ORDER DIFFERENTIAL EQUATIONS SUPPLIMENTARY PROBLEMS 1. Write the given equation in standard form 3.16. exy'-x=y' solution exy'-x=y' =exy'-y'=x ex-1y'=x y'=xex-1 ANS 3.25 dy+dx=0 Solution. dy+dx=0 dydx+1=0 y'=-1 2. The differential equations are given in both standard and differential form. Determine whether the equation in standard form are homogeneous and/or linear, if not linear, whether they are Bernoulli: determine whether the equations in differential
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calculators (non-programmable and non-graphing) are allowed to be with students during exams. Students are not allowed to take an exam in a lecture section in which they are not registered. Chapter 4 – sections 4.1 – 4.8 Given a balanced chemical equation, you should be able to calculate grams (or moles) of a product (or reactant) given the grams (or moles) of another product (or reactant). Remember: grams A ( moles A ( moles B ( grams B (p. 118). Practice Example 4.1
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Magnetic flux: The force of a magnet from the north pole to the south pole. Magnetic flux density: The amount of flux per unit area perpendicular to the magnetic field. Weber: SI unit of magnetic flux. (Wb) Tesla: SI unit of flux density, equal to one weber per square meter. Gauss: unit from the CGS (centimeter-gram-second) system, unit of flux density. Hall Effect: The change in current density produces a small trans-
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93 105 M s 1 t 8.25 min 60 s rate of reaction = rate of consumption of A2 = 8.93 105 M s 1 4.46 105 M s 1 2 1B (E) We use the rate of reaction of A to determine the rate of formation of B, noting from the balanced equation that 3 moles of B form (+3 moles B) when 2 moles of A react (–2 moles A). (Recall that “M” means “moles per liter.”) 0.5522 M A 0.5684 M A 3moles B rate of B formation= 1.62 104 M s 1 60s 2 moles A 2.50 min 1min 2A (M)
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data below to help answer the following questions: * Red Bird starts his flight from point (10, 0). His flight path reaches a maximum height of 18 yards and lands at point (38, 0). * Yellow Bird’s flight path can be modeled by the quadratic equation y=-x2+14x-24 * Blue Bird’s flight is modeled by the following graph: * The table below contains partial data points of Black Bird’s trajectory: x | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | y | 0 | 7.5 | 14 | 19.5 | 24
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x h 5 3. If f ( x ) x 2 , find f ( x h) f ( x ) h Answer: ( x h)2 x 2 f ( x h) f ( x ) = h h x 2 2hx h 2 x 2 = h = 2hx h2 h = h( 2 x h) = 2x + h h 4. Determine whether the given equation is a function (i) (ii)
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The Future for Super Wi-Fi By Chris Riley What the heck is super Wi-Fi anyway? First let us explore the history of wireless communications. In 1747, Benjamin Franklin proposed that electricity could move through air. In 1819, Danish physicist Hans Christian Oersted noted that a compass needle moved in the presence of an electrical field. Michael Faraday demonstrated the first electromagnetic induction and built the first direct current generator in 1831. In 1865 and again in 1873,
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| Unit Test Slope and Proportional Thinking Unit Test, Part 2 Answer each question in the space provided. (7 points) |Score | | | 1. Refer to the equation 2x – 6y = 12. a) What is the x-intercept? Show your work. b) What is the y-intercept? Show your work. c) Use the x- and y-intercepts to graph the line. [pic] Answer: (8 points) |Score
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Points Missed 0.00 Percentage 100% Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist. 1. A) one and only one solution 1. B) one and only one solution 1. C) one and only one solution 1. D) infinitely many solutions 1. E) no solution Points Earned: 4.0/4.0 Solve the linear system of equations 1. A) Unique solution: 1. B) Unique solution: 1. C) Infinitely many
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reaction kinetics, but you should know that other orders such as zeroth-order and 3rd order may also be involved in chemical kinetics. Reaction Rates and Stoichiometry In acidic solutions, hydrogen peroxide and iodide ion react according to the equation: H2O2 + 2H+ + 3I- = 2 H2O + I3-. In this reaction, the reaction Rate can be expressed as decreasing Rate of H2O2, - d[H2O2]/dt decreasing Rate of H+, - d[H+]/dt decreasing Rate of I-, - d[I-]/dt increasing Rate of H2O, + d[H2O] /dt increasing
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