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3) β bg mg sinθ J=∫r²dr = ml²/3 The system will have the differential eqn. like below; Jθ̈+βθ̇+mg l/2 sinθ=0 Let θ=x₁ θ̇=x₁=x₂ J ẍ₂+βx₂+mg l/2 sin x₁=0 6 ẋ₁=x₂ ẋ₂=-β/J x₂-mg l/2J sinθ The equilibrium pts are; 0=x₂e 0=-β/J x₂e-mg l/2J sin x₁e ⇒ x₁e=(kπ) where k is an integer. If β=0; ẋ₁=x₂ ẋ₂=-mg l/2J sin x₁ for x=[(2k+1)π] [0] If we start in the neighborhood of these equilibrium pts, the system will stay there, oscillating around the equilibrium pt. For ∀ε>0 and ∀t₂>t₁ there exist δ(∃δ>0) such that if ||x(t₂)-xₑ||<δ, then ||x(t)-xₑ||≤ε ∀t>t₂, Then the equilibrium pts are stable in the sense of Lyapunov. for x=[2kπ] [0] If we start in the neighborhood of these equilibrium pts, the states will tend away from these eq. pts. So that they're unstable equilibrium points. If β>0 ẋ₁=x₂ ẋ₂=-β/J x₂-mg l/2J sin x₁ for x=[(2k+1)π] [0] If we start in the neighborhood of these equilibrium pts, the states will converge to that eq. pt. If ∀t₂>t₁, ∃δ>0 ||x(t₂)-xₑ||<δ lim t→∞ x(t)=xₑ So that they're asymptotically stable.

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in the recovery of iron from iron are, the reduction of the ore is actually accomplished by reaction involving carbon monoxide. Use the following thermochemical question. To calculate delta H for the reaction FeO(s) + CO(g) > Fe(s) + CO2(g)

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Compare and contrast schizoaffective disorder with schizophrenia. For this discussion, you will need to place particular emphasis on how comprehensive assessment could help us arrive at the correct diagnosis. Give evidence in in-text citations and reference lists in the current APA format

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One rescuer is performing CPR on a person in cardiac arrest. Which task should the second rescuer arriving on the scene do first?Select one answer. Get the AED Manage the airway Take over compressions for the first rescuer Confirm that emergency medical services (EMS) has been summoned

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Suppose that a persons nominal income crisis from $10,000-$11,000 and the consumer price index prices from 100 to 105 the persons real income will

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For this assignment, your submission must include the following information: Official Gene Name: Chromosome number where gene is located: Specific chromosome locus (i.e., specific location on the chromosome, ex. 1p21.1): Break down the locus name information: - The first number is the chromosome - Next will be a p or q. P indicates the gene is on the long arm of the chromosome. Q indicates it is on the short arm of the chromosome. - The remaining numbers indicate the specific cytogenetic band (i.e., a recognized stained section of the chromosome). Image from a database that shows the gene on the chromosome. This will look a little different depending on which database you are using. You are also not limited to the ones listed here, but make sure you are using an academic-level database (i.e., not Wikipedia or a google image). Be sure to note where you obtained the image from (i.e., cite it).

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3. The system shown below consists of a bar of mass m. In terms of the variable $\theta$, what is the equation of motion? A) $\frac{mL^2}{3}\ddot{\theta} + \frac{cL^2}{4}\dot{\theta} + kL^2\theta = LF(t)$ B) $\frac{mL^2}{12}\ddot{\theta} + \frac{cL^2}{4}\dot{\theta} + kL^2\theta = LF(t)$ C) $\frac{mL^2}{3}\ddot{\theta} + \frac{cL^2}{2}\dot{\theta} + kL\theta = F(t)$ D) $\frac{mL^2}{12}\ddot{\theta} + c\dot{\theta} + k\theta = F(t)$ E) None of the above

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31, Without Donor Restrictions With Donor Restrictions Account Title Debit Credit Debit Credit Cash 3,000 1,600 Pledges receivable 1,000 500 Allowance for uncolectible pledges 300 Investments 3,200 Accrued interest receivable 100 Net assets, January 1 2018 6,700 2,000 Contributions 1,000 500 Membership Dues 1,500 Program service fees 3,000 Grant from county 2,500 Grant from state 2,500 Unrealized and realized gains on investments 200 Investment income 100 Luncheon Program Expense 7,200 Recreation program expense 3,400 Administration expenses 300 Net assets with donor-reclassifications out- satisfaction of program restrictions 400 Net assets with donor-reclassifications in- satisfaction of program restrictions 400 18,200 18,200 2,500 2,500

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Rose lived with her for 7 months in 2016. In 2018, she paid $8000 in charges. He paid $12,000 in alimony to his ex-wife, and Emily received $10,000 in alimony from her ex-husband. They were both divorced in 2014. Emily was out of work for 3 months and received $6200 in unemployment benefits. They live in a 2-family house, which is 70% personal and 30% rental. They received $19,200 in rental income. The total mortgage interest for the property is $19,300, and the realtor repaired the tenant's kitchen for $1100 and their own kitchen for $900. They contributed $3800 to their church and $7000 to the Democratic Party. They had $16,900 in unreimbursed medical bills and a $29,000 casualty loss. Their area was deemed a Federal Disaster area. Emily paid $500 for an early withdrawal penalty. They paid $580 in state and local taxes in 2017. They won a lawsuit - $6,000 in compensatory damages and $9,000 in punitive damages. Emily inherited $2,500 from an aunt. They earned $175 in stock dividends. Emily spent $5,000 on cosmetic surgery. What is their filing status? Find total income, AGI, and taxable income.

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9. Explain the stages of annealing and the impacts of heat treatment process. 10. Explain the evolution of ductile fracture with a neat sketch.

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destiny r.