Displayed to the right are two carts connected by a cord that passes over a small frictionless pulley. Each cart rolls freely with negligible friction. Consider the mass of the cart to be m1 and the angle the first cart sits on to be θ1, while the mass of the second cart as m2 and the angle it sits on to be θ2.
Answers
The acceleration is given by the tension in the rope and the component
of the component of the weight acting along the plane.
Response:
[tex]The \ expression \ for \ the \ acceleration, \ a \ is\ \underline{a = \dfrac{m_2 \cdot g \cdot sin \left(\theta_2 \right) - m_1 \cdot g \cdot sin \left(\theta_1 \right) }{m_1 + m_2}}[/tex]
How can the expression for the acceleration be derived?A possible question is the expression for the acceleration, a in terms of the mass, m₁, m₂, and the angles θ₁ and θ₂.
The drawing representing the situation, obtained from a similar question and created with MS Visio, is attached
From the drawing, we have;
By equilibrium of forces, the tension in the cable, T, is given as follows;
For the cart, m₁; T = m₁·a + m₁·g·sin(θ₁)
For the cart, m₂; T = m₂·g·sin(θ₂) - m₂·a
Where;
a = The acceleration that the two carts experience
Equating both values of T gives;
m₁·a + m₁·g·sin(θ₁) = m₂·g·sin(θ₂) - m₂·a
m₁·a + m₂·a = m₁·g·sin(θ₁) - m₂·g·sin(θ₂)
The
[tex]a = \mathbf{\dfrac{m_2 \cdot g \cdot sin \left(\theta_2 \right) - m_1 \cdot g \cdot sin \left(\theta_1 \right) }{m_1 + m_2}}[/tex]
The acceleration, a, that the two carts experience in terms of m₁, m₂, θ₁, θ₂,
is therefore;
[tex]a = \underline{\dfrac{m_2 \cdot g \cdot sin \left(\theta_2 \right) - m_1 \cdot g \cdot sin \left(\theta_1 \right) }{m_1 + m_2}}[/tex]Learn more about equilibrium of forces here:
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Related Questions
In a multiple choice exam, there are 5 questions and 4 choices for each question (a, b, c, d). Nancy has not studied for the exam at all and decides to randomly guess the answers. What is the probability that:.
Answers
Using the binomial distribution, it is found that there is a 0.6836 = 68.36% probability that she guesses at least one right.
For each question, there are only two possible outcomes, either she gets it right or she does not get it right. The probability of getting a question right is independent of any other question, hence the binomial distribution is used to solve this question.
What is the binomial distribution formula?The formula is:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]C_{n,x} = \frac{n!}{x!(n-x)!}[/tex]
The parameters are:
x is the number of successes.n is the number of trials.p is the probability of a success on a single trial.In this problem:
There are 5 questions, hence n = 5.For each question, she guesses one out of 4 options, hence p = 1/4 = 0.25.The probability that she guesses at least one right is:
[tex]P(X \geq 1) = 1 - P(X = 0)[/tex]
In which:
[tex]P(X = x) = C_{n,x}.p^{x}.(1-p)^{n-x}[/tex]
[tex]P(X = 0) = C_{4,0}.(0.25)^{0}.(0.75)^{4} = 0.3164[/tex]
Hence:
[tex]P(X \geq 1) = 1 - P(X = 0) = 1 - 0.3164 = 0.6836[/tex]
0.6836 = 68.36% probability that she guesses at least one right.
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A cart is pulled a distance d on a horizontal surface while it is acted on by five forces, as shown in the diagram. Normal forces of magnitudes n1 and n2 are directed upwards at the rear and front wheels, respectively. Rolling frictional forces of magnitudes f1 and f2 are opposite in direction to the displacement and act on the rear and front wheels, respectively. The weight of the cart, with magnitude w, is directed downward. Finally, a pulling force of magnitude p makes and angle of φ with horizontal. The direction of the displacement is to the right in the diagram.
