The center of mass of the rod of length L whose mass density changes from one end to the other quadratically is; X_cm = ³/₄L(ρ₀ + ρ₀)/(2ρ₀ + ρ₁)
What is the center of mass?The formula for the center of mass of a body is defined as;
X_cm = (1/M) ∫r.dm
Where;
X_cm is the position of the center of mass
M is the total mass of the body
r is the position with respect to an origin
The density of a body is the relationship between two of its magnitudes that change constantly and so we have;
ρ = m/x
Applying small changes and we have;
ρ = dm / dx
dm = ρ*dx
We are given the expression;
ρ₀ = ρ₀ + (ρ₁ -ρ₀) (x/L)²
Thus;
dm = (ρ₀ + (ρ₁ -ρ₀) (x/L)²)dx
Since the whole system is on the x-axis, we integrate from the initial point x = 0 to the upper limit X = L. This gives;
X_cm = M⁻¹ ∫ x [ρ₀ + ( ρ₁-ρ₀) (x/L)²] dx
X_cm = M⁻¹ [∫ ρ₀ x dx + I (ρ₁-ρ₀) / L² x³ dx]
X_cm = M⁻¹ [ρ₀ x²/ + (ρ₁ -ρ₀) / L² x⁴/4]
X_cm = M⁻¹ [ρ₀/2 (L2-0) + (ρ₀₁ -ρ₀) /4L² (L⁴-0)
X_cm = M⁻¹ [ρ₀ L²/2 + (ρ₁ -ρ₀)/4 L²]
X_cm = M⁻¹ L² [ρ₀/4 + ρ₁/4]
X_cm = M⁻¹ L²/4 ( ρ₀ +ρ₁)
The only parameter that we don't know explicitly is the total mass, but we can look for their relationship using the concept of density.
M = ∫dm = ∫ρ.dx
M = ∫[ρ₀ + (ρ₁ -ρ₀)/L²x²] dx
We integrate between the limits of integration x = 0 and x = L to get;
M = ρ₀ x + (ρ₁ -ρ₀)/L² *x³/3
M = ρ₀ L + (ρ₁ -ρ₀)/3L² L³
M = ρ₀ L + (ρ₁-ρ₀)/3 L
M = L(ρ₀ + ρ₁/3 -ρ₀/3)
M = L(2/3 ρ₀ + ρ₁/3)
M = ¹/₃L(2ρ₀ + ρ₁)
We will replace and simplify in the center of mass equation to get;
X_cm = ¹/₄L²[ρ₀ + ρ₁] / [L/3 (2ρ₀ + ρ₀)/L]
X_cm = ³/₄L(ρ₀ + ρ₀)/(2ρ₀ + ρ₁)
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Follow the directions to convert the analog sound wave into a digital signal. the lines on the grid intersect at various points (x, y). for each whole-number value of x, find the intersection point that is closest to the wave. draw a small circle on that point, and record its y-value. the circles for the x-values 0 through 3 are already done for you. draw circles for the x-values 4 through 18. in a textbox, write down all 19 y-values obtained by sampling the wave.
In this exercise we have to observe the axes of the graph to associate the values of X with those of Y that correspond to 0, 5, 5, -3, -5, -3, 2, 0, 0, -1, -2, 1, 1, -1, -1, -2, 2, 3, -1.
How to calculate the Cartesian plane?Just draw two lines: one of them vertical, starting from the point until it finds the x axis; another horizontal, starting from the point until it meets the y-axis.
Then plotting the value of X on the graph we find the following for each value of X to Y:
X= 0 ; Y= 0; X= 1 ; Y= 5; X= 2 ; Y= 5;X= 3 ; Y= -3;X= 4 ; Y= -5;X= 5 ; Y= -3;X= 6 ; Y= 2; X= 7 ; Y= 0; X= 8 ; Y= 0; X= 9 ; Y= -1; X= 10 ; Y= -2; X= 11 ; Y= 1; X= 12 ; Y= 1; X= 13 ; Y= -1;X= 14 ; Y= -1; X= 15 ; Y= -2; X= 16 ; Y= 2; X= 17 ; Y= 3; X= 18 ; Y= -1;See more about coordinates at brainly.com/question/23450276
Currently, the rooftop solar panels produce only a fraction of the electricity used in the buildings on which they are installed. which of following strategies would best combat the problem of insufficient electricity generation from the rooftop solar panels?
The strategies that would best combat the problem is: Installing active solar energy on unshaded rooftop space and placing them to face south.
