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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The ability of an apple to change color when exposed to air is a
Answer:
chemical reaction
Explanation:
6-5 additional practice properties of special parallelograms
The properties of parallelograms are contained below:
They have opposite sides which are congruent to each other. BC = EDThey have Opposite angles which are congruent also.Consecutive angles are known to sum up to 180 degrees. They are supplementary.If an angle is right, all other angles are right.The diagonals are said to bisect each other.What is a parallelogram?This is a shape that is known to have four sides. Each of the sides is parallel to the side that is oppositev it.
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You cook a turkey until the internal temperature reaches 180°f. the turkey is placed on the table until the internal temperature reaches 100°f, and it can be carved. when the room temperature is 72°f, the cooling rate of the turkey is $r=0.067$ . how long do you have to wait until you can carve the turkey? use newton's law of cooling to solve the problem. round your answer to the nearest whole minute.
The newton's law of cooling is used to determine the waiting time
You will have to wait for 20 minutes to carve the turkey
How to determine the time?By newton's law of cooling, we have:
[tex]T = (T_o - T_R) e^{-rt} + T_R[/tex]
From the question, we have:
T = 100°f ---- The serving temperature
To = 180°f --- The initial temperature
TR = 72°f ----- the room temperature
r = 0.067 -- the cooling rate
So, we have:
[tex]T = (T_o - T_R) e^{-rt} + T_R[/tex]
[tex]100 = (180 - 72) e^{-0.067t} + 72[/tex]
Subtract 72 from both sides
[tex](180 - 72) e^{-0.067t} = 28[/tex]
Evaluate the difference
[tex]108 e^{-0.067t} = 28[/tex]
Divide both sides by 108
[tex]e^{-0.067t} = 0.25923[/tex]
Take the natural logarithm of both sides
[tex]-0.067t = -1.3500[/tex]
Divide both sides by -0.067
[tex]t = 20.149[/tex]
Approximate
[tex]t = 20[/tex]
Hence, you will have to wait for 20 minutes to carve the turkey
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According to roosevelt, what was the true goal of the new deal? to rebuild the us to restore us values to remind people of the us how to work
According to Franklin Delano Roosevelt, the true goal of the New Deal is: B. to restore US (American) values.
Who is Roosevelt?Franklin Delano Roosevelt was an American politician and statesman who was elected to serve as the 32nd President of the United States of America in 1933. Also, he was born on the 30th of January, 1882 in Hyde Park, New York, United States of America.
What is the New Deal?The New Deal was a collection of government reform programs that were established by President Franklin Delano Roosevelt between 1933 and 1939 in the United States of America so as achieve the following:
Boost the economy.Guard against economic disasters.Provide employment opportunities for the people.In conclusion, we can deduce that in accordance with Franklin Delano Roosevelt, the true goal of the New Deal is to restore US (American) values.
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Answer:
B. to restore US values
Explanation:
Edge 2022
Which of these is not a form of electromagnetic radiation?
Answer:
where are the options without options how do i answer sorry
Which design element is used to organize the text in orderly fashion? a. Proximity b. Alignment c. White space d. Balance
Answer:
Explanation:
The correct answer is the option B: alignment.
Explanation:
On one hand, design elements comprehends the term that describes fundamental ideas about the practice of visual design, such as the color, the points the lines, etc.
On the other hand, alignment is the name given, in the field of design, to the term that describes how a text is placed in order on the screen. Moreover, it enables the composition of a text document using different text positioning on the whole or selected part of a page.
Answer:B.