Answers
The work done by the pulling force is [tex]P\cdot d \cdot \cos \theta[/tex].
The work done by rear wheels normal force is 0.
The work done by front wheels normal force is 0.
The work done by rear wheels friction force is [tex]-f_{1}\cdot d[/tex].
The work done by front wheels friction force is [tex]-f_{2}\cdot d[/tex].
The work done by weight is 0.
How to determine the work done by a force
In this question, we see a system with six uniform and stable forces. The equation of work done by a uniform and stable force is:
[tex]W = F\cdot s\cdot \cos \theta[/tex] (1)
Where:
[tex]F[/tex] - Force, in newtons. [tex]s[/tex] - Traveled distance, in meters.[tex]\theta[/tex] - Angle of force respect to displacement direction, in degrees.Now we proceed to calculate the work done by each force:
Pulling force ([tex]P[/tex])[tex]W_{P} = P\cdot d\cdot \cos \theta[/tex] (2)
The work done by the pulling force is [tex]P\cdot d \cdot \cos \theta[/tex]. [tex]\blacksquare[/tex]
Rear wheels normal force ([tex]N_{1}[/tex])
[tex]W_{N_{1}} = N_{1}\cdot d\cdot \cos 90^{\circ}[/tex]
[tex]W_{N_{1}} = 0[/tex] (3)
The work done by rear wheels normal force is 0. [tex]\blacksquare[/tex]
Front wheels normal force ([tex]N_{2}[/tex])
[tex]W_{N_{2}} = N_{2}\cdot d\cdot \cos 90^{\circ}[/tex]
[tex]W_{N_{2}} = 0[/tex] (4)
The work done by front wheels normal force is 0. [tex]\blacksquare[/tex]
Rear wheels friction force ([tex]f_{1}[/tex])
[tex]W_{f_{1}} = f_{1}\cdot d\cdot \cos 180^{\circ}[/tex]
[tex]W_{f_{1}} = - f_{1}\cdot d[/tex] (5)
The work done by rear wheels friction force is [tex]-f_{1}\cdot d[/tex]. [tex]\blacksquare[/tex]
Front wheels friction force ([tex]f_{2}[/tex])
[tex]W_{f_{2}} = f_{2}\cdot d\cdot \cos 180^{\circ}[/tex]
[tex]W_{f_{2}} = -f_{2}\cdot d[/tex] (6)
The work done by front wheels friction force is [tex]-f_{2}\cdot d[/tex]. [tex]\blacksquare[/tex]
Weight ([tex]W[/tex])
[tex]W_{W} = W\cdot d\cdot \cos 270^{\circ}[/tex]
[tex]W_{W} = 0[/tex] (7)
The work done by weight is 0. [tex]\blacksquare[/tex]
Remark
The question is poorly formatted and a figure is missing. Correct form is shown below:
A cart is pulled a distance [tex]d[/tex] on a horizontal surface while it is acted on by forces, as shown in the diagram. What is the work done by each force?
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To find the number of molecules in the given sample of her compound, which of these values must also be used in her calculation?.
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The value which must be used to find the number of molecules in the given sample of her compound is; Avogadro's number.
Avogadro's number and the Number moleculesThe Avogadro's constant, otherwise known as the Avogadro's number is the proportionality constant that relates the number of constituent particles in a sample with the amount of substance in the sample in discuss.
Its SI unit is the reciprocal of mole, and it is estimated exactly as Na = 6.02214076×10²³ mol⁻¹.
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According to many antebellum southerners, the issue of "states' rights" revolved around their right to.
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According to many antebellum southerners, the issue of "states' rights" revolved around their right to own slaves.
What is Antebellum slavery?Antebellum is known to be a time before a war and the term is said to be widely linked with the pre-Civil War period in the United States when the act of slavery was been practiced.
The Antebellum South was said to be characterized by the use of slavery and the culture was said to be promoted.
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Answer:
own slaves.