What is solar panel?Solar panel can be defined as a panel that help to provide electricity by making use of sunlight as energy.
Based on the given scenario the best strategies to overcome the problem is to install the active solar energy systems on unshaded rooftop space and to as well position the solar energy to face south.
Inconclusion install active solar energy on unshaded rooftop space.
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which of the following solutions is a good buffer system?
Answer:
A Solution that is 0.10m HC2H3O2 And 0.10m LiC2H3O2
Imagine that we randomly select a day from the past 10 years
Answer:
which day will you select?:-)
What concept would not be a correct addition to the student's explanation about how energy flows and matter cycles through an ecosystem?
Plants use cellular respiration to break down molecules and then they use them is NOT correct to explain how energy flows and matter cycles in an ecosystem.
How do energy and matter flow in the ecosystem?The ecosystem can be considered as the interaction between abiotic (e.g., water) and biotic factors (organism) in a given area.
In an ecosystem, the matter cycle and energy flow by crossing across different trophic levels.
The trophic levels are composed of organisms that show a special localization in the food web (e.g., herbivores).
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Read the excerpt from "a worn path." 'phoenix spoke unasked now. "no, missy, he not dead, he just the same. every little while his throat begin to close up again, and he not able to swallow. he not get his breath. he not able to help himself. so the time come around, and i go on another trip for the soothing-medicine." "all right. the doctor said as long as you came to get it, you could have it," said the nurse. "but it's an obstinate case."' what is the most likely the meaning of obstinate?
The most likely meaning of the word Phoenix from the given excerpt titled "a worn path" is; Stubborn
What does the phoenix symbolize?The phoenix bird is one that symbolizes immortality, resurrection, and life after death. In the ancient Greek and Egyptian mythology, it was usually associated with the sun god.
Obstinate, dogged, stubborn, and mulish all mean that someone is unwilling to change course or give up a belief or plan.
Obstinate means an unreasonable persistence which is a negative word.
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Solve the given integral equation or integro-differential equation for y(t)
An integral equation is the equation where an unknown function appears under the integral sign.
What is an integral equation?Your information is incomplete. Therefore, an overview will be given.
An integral equation simply means the equation where an unknown function appears under the integral sign.
It should be noted that integral equation can be solved numerically and doesn't usually require an analytical solution.
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Very small incidents may lead to great achievements
Answer:
True
Explanation:
A new car is purchased for 22300 dollars. The value of the car depreciates at 10. 25% per year. What will the value of the car be, to the nearest cent, after 6 years?
Answer:
8,585.5
Explanation:
first you multiply 22300 by 10.25% thats the number at which it decreases every year, then multiply by 6, then subtract that from 22300
In a certain video game, the variable maxps represents the maximum possible score a player can earn. the maximum possible score depends on the time it takes the player to complete the game. the value of maxps should be 30 if time is greater than 120 and 50 otherwise.
The code segment that best sets the value of maxPS is the first one because it includes complete and correct information.
What is a code segment?
As indicated by its name, it refers to a small section in the program's executable instructions.
How to select the best code segment?The code segment should include complete and accurate information. In this case, we know:
The maxPS is directly related to time.The maxPS is usually 50.This condition is not Met if the time is over 120 which would lead to 30 maxPS.Based on this, the best code segment is A because this accurately shows the maxPS is 50 except when time is over 120 as this changes the maxPS to 30.
Note: This question is incomplete because the options are missing; below I attach the missing section:
Which of the following code segments correctly sets the value of maxPS based on the value of time?Learn more about code segment in: https://brainly.com/question/26683418
A polygon with all equal sides and equal angles is brainly
Answer:
It's a regular polygon
Explanation:
A polygon having equal sides and equal angles is a regular polygon. A regular polygon has three parts: Sides.
There are many factors that contribute towards one's personal values and views toward nature. based on the information from this lesson, identify one or two factor(s) important to your own views on nature and natural landscapes.
The contributing factors to the personal values I have towards nature are:
Its beautyHow unique it appearsIts complex natureWhat is nature?This is a term that is used to refer to the physical world that we live in as well as all the components that exists in it.
By the word nature, it refers to the plants, animals, environment and other features in the environment.
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Suppose you are standing in the middle of the platform
The question is about the angle of depression (see full question below). Please note that the correct answer, that is, the angle of depression from the platform to the center of the bridge, is 16.6⁰.
What is the solution for the Angle of Depression above?
Step 1
Recall that the bottom of the rectangle has the same dimensions as the top.