Explanation:
In the interview, dr. Dowell mentions that we live in a "small world. " the video explains that disease can spread in a matter of hours when people travel by airplane. How does the video connect to what dr. Dowell says? the video discusses disease but avoids how diseases spread. The video gives the same information as the interview about the spread of disease. The video gives less information than the interview about how easily disease can spread. The video gives more specific information about how easily diseases can spread
Answer:
D
Explanation:
edge 2022
the answer is right all you have to do is trust me
Answer:
D
Explanation:
Christopher runs a farm stand that sells apples and bananas. Yesterday christopher sold 35 pounds of apples and 34 pounds of bananas for a total revenue of $163. 50. Today he sold 15 pounds of apples and 17 pounds of bananas for a total revenue of $76. 75. Determine the price of each pound of apples and the price of each pound of bananas
The equation computed shows that the price of apple is $2 and the price of banana will be $2.75.
How to compute the equation?Christopher sold 35 pounds of apples and 34 pounds of bananas for a total revenue of $163.50. This will be:.
35a + 34b = 163.50
He also sold 15 pounds of apples and 17 pounds of bananas for a total revenue of $76.75. This will be:
15a + 17b = 76.75
Equate both equations
35a + 34b = 163.50 ..... i
15a + 17b = 76.75 ...... ii
Multiply equation i by 15.
Multiply equation ii by 35
525a + 510b = 2452.50 .... iii
525a + 595b = 2686.25 .... iv
Subtract equation iii from iv
85b = 233.75
b = 233.75/85
b = 2.75.
The price of banana is $2.75.
The price of apple will be:
35a + 34b = 163.50
35a + 34(2.75) = 163.50
35a + 93.50 = 163.60
35a = 163.50 - 93.50
35a = 70
a = 70/35
a = 2
The price of apple is $2.
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A conservation agency tracks the sea turtle population by counting the number of nesting sites where the turtles lay their eggs. The table shows the numbers of nesting sites for several years since 2001. The data can be modeled by an exponential function
Based on the number of years, and the number of nesting sites, the exponential function that best models the data is B. n(x) = 46,797(0.93)ˣ.
What function best models the data?You can find the correct function by testing out the options with the given x value to see if it correctly predicts the number of nesting sites.
Function n(x) = 25,956.80(1.08)ˣ
Assuming x is 3:
= 25,956.80(1.08)³
= 32,698 sites
This function does not predict the correct number of sites which is 40,513.
Function n(x) = 46,797(0.93)ˣ
Assuming x is 3:
= 46,797(0.93)³
= 37,438 sites
This is closer to the predicted number of 40,513 sites with some discrepancy.
In conclusion, option B is correct.
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Mathematics course 3 common core 2013 edition solutions
Fill in the blank with the comparative form of the underlined modifier
Answer:
The following are the answers for each questions:
1. It was worse than the movie we saw last week
2. Felipe showed much concern about the poor quality of the movie.
Belinda showed even more concern than Felipe
3. A lot of movies are filmed in New York
Explanation:
Brainlyest pleas
Which newspaper headline was most likely published in 1803?
Answer:
I'm not completely sure but I would say "The Young Republic doubles in size" was the headline that was most likely published in 1803.
17.1 equation of a circle evaluate homework and practice answer key
The evaluation using the equation of circle for the practice question is (x - 4)² + (y + 11)² = 256
What is the equation of the Circle Distance Formula?With respect to the distance formula, a point location in space (x,y) at a distance (r) from the origin is valid if [tex]\mathbf{\sqrt{x^2 + y^2} = r}[/tex]. Hence this refers to the equation of the circle centered at the origin.
For Conic Sections:
[tex]\mathbf{(x-h)^2 (y-k)^2 = r }[/tex]where;
center = (h,k)radius = rLet's assume we have a circle with C(4,-11) and radius r = 16;
Then, we have:
(x-h)² +(y -k)² = r²
(x-4)² + (y - (-11))² = 16²
(x - 4)² + (y + 11)² = 256
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projects s and l are equally risky, mutually exclusive, and have normal cash flows. project s has an irr of 15%, while project l’s irr is 12%. the two projects have the same npv when the wacc is 7%. which of the following statements is correct?
Based on the IRR of Projects S and L, their risk, and the WACC, the correct statement is b. If the WACC is 13%, Project S will have the higher NPV.