Explanation:
I did this quiz lol
Which statement best explains what would happen if a reactant were added to a system in equilibrium?.
Answers
The statement that best explains what would happen if a reactant was added to a system in equilibrium is: The system would shift toward the products to oppose the change.
What is a System in Equilibrium?When a system that is in equilibrium, it means that the rates of the forward and reverse reactions are equal to each other.
If additional reactant is added to the system in equilibrium, the rate of forward reaction increases as the equilibrium shifts to the right towards the side of the products.
Therefore, the statement that best explains what would happen if a reactant was added to a system in equilibrium is: The system would shift toward the products to oppose the change.
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The local driver’s license center processes applications for driver’s license renewals through the following three steps. First, the customer registers with the receptionist, who updates the customer’s information in the database. This first step takes 3 minutes per customer. Then, the customer visits one of two cashiers to pay the associated fees for the license renewal. This takes 7 minutes per customer because several forms must be printed from the computer and signed by the customer. Finally, the customer visits one of three license processing stations where the customer’s picture is taken, and the license is printed. This final step takes 12 minutes per customer.
Answers
The license station has the lowest with 12 customers per hour assuming an unlimited demand.
Given the following data:
First step = 3 minutes per customer. Second step = 7 minutes per customer. Final step = 12 minutes per customer.To determine the flow rate of the process in customers per hour assuming unlimited demand:
What is a flow rate?A flow rate is an average rate and it can be defined as the number of flow units that goes through a business process per unit time such as served customers per hour.
Some examples of flow units in a business firm include:
MoneyGoodsServicesCustomersGenerally, the flow rate of a business process is highly dependent on the capacity of the bottleneck and the license station has the lowest with 12 customers per hour assuming an unlimited demand.
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Which of the following are coefficients you could use in a balanced equation? (select all that apply).
Answers
The complete question has options given are; 1, 9, 1/2, .5, 2, 3/4 and 6.
The coefficients which could be used in a balanced equation are; 1, 9, 2, and 6.
Coefficients in balanced equationsThe coefficients which can be used in balanced equations are whole numbers.
Although, other type of numbers such as fractions and decimals can be used, they may need to be simplified into whole number forms by multiplying the whole equation by a required factor for ease of computation
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A positively-charged piece of plastic is placed next to an electrically neutral piece of paper. What is the force between them?.
Answers
The force between a positively charged plastic and a neutral paper is :
Attractive because the plastic polarizes the paper Force of attractionThe force of attraction between a positively charged material and a neutral material becomes stronger as the positively charged material polarizes the neutral material which enables it to exert an attractive force on the neutral material. while
The electrical force of attraction between charged materials reduces with the increase in distance between them.
Hence we can conclude that the force between a positively charged plastic and a neutral paper is attractive because the plastic polarizes the paper.
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The solubility of glucose at 30°c is 125 g/100 g water. A solution is made by adding 250 g of glucose to 100 ml of water at 30°c. Remember that 1 g water = 1 ml water. How would you classify this type of solution? heterogeneous saturated supersaturated unsaturated.
Answers
Answer:
C. Supersaturated
Explanation:
I know this is late but for others in the future who may need help.
Considering the definition of supersaturated solution, this type of solution is supersaturated.
Supersaturated solutionA solution is a supersaturated solution when it contains more solute than the amount supported under equilibrium conditions by the solvent at a given temperature.
In other words, supersaturated solutions are those in which more solute has been added than can be dissolved in the solvent. For this reason, it is observed that a part of the solute goes to the bottom of the container. That is, the observed solution is saturated (it contains the maximum amount of dissolved solute), and the excess settles at the bottom of the container.
This caseA solution is made by adding 250 g of glucose to 100 ml of water at 30°c. Remembering that 1 g water = 1 ml water, then a solution is made by adding 250 g of glucose to 100 g of water at 30°c.
The solubility of glucose at 30°c is 125 g/100 g water.
