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6) Consider the following Lagrangian for a point particle of charge q and mass m: $$L = \frac{1}{2}m \vec{v} \cdot \vec{v} - qU + q \vec{A} \cdot \vec{v}$$ where $\vec{v}$ is the velocity of the particle and $U$ & $\vec{A}$ are time and position dependent fields. Defining new fields via $$\vec{E} = -\nabla U - \frac{\partial \vec{A}}{\partial t}, \quad \vec{B} = \nabla \times \vec{A}$$ find the Euler-Lagrange equations (equations of motion) in terms of $\frac{d\vec{v}}{dt}$, $\vec{v}$, $\vec{E}$, and $\vec{B}$. What do you infer?

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6. [25] Donkey has been up all morning making an enormous amount of waffles. He decided to hang a plate of them on a hook in Shrek's cabin. It may be modelled as a cantilever beam with a 90° angle. The waffles apply a load of 300 lbf in the negative z-direction. Identify the location of critical stress element and determine the factor of safety using maximum-shear-stress (MSS) and distortion-energy (DE) failure theories. Ignore transverse shear stress. Assume ductile material and Sy = 81 kpsi. (If you have something against waffles, see the other diagram. Identify the location of critical stress element and determine the factor of safety using maximum-shear-stress (MSS) and distortion-energy (DE) failure theories. Ignore transverse shear stress. Assume ductile material and Sy = 81 kpsi.) ZI X D = 1 in. 18 in 18 in 300 lbf D = 1 in. <-B 12 in 12 in Sy=81epsi n=?

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Bank USA invested $8 million in euro-denominated one-year CDs with a 9 percent interest rate. The initial spot exchange rate is $1.135 per €1. a. Is Bank USA exposed to an appreciation or depreciation of the dollar relative to the euro? Exposure (appreciation/depreciation): b. What will be the return on the one-year CD if the dollar appreciates relative to the euro such that the spot rate of U.S. dollars for euros at the end of the year is $1.035 per €1? Return (Rate): % Note: Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161) c. What will be the return on the one-year CD if the dollar depreciates relative to the euro such that the spot rate of U.S. dollars for euros at the end of the year is $1.235 per €1? Return (Rate): % Note: Do not round intermediate calculations. Round your answer to 3 decimal places. (e.g., 32.161)

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Required: For each item, select 1. whether it is reported on the income statement or balance sheet and 2. the type of account. Account 1. Accounts Receivable 2. Sales Revenue 3. Equipment 4. Supplies Expense 5. Cash 6. Advertising Expense 7. Accounts Payable 8. Retained Earnings Statement Account Type Asset Revenue Asset Asset Liability Stockholders' Equity

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What overall charge do DNA-binding motifs of transcription factors have?

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Curve sketching is a process you saw in Precalculus 1 and will revisit in calculus. Curve sketching is a process of using the information you can gather about a curve to sketch a good approximation of a function. I know what you are thinking: \"Why sketch a curve by hand when desmos can do it more quickly and more precisely?\" That is a good question. The goal of curve sketching is not to get a picture of the curve, we could do that with technology. The goal is to gain a better understanding of the curve, and the best way for you to gain an appreciation of the relationship between the function and its curve is to gather as much information as you can and use that information to sketch the curve. You will examine points called critical values (also called turning points). These are the points where the function changes from increasing to decreasing or from decreasing to increasing. An example you are familiar with would be the vertex of a parabola, which is the point where the function changes from decreasing to increasing if the parabola opens upwards. These are points you could not find last semester, but will have the ability to find next semester with some calculus. The curve below is a function, which means it passes the vertical line test. It is also a smooth curve, which means there are no sharp corners in the curve. Most of the functions you have ever worked with are smooth curves (except the absolute value function). Consider the function $f (x) = \sin x - \cos(2x)$ on the interval $[0, 2\pi]$ 1. Find the exact coordinates of the x-intercepts on the interval. Write the intercepts as coordinate points $(x,y)$. 2. Find the exact coordinates of the endpoints of the interval. Write the endpoints as coordinate points. 3. The critical values of the function occur where the derivative is equal to zero. The derivative of this function is identified as $f' (x)$ and is a new function: $f' (x) = \cos x + 2 \sin(2x)$. Find the critical values on the interval by solving the equation $f' (x) = 0$. Find the exact coordinate points of those critical values. 4. Plot the x-intercepts and critical values and then use those points to sketch the curve by hand. No credit will be given for submission of technology-generated curves.

