcosФ.
The work done by this force moving a distance, d along the grade is
W = (mgsinФ - μmgcosФ)d
This work equals the change in kinetic energy of the car. So ΔK = 1/2m(v₂² - v₁²) = W = (mgsinФ - μmgcosФ)d
1/2m(v₂² - v₁²) = (mgsinФ - μmgcosФ)d
1/2(v₂² - v₁²) = (gsinФ - μgcosФ)d
(v₂² - v₁²)/2d = (gsinФ - μgcosФ)
dividing through by gcosФ, we have
(v₂² - v₁²)/2dgcosФ = (gsinФ/gcosФ) - μgcosФ/gcosФ
(v₂² - v₁²)/2dgcosФ = tanФ - μ
μ = tanФ - (v₂² - v₁²)/2dgcosФ
given that tanФ = 3% = 3/100 and 1 + tan²Ф = 1/cos²Ф, cosФ = 1/(√1 + tan²Ф) = 1/(√1 + (3/100)²) = 1/(√1 + (9/10000)) = 1/(√10000 + 9/10000) = 1/√(10009/10000) = 100/√10009 = 100/100.05 = 0.9995.
Also, given that v₁ = 90 km/h = 90 × 1000/3600 m/s = 25 m/s and v₂ = 45 km/h = 45 × 1000/3600 m/s = 12.5 m/s, d = 75 m and g = 9.8 m/s².
So, substituting the values of the variables into the equation, we have
μ = tanФ - (v₂² - v₁²)/2dgcosФ
μ = 3/100 - ((12.5 m/s)² - (25 m/s)²)/(2 × 75 m × 9.8 m/s² × 0.9995)
μ = 3/100 - ((156.25 m/s)² - (625 m/s)²)/1,469.265 m²/s²
μ = 3/100 - (-468.75 m²/s²)/1,469.265 m²/s²
μ = 3/100 + 468.75 m²/s²/1,469.265 m²/s²
μ = 0.03 + 0.32
μ = 0.35
So, theoretical friction coefficient is 0.35
If the variation of the acceleration of gravity, in m/s2, with elevation z, in m, above sea level is g = 9.81 – (3.3 x 10-6) z, determine the percent change in weight of an airliner landing from a cruising altitude of 10 km on a runway at sea level.
Answers
The percent change in weight of an airliner landing from a cruising altitude of 10 km on a runway at sea level is approximately -0.336%.
How do you calculate the percent change in weight?To determine the percent change in weight of an airliner landing from a cruising altitude of 10 km on a runway at sea level, we need to calculate the acceleration of gravity at sea level (z = 0) and at the cruising altitude (z = 10,000 m), and then find the percent change between these two values.
1. Calculate the acceleration of gravity at sea level (z = 0):
g₀ = 9.81 - (3.3 × 10⁻⁶) × 0 = 9.81 m/s²
2. Calculate the acceleration of gravity at cruising altitude (z = 10,000 m):
g₁₀₀₀₀ = 9.81 - (3.3 × 10⁻⁶) × 10,000 = 9.81 - 0.033 = 9.777 m/s²
3. Calculate the percent change in acceleration of gravity:
Percent change = (g₁₀₀₀₀ - g₀) / g₀ × 100
Percent change = (9.777 - 9.81) / 9.81 × 100 = -0.336 %
The percent change in weight of an airliner landing from a cruising altitude of 10 km on a runway at sea level is approximately -0.336%. This means that the airliner's weight decreases by about 0.336% as it lands at sea level from a cruising altitude of 10 km.
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You are driving on a roadway with multiple lanes of travel in the same direction, and are approaching an emergency vehicle parked along the roadway. You must:a. Leave the lane closest to the emergency as soon as it is safe to do so, or slow down to a speed of 20 MPH below the posted speed limit.b. Yield to the emergency vehicle.c. If you are in the lane closest to the emergency vehicle, immediately come to a complete stop and ask if anyhelp is needed.d. All of the above.
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Answer: a. Leave the lane closest to the emergency as soon as it is safe to do so, or slow down to a speed of 20 MPH below the posted speed limit.
Explanation:
Giving a way to the law enforcement vehicle and a medical emergency vehicle is necessary. If one approaches an emergency vehicle parked along the roadway one should change the lane as the vehicle may not move and the driver may also waste his or her time also one should also slow down his or her speed while approaching the vehicle as most of the emergency vehicle are in rush to reach the hospital so the driver should maintain some distance with the medical emergency vehicle.
What is the relationship between green building and self-interest? (Select all that apply.)
Green building is burdensome but has advantages in terms of public image.
Green building should be considered when necessary resources are in short supply.
Green building practices can lead to planning and budget efficiencies in general.
Green building is attractive because of its long-term growth potential as a market.
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The relationship between green building and self-interest include the following:
Green building is burdensome but has advantages in terms of public imageGreen building is attractive because of its long-term growth potential as a market.What is Green building?This is the process of reducing the environmental impact of buildings. This therefore leads to enhancement of the health of people.
Its relationship with self interest can seen listed above as the most appropriate choice.
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Problem 6. 81 The beam is made of material having an allowable tensile and compressive stress of (σallow )t 125 MPa and ▼ Part A allow c 138 MPa, respectively. (Figure 1) Determine the maximum allowable internal moment M that can be applied to the beam. Express your answer to three significant figures and include the appropriate units "-. | Value kN·m | Submit X Incorrect; Try Again Provide Feedback Figure 〈 1of1 > 300 mm 30 mm, 30 mm 50 mm 150 mm
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The maximum allowable internal moment for the beam is 93.8 kN·m for tensile stress and -103.2 kN·m for compressive stress.
To determine the maximum allowable internal moment (M) that can be applied to the beam, we need to consider the bending stress at the critical section of the beam.
The bending stress (σ) in a beam can be calculated using the formula:
σ = (M * c) / I
where M is the internal moment, c is the distance from the neutral axis to the outermost fiber, and I is the moment of inertia of the beam section.
Given the dimensions of the beam in the figure, we can calculate the moment of inertia (I) using the formula for a rectangular cross-section:
I = (b * h^3) / 12
where b is the width of the beam and h is the height of the beam.
Substituting the values into the formulas:
I = (30 mm * 150 mm^3) / 12 = 11,250,000 mm^4
Now, we can calculate the maximum allowable bending stress for both tensile and compressive cases:
σallow_t = 125 MPa
σallow_c = -138 MPa (negative sign indicates compressive stress)
We can rearrange the bending stress formula to solve for the maximum allowable moment:
M = (σallow * I) / c
For tensile stress:
M_t = (σallow_t * I) / c = (125 MPa * 11,250,000 mm^4) / 15 mm = 93,750,000 mm^3 = 93.8 kN·m
For compressive stress:
M_c = (σallow_c * I) / c = (-138 MPa * 11,250,000 mm^4) / 15 mm = -103,200,000 mm^3 = -103.2 kN·m
Therefore, the maximum allowable internal moment for the beam is 93.8 kN·m for tensile stress and -103.2 kN·m for compressive stress.
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