You can see that there is more solute than the solvent can incorporate (the solution can incorporate 125 g of glucose). Therefore the solution is supersaturated.
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In (figure 1), what is the magnitude of the current in the wire above the junction?.
Answers
The magnitude of the current in the wire above the junction is;
5 A
Calculations using Kirchoff's Current Rule
From the image of the circuit attached, we see that;
For wire 1, current is flowing towards the junction and that;
Resistance; R₁ = 2Ω
Voltage; V₁ = 6V
For wire 2, current is flowing towards the junction and that;
Resistance; R₂ = 5 Ω
Voltage; V₂ = 10 V
Formula for current is;
I = V/R
Thus;
I₁ = V₁/R₁
I₁ = 6/2
I₁ = 3 A
I₂ = V₂/R₂
I₂ = 10/5
I₂ = 2 A
Now, kirchoff's current law or junction law states that the total current flowing into the junction is equal to the total current flowing out of the junction.
We see that the third wire which is above the junction has it's current flowing out of the junction. Thus;
I₁ + I₂ = I₃
3 + 2 = I₃
I₃ = 5 A
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Altering the three-dimensional structure of an enzyme is referred to as.
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Altering or changing the three-dimensional (3D) structure of an enzyme is referred to as: denaturation.
What is an enzyme?An enzyme can be defined as a biological catalyst that typically speeds up (increases) the rate of a chemical reaction, by lowering (decreasing) the activation energy of its constituent chemical elements (reactants).
What is denaturation?In Science, denaturation can be defined as a biological process that involves altering or changing the three-dimensional (3D) structure of an enzyme. Also, it prevents the substrate in a chemical reaction from binding the enzyme's active site.
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Suppose a sugar cone is 10 centimeters deep and has a diameter of 4 centimeters. A spherical scoop of ice cream with a diameter of 4 centimeters rests on the top of the cone. (i) if all the ice cream melts into the cone, will the cone overflow? explain. (ii) if the cone does not overflow, what percent of the cone will be filled?.
Answers
Answer:
i)no as 42>33.5
ii)around 82 %
Explanation:
volume of the scoop - 4/3 pi r cube = ~33.5
volume of cone - 1/3 pi r square = ~42
Percent of cone will be filled is 81%
Volume base problem:Given that;
Length of sugar cone = 10cm
Diameter of sugar cone = 4 cm
Diameter of spherical scoop = 4 cm
Computation:
Diameter of sugar cone = 4 cm
Radius of sugar cone = 4/2 = 2 cm
Diameter of spherical scoop = 4 cm
Radius of spherical scoop = 4/2 = 2 cm
Volume of cone = [tex]\frac{1}{3}[\pi r^2h][/tex]
Volume of cone = [tex]\frac{1}{3}[(3.14) (2)^2(10)][/tex]
Volume of cone = 41.86 cm³
Volume of spherical scoop = [tex]\frac{4}{3}[\pi r^3][/tex]
Volume of spherical scoop = [tex]\frac{4}{3}[(3.14) (2)^3][/tex]
Volume of spherical scoop = 33.49 cm³
Cone is enough big.
Percent of cone will be filled = [tex]\frac{33.49}{41.86} \times 100[/tex]
Percent of cone will be filled = 81% (Approx.)
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When we react a weak base with a strong acid, the component of the base that contributes to the ph of the solution is the:.
Answers
The component of the base that contributes to the pH of the solution when a weak base reacts with a strong acid is referred to as the: conjugate base.
What is a Conjugate Base?A conjugate base can b described as the base which differ from an acid based on the presence or absence of proton.
For example, the conjugate base of [tex]NH_{4+}[/tex] is [tex]NH_{3}[/tex].
Therefore, the component of the base that contributes to the pH of the solution when a weak base reacts with a strong acid is referred to as the: conjugate base.
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Answer:
conjugate acid
Explanation:
It is the conjugate acid of the weak base that generates hydronium and therefore contributes to the pH.