Therefore,
tan = [tex]\frac{opposite}{adjacent}[/tex]
Thus, tan x = 297/995
Step 2 - We locate or calculate the inverse tangent of both sides. This results in:
x = tan⁻¹ ([tex]\frac{297}{995}[/tex])
Hence, x = 16.6⁰ approximately.
The full question is given here:
Suppose you are standing in the middle of the platform of the world's longest suspension bridge, the Akashi Kaikyo Bridge. If the height from the top of the platform holding the suspension cables is 297 meters, and the length from the platform to the center of the bridge is 995 meters, what is the angle of depression from the platform to the center of the bridge?
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Big ideas math: modeling real life grade 6 assessment book answer key
There are different ways to model real life grade scenario. An example is Numerical Expressions and Factors.
An example is: create a Venn diagram that represents the prime factorizations of 36 and 48.
What is Big Ideas Math 6 Book about?They are known to be a form of well organized and lucidly explained text about mathematics that is aimed towards students. They are made up of tests, quizzes, assessments and others.
The Venn diagram that represents the prime factorizations of 36 and 48 is in the image attached.
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according to carl jung, which of the following best served the goal of self-realization?
Find the value of x given the area of the quadrilateral
Answer:
Wait. where is the exact question?
You are a driver of a dump truck with a trailer (dump bin) that is 21 feet long, 8 feet wide, and 6 feet tall. daily, you haul full loads of dirt from one location to another. the dump bin can hold dirt equivalent to 1.2 times its capacity. what is the minimum number of trips needed to haul 20,000 cubic feet of dirt?
Answer: I think A
Explanation:
Hi, Does anyone have Collabify too?
Answer:
probably
Explanation:
there are a lot of people
Suppose the microwave’s power is 900w (1watt=1joule/sec). how long would you have to heat the coffee in part a?
The amount of time that is required for the microwave to heat the coffee is 34.4 seconds.
Given the following data:
Microwave’s power = 900 Watts.Quantity of energy = 30,962 Joules.How to calculate the time.In order to determine the amount of time that is required for the microwave to heat the coffee, we would use this formula:
[tex]Energy = power \times time\\\\[/tex]
Making time the subject of formula, we have:
[tex]Time = \frac{Energy}{Power}[/tex]
Substituting the given parameters into the formula, we have;
[tex]Time = \frac{30962}{900}[/tex]
Time = 34.4 seconds.
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Of the 10,000 clocks from which the sample was chosen, about how many clocks are probably not defective?
The number of clocks that are not defective is an illustration of proportions
Of the 10000 clocks, 9250 are probably not defective
How to determine the number of clocks that are not defective?From the complete question, we have the following parameter:
15 out of 200 clocks are defective
The above means that the number of clocks that are not defective is:
Not defective = 200 - 15
Not defective = 185
Express as percentage
Not defective = 185/200
Not defective = 92.5%
In 10,000 the number of clocks that are not defective would be:
Not defective = 92.5% * 10000
Not defective = 9250
Hence, 9250 of the 10000 clocks are probably not defective
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what is the angular speed, in rad/s, of a flywheel turning at 813.0 rpm?
Answer:
85.14 rad/s
Explanation:
Since we know that 1 revolution is equal to 2pi rad:
813(rev)/1(min) x 2pi/1 x 1(min)/60(seconds) = 85.14 rad/s
According to the video, what types of education and experience are environmental scientists and specialists most likely to need? check all that apply. bachelor’s degree high-school degree five years of experience two years of experience
Environmental scientists and specialists need a bachelor’s degree
and five years of experience.
Who are Environmental scientists?Environmental scientists are professionals who work aims at protecting the environment and whole ecosystems.
Environmental scientists understand issues related to the sustainability of natural resources and how these resources can be used by society.
Environmental science is a career (i.e., a bachelor's degree) that takes five (5) years to be completed.
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Answer:
A and C
Explanation:
Which inequality represents the number line:
Answer:
The answer is A
Explanation:
[tex]\frac{7}{7}[/tex] = 1 whole
[tex]\frac{7}{1}[/tex] = 7 wholes
The rest of the answer choices do not equal a whole.
Two identical regular hexagons are joined together
Answer:
The answer is x=120 °
Explanation:
The lengths of the diagonals of a rhombus are 18 and 24
The length of each of the sides of the rhombus is 15.