What happens when WACC is 13%?The IRR is rate of return that takes the NPV to zero. This means that if a project's WACC is less than IRR, then the NPV for that project will be less than 0.
Project L has an IRR of 12% which means that if the WACC is 13%, the NPV for this project will be negative.
Project S on the other hand would still have an IRR that is larger than the WACC and so would have a positive NPV.
In conclusion, option B is correct.
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Select one issue in our society today how do you apply methods of philosophizing
Answer:
We can apply the method of philosophizing known as "logic and critical thinking" to interpret and determine a truth about racism in our society.
Explanation:
Logic and critical thinking, assesses assumptions and elements of a given problem in society and through the investigation of facts and evidence about that problem it is able to determine whether there is a truth about it and whether we should follow it or not. This method of philosophizing is one of the most ideal and adaptable in our modern society because it uses rationality through evidence and hard facts.
This method can be used to discover truths about racism in our society. Through it we can analyze the origins of racism, how it accompanied the formation of American society and how to conclude from this whether it is still influential and strong today. Critical thinking will show us that racism is still influential as it will show various truths about it and its establishment in modern society.
Algebra structure and method book 1 mcdougal littell answer key
An example of Algebra structure work is simplify (8-3)+3.
What is algebraic structure?In mathematics, an algebraic structure is known to be a term that is made up of a nonempty set A, a combination of operations on A of finite series and a finite group of identities.
To simply this equation, (8-3)+3.
One has to follow the order of operations using the P.E.M/D.A/S technique, the expression that are in the parenthesis have to be solved first.
2 of 3
(5)+3 = 8
Therefore, the answer is 8
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Fluency and skills practice lesson 28 finding volume answer key
An example of Fluency and skills practice questions is "What does being fluent with a math skill mean to you?
What is Fluency?This is a term that connote is one's capability to be able to read with ease and fast, been accurate and having the right diction.
The question of what being fluent with a math skill mean to you is that it mean a lot to me as if I am fluent in math, I can be able to answer any difficult questions in math and then apply those skills in problem solving in real life.
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How does this complication contribute to the central conflict of the play? when romeo kills tybalt, he increases the friction with juliet’s family. when romeo kills tybalt, he impresses friends with his bravery. when romeo avenges mercutio’s death, the prince is grateful. when romeo avenges mercutio’s death, romeo is injured.
In the excerpt, the complication contribute to the conflict as at when Romeo kills Tybalt, he increases the friction with Juliet’s family.
What's a central conflict?A Central conflict that is found in a play or a novel is known to be when the main character's strong zeal or desire is said to be in form of clashes with an internal or external obstacle.
Note that in the start of most stories, a powerful alteration can bring about the main conflict for your protagonist as in the case of Juliet's family.
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Answer: A) When Romeo kills Tybalt, he increases the friction with Juliet’s family.
Explanation:
Edge 2023
Each month, elizabeth budgets $760 for fixed expenses, $620 for living expenses, and $80 for annual expenses. her annual net income is $32,580. which sentence best describes her monthly budget?
Answer:
760
Explanation:
it'd the budget that's what it says
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
Sodium hypochlorite, naocl, is the active ingredient in household bleach. what is the concentration of hypochlorite ion if 20.00 ml of bleach requires 32.00 ml of 0.500 m hcl to reach the equivalence point?
The concentration of hypochlorite ion if 20.00 ml of bleach requires 32.00 ml of 0.500 m hcl to reach the equivalence point is: 0.800 M.
Concentration of hypochlorite ionGiven:
Ca = concentration/molarity of acid=0.500 M
Va = volume of acid= 32.00 cm3
Cb = concentration/molarity of base=?
VB =volume of base= 20.00 cm3
Hence:
Concentration of hypochlorite ion=0.500 × 0 × 1/ 20.00
Concentration of hypochlorite ion=0.800M
Inconclusion the concentration of hypochlorite ion if 20.00 ml of bleach requires 32.00 ml of 0.500 m hcl to reach the equivalence point is: 0.800 M.