Canis familiaris (dogs) and canis lupus (wolves) are a different brainly.
Answers
Canis familiaris (dogs) and canis lupus (wolves) are a different taxonomic subcategory.
What is a subspecies?A subspecies is a taxonomic subcategory that refers to each of the groups in which a species is found.
Characteristics of a subspeciesThese groups, in addition to having the characteristics of the species in which they are found, have special morphological characters that make them different from each other.Dogs and wolves belong to the same zoological species that is the Canis lupus species.This classification into subspecies is mainly due to the domestication process that gave rise to dogs, in addition to important physiological and anatomical differences.Therefore, we can conclude that dogs are a subspecies, called Canis lupus familiaris, Canis lupus is the species, in which both dogs and wolves are included, being the "familiaris" what refers to the domestic dog.
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Answer:
Species
Explanation:
Over a 24-hour period, the tide in a harbor can be modeled by one period of a sinusoidal function. The tide measures 4. 35 ft at midnight, rises to a high of 8. 3 ft, falls to a low of 0. 4 ft, and then rises to 4. 35 ft by the next midnight. What is the equation for the sine function f(x), where x represents time in hours since the beginning of the 24-hour period, that models the situation? enter your answer in the box.
Answers
Answer:
f(x) = 3.95sin (πx/12) + 4.35
Explanation:
Answer:
f(x) = 3.95sin (πx/12) + 4.35
Explanation:
I took the test k-12
How is a phylogenetic tree similar to a dichotomous key.
Answers
A phylogenetic tree represents the history of lineages of organisms, a dichotomous key is a tool to discover which group an organism belongs to, using taxonomic keys, both structures were founded by Carl Linneaus.
What is a phylogenetic tree?It is a schematic diagram used to illustrate or represent hypotheses about the evolutionary relationships between a group of organisms.
What is a dichotomous key?It consists of a model or scheme that allows the determination of different species.
Therefore, we can conclude that a phylogenetic tree is a structure used to represent ancestor-descendant relationships, a dichotomous key identifies the species to which an organism belongs, both structures were founded by Carl Linneaus.
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Answer:
Both focus on illustrating taxonomic relationships between organisms.
In order to reduce production costs, autoworks an automobile manufacturer, decided to buy out a glass plant and begin manufacturing the glass for the windows of cars on its own. The corporate strategy adopted by the company is known as.
Answers
Answer:
the glass for the windows of cars on its own.
Explanation:
lol
The glass for the windows of cars on its own.
What is Corporate Stratergy?Corporate strategy is the strategy level that concerns itself with the entirety of the organization, where decisions are made with regard to the overall growth and direction of a company.
Corporate strategies are arguably the most essential and broad-ranging strategy level within an organizational strategy.
Corporate level strategy refers to the highest level of corporate strategic planning. In this article, we dive deeper into it, but it’s useful to understand the other strategic levels as well and how they are related.
Therefore, The glass for the windows of cars on its own.
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On a particular day, caroline decided to run two laps of a park of which each lap is 1. 2kms. She takes 12 minutes to run her first lap, and she runs her second lap at an average speed of 7 km/h. Determine her average speed over the two laps.
Answers
Answer:
6.46 km/h
Explanation:
Total distance d = 2 * 1.2 = 2.4 km
Total time t = 12 min + t' where t' is the time taken for second lap.
t' = 1.2 km/(7 km/h) = 1.2/7 hours
so t = 12/60 hours + 1.2/7 hours = 0.3714 hours
The average speed = d/t - 2.4/0.3714 = 6.46 km/h
You leave on a 546-mi trip in order to attend a meeting that will start 10. 8 h after you begin your trip. Along the way you plan to stop for dinner. If the fastest you can safely drive is 65 mi/h, what is the longest time you can spend over dinner and still arrive just in time for the meeting?.