This question is incomplete, the complete question is:
The length of the diagonals of a rhombus are 18 and 24. Find the length of each side of the rhombus
Given the data in the question;
Diagonal 1 of the rhombus; [tex]p = 18[/tex]Diagonal 2 of the rhombus; [tex]q = 24[/tex]Length of each side of the rhombus; [tex]a = \ ?[/tex]RhombusA Rhombus is simply a quadrilateral whose four sides are all equal in length i.e its an equilateral quadrilateral.
Now, to determine the length of each sides of the rhombus, we create ab expression from Pythagoras theorem:
[tex]a = \frac{\sqrt{p^2+q^2} }{2}[/tex]
Where a is the length of the sides and pq are the diagonals.
We substitute our given values into the expression above.
[tex]a = \frac{\sqrt{p^2 + q^2} }{2} \\\\a = \frac{\sqrt{18^2 + 24^2} }{2}\\ \\a = \frac{\sqrt{324 + 576} }{2}\\ \\a = \frac{\sqrt{900} }{2}\\ \\a = \frac{30}{2}\\ \\a = 15[/tex]
Therefore, the length of each of the sides of the rhombus is 15.
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You are given some ferrous iodide, fei2 , and are asked to extract the iron through electrolysis. what can be said about the merits of molten versus aqueous fei2 ?
It is impossible to extract or derive iron metal from the electrolysis of the aqueous solution provided. The option left is to carry out the electrolysis on the molten salt.
What is Electrolysis?
Electrolysis refers to the process of causing a chemical decomposition in a liquid or solution that contains ions by sending electric currents via such a solution.
Electrolysis is used primarily for:
Extraction (also known as electrowinning); orPurification (also known as electrorefining) of metals from their ore state.Learn more about Electrolysis at:
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10.1 inverses of simple quadratic and cubic functions
The inverse function of the cubic function is its opposite
The inverse function of [tex]f(x) = 5x^3[/tex] is [tex]f^{-1}(x) = \sqrt[3]{\frac x5}[/tex]
How to determine the inverse of the function?The cubic function is given as:
[tex]f(x) = 5x^3[/tex]
Express f(x) as y
[tex]y = 5x^3[/tex]
Swap the positions of x and y
[tex]x = 5y^3[/tex]
Divide both sides by 5
[tex]y^3 = \frac x5[/tex]
Take the cube roots of both sides
[tex]y = \sqrt[3]{\frac x5}[/tex]
Express y as an inverse function
[tex]f^{-1}(x) = \sqrt[3]{\frac x5}[/tex]
Hence, the inverse function of [tex]f(x) = 5x^3[/tex] is [tex]f^{-1}(x) = \sqrt[3]{\frac x5}[/tex]
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Schrank company is trying to decide how many units of merchandise to order each month. company policy is to have 20% of the next month's sales in inventory at the end of each month. projected sales for august, september, and october are 30,000 units, 20,000 units, and 40,000 units, respectively. how many units must be purchased in september?
Assuming the company decide how many units of merchandise to order each month. The number of units that mus be purchased in september is 24,000 units.
Number of unitsUsing this fomula
Number of units=September sales units-Beginning inventory +Desired ending inventory
Hence:
September sales units 20,000
Beginning inventory (4,000)
(20,000 x 0.20)
Desired ending inventory 8,000
(40,000×0.20)
Number of units 24,000
(20,000-4,000+8,000)
Inconclusion the number of units that mus be purchased in september is 24,000 units.
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Each of the following statements is arguably true of thermometers. Which of them is most helpful to keep in mind if you are conducting an experiment to measure the specific heat of a material?
The statement that is true of thermometers is; The temperature reported by a thermometer is never precisely the same as its surroundings.
What is the function of thermometer in an experiment?In the experiment to determine the specific heat of a material, the theory will be one which explains that when a heat interchange takes place between two bodies that were having different temperatures at the beginning, the quantity of heat the warmer body looses is equal to that gained by the cooler body to reach the equilibrium temperature. This is true only if no heat is lost or gained from the surrounding.
Now, If heat is gained or lost from the surrounding environment, the temperature readings by the thermometer will be incorrect. The experimenter should therefore have in mind that for accurate results, the temperature recorded by the thermometer is similar to that of the surrounding at the beginning of the experiment and if it differs then note that heat is either gained or lost to the environment.
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what is the major organic product obtained from the following reaction?
In the image attached of the question, the major organic product obtained from the reaction is the second option.
What is an organic element?The organic elements are known to be some chemical elements that are said to be useful to life and are known to be found in almost all organic molecule such as carbon and hydrogen.
Conclusively, In the image attached of the question, we can see the major organic product obtained from the reaction is have a double bond of oxygen as the key product of the reaction.
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