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A(n) ________ is a coherent set of interdependent processes and structures that dictates how the company searches for novel problems and solutions, synthesizes ideas into a business concept and product designs, and selects which projects get funded
Based on business analysis, an innovation system is a coherent set of interdependent processes and structures that dictates how the company searches for novel problems and solutions.
What is innovation systems?Innovative systems is a process that break ideas into a business concept and product designs and then select which projects get funded.
Innovation system comprises components like:
TechnologyEnterprisesInformationPeopleInstitutionHence, innovation systems is a coherent set of interdependent processes and structures that dictates how the company searches for novel problems and solutions.
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Nonverbal communication such as posture, gestures, expressions, and eye
movement are all examples of:
A. body language.
B. opposing signals.
Ο Ο Ο Ο
C. presentation cues.
D. supporting signals.
There are all examples of: A. body language.
The base of a jewelry box is shaped like a regular hexagon. what is the measure of each interior angle of the jewelry box base?
120 degrees is the answer too, the base of a jewelry box is shaped like a regular.
What is Interior angle?Inferior angle of scapula fractures (IAS) are uncommon injuries caused by the periscapular shoulder muscles avulsing the inferior scapula tip.
Since only case reports are now available to inform management, the purpose of this study was to look into the processes of damage, investigations, and treatment outcomes.
Computer tomography (CT) pictures were used to find patients with an IAS fracture. To acquire information regarding the injury, treatment, and outcome, case notes were examined and patients were contacted.
Therefore, 120 degrees is the answer too, the base of a jewelry box is shaped like a regular.
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#SPJ3
If a+b=-8 and a + b = 50, what is the
a
value of ab?
Answer:
sorry is that question correct pls
A parking lot in the shape of a trapezoid has an area of 12,052.1 square meters. the length of one base is 82.4 meters, and the length of the other base is 108.6 meters. what is the width of the parking lot?
Answer:
When you solve for the area of a trapezoid, you have this formula:
A = ((a + b)/2) * h
where: a & b are the bases ; h is the height
We just plug in the figures on the formula to get the needed information.
A = 12,052.10 square meters
a = 82.4 meters
b = 108.6 meters
12,052.10 = ((82.4 + 108.6)/2) h
12,052.10 = 191/2 * h
12,052.10 = 95.5 * h
12,052.10 / 95.5 = h
126.2 = height
The height of the parking lot is 126.20 meters.
Explanation:
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:
A customer opened a file attachment and now her pc is infected with ransomware
The action that one should do first is to Disconnect the PC from the network.
What do one do in case of ransomware?When a person is attacked by this worm, experts has stated that the right thing to do is to quickly disconnect the computer from the network.
One can do so by turning off Wi-Fi. Then one can use another device to make an online search to see the kind of ransomware that has been used on your system.
See full question below
A customer opened a file attachment, and now her PC is infected with ransomware. She's unable to open any of her files. Which action would you take first?
A. Reinstall the operating system
B. Run an antivirus scan
C. Pay the ransom to recover the data
D. Disconnect the PC from the network
E. Restore files from backup
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Chord ac intersects chord bd at point p in circle z. ap=4 cm bp=5 cm pc=8 cm what is pd? enter your answer as a decimal in the box.
For this question, PD = 6.4 cm
Mañana rewrite the sentences using ir a + [infinitive] to say that these people will do the same activities again tomorrow. follow the model.
The correct way of rewriting the sentences, using the form "ir a," are:
Rosa va a patinar en línea mañana de nuevo. Nosotros vamos a ver una película mañana otra vez. Tú vas a tomar el sol mañana también. Yo voy a leer un mensaje electrónico mañana de nuevo. Mis abuelos van a escribir una carta mañana también.How do a person write sentences in Spanish?There are different rules used in sentences that are in Spanish. One is that a person has to place the subject first, before adding a verb and a complement.
Note that Spanish sentences needs to have a period at the end of your sentences and have to also start with a capital letter.
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