Answers
Answer:
Explanation:
To find the time the driver can stop for, we must calculate the time it takes him to complete the trip without any stops:
Time without stops = [tex]\frac{546 miles}{65miles/hour} = 8.32 hours[/tex] (approximated)
Since the driver has 10.8 hours to complete the journey, thus the driver can stop for 10.8hrs - 8.32hrs = 2.48hrs
Answer:
2,48 hours
100% correct...........
The meiji government’s ""emulation of foreign ways"" was most directly a response to which of the following nineteenth-century developments?.
Answers
The meiji government’s ""emulation of foreign ways"" was most directly a response to western states forcing japan to open itself to trade.
What is Meiji government?Meiji the Great was emperor of Japan, he was the 122nd traditional ruler of Japan.
His reign brought about the end of the shogunate and he implement various tax and reformation.
Meiji responded to western states that were forcing japan to open up to different trade by eliminating them.
Therefore, the meiji government’s ""emulation of foreign ways"" was most directly a response to western states forcing Japan to open itself to trade.
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In "before giving to a charity," what does the symbol of the eye and its corresponding text box in the chart reveal about charitable giving?.
Answers
Answer: sometimes scams use similar to legitimate charities in order to trick people into giving
Explanation:I took the test
Answer: Sometimes scams use names similar to legitimate charities in order to trick people into giving.
Explanation: Not only did i take the quiz but i also got it correct by guessing because the others guy does not have a good answer.
chicken nuggies are good
Answers
Answer:
tree bark tastes better (:
Explanation:
because jrodtheboss said so
Both prokaryotic and eukaryotic cells have all of the following except.
Answers
Answer:
Endoplasmic, reticulum, microtubules, and Golgi apparatus
Explanation:
t
When is it okay to touch the inside of a computer that is turned on?.
Answers
A stunt person jumps from the roof of a tall building, but no injury occurs because the person lands on a large, air-filled bag. Which one of the following best describes why no injury occurs?.
Answers
The bag increases the amount of time during which the momentum is changing and reduces the average force on the person.
Eighty percent of a roof, or 2800 square feet of the roof, has been re-shingled. What is the total area of the roof?.
Answers
Answer:
The total area of the roof is 3500 ft^2
Explanation:
2800ft^2 = 80% of roof
Divide by 0.8 to solve for the total area.
2800 / 0.8 = 3500 ft^2
What is the suggested solution to the problem according to the author.
Answers
Answer:
here
Explanation:
1 Define the problem. Diagnose the situation so that your focus is on the problem, not just its symptoms. ... 2 Generate alternative solutions. Postpone the selection of one solution until several problem-solving alternatives have been proposed. 3 Evaluate and select an alternative. ... 4 Implement and follow up on the solution. ...
Immediately after digestion in the small intestine, most dietary fats are absorbed into the.
Answers
Immediately after digestion in the small intestine most dietary fats are absorbed into the bile.
What is the bile?This is the part that is secreted by the liver that is able to perform these functions
Carrying wasteBreaking down of fats during digestion.The bile is where the emulsification of the fats happen after they have been absorbed.
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If a gas has a volume of 750 l at 298 k, what would the volume of the gas be at 328 k?.
Answers
Answer:
826 l
Explanation:
V1 = 750 l, T1 = 298 K
V2 = ?, T2 = 328 K
If the pressure is constant,
V1/T1 = V2/T2
so
V2 = V1 * (T2/T1) = 750 *(328/298) = 826 l
How does addie in the selection from the boston girl differ from sybil in the poem ""sybil ludington’s ride""?.
Answers
People do differs. Addie differs from Sybil due to the fact that Addie has doubts about her abilities such that she often feels nervous when she wants to practice the poem and she tends to be very embarrassed when she do not know the meaning of impetuous.
But in Sybil case she was very certain about her abilities in that she influence her father decision that she is the right person to be able to deliver the message.What do you mean by selection?The definition of a selection is known to be one where a person or thing is said to be picked or are available over another. An example of a selection is a dog chosen from among other dogs.
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