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Graph Input Tool Market for Shoes Quantity (Pairs of shoes) Demand Price (Dollars per pair) 75.00 Supply Price (Dollars per pair) 17.00 Supply Shifter Tax on Sellers (Dollars per pair) Fill in the following table with the quantity sold, the price buyers pay, and the price sellers receive before and after the tax. Quantity (Pairs of shoes) Price Buyers Pay (Dollars per pair) (Dollars per pair) Price Sellers Receive (Dollars per pair) Before Tax After Tax Using the data from the previous table, the tax burden that falls on buyers is and the tax burden of sellers is The burden of the tax falls more heavily on the elastic side of the market. Graph Input Tool 50 Market for Shoes Quantity (Pairs of shoes) Demand Price (Dollars per pair) 10 o Supply PRICE(Dollars per pair emand 10 5 0 102030405060708090100 QUANTITY(Pairs of shoes) 75.00 Supply Price (Dollars per pair) 17.00 Supply Shifter Tax on Sellers (Dollars per pair) 0.00 Fill in the following table with the quantity sold, the price buyers pay, and the price sellers receive before and after the tax. Quantity Price Buyers Pay Price Sellers Receive (Dollars per pair) (Pairs of shoes) (Dollars per pair) Before Tax After Tax Using the data from the previous table,the tax burden that falls on buyers iss and the tax burden of sellers iss The burden of the tax falls more heavily on the elastic side of the market

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d) A time division multiple access (TDMA) system operates at 20 Mbps with a frame length of 1 ms. Assume that all the time slots are of equal duration and require a preamble of 100 bits in addition to a time guard band of 1 ?s. (i) Determine the maximum number of equal data-rate users that can be multiplexed if the system efficiency must be kept at 95% or above. (ii) Can this system accommodate 100 equal data-rate users? Show your calculations to justify your answer. (iii) If the minimum data rate per user is to be maintained at no less than 1 Mbps, what is the maximum number of users that can be multiplexed and what would be the exact bit rate per user? [3, 3, 3 marks] (e) Consider 33 equal power terminals transmitting signals towards a central access point using direct sequence code division multiple access (DS-CDMA). Each terminal transmits information at 5 kbps on a 300 kilo chip per second (kcps) direct pseudonoise (PN) spreading code using BPSK. (i) If the receiver's noise is negligible relative to the interference from the other users, find the ratio of bit energy to interference power spectral density ($E_b/J_o$) in decibels for one user at the access point. (ii) Assume that the access point is to service 66 equal power users, and the value of $E_b/J_o$ is to be increased to 7dB without changing the transmit power and data rate. What must be done to achieve this? Show your calculations to justify your answer.

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#3 For parts a-d use limits, as we did in class, to determine whether f(n) e o(g(n)), g(n) e o(f(n)), or if f(n) 2 0 (g(n)). (Hint: Use L'Hopital's Rule when appropriate and helpful) (a) f(n) = ln n, g(n) = 6lgn (b) f(n) = 2n, g(n) = en (c) f(n) = nlnn, g(n) = ln2n (d) f(n) = ?n, g(n) = ?n [Hint, remember ?n = n1/2 and ?n = n1/3] CS 502 - Analysis of Algorithms Homework #4 #4 Given the recurrence T(n) = T(n/2) + T(n/2) + n (a) How much actual work is being done in level 0? (b) How much actual work is being done in level 1? (c) Below the recursion tree showing levels 0, 1 and 2 and the total work for each of these levels (similar to the recursion tree in the lec2.pdf slides from class. (d) If we assume the tree has an infinite number of levels, calculate the sum of the total work in the entire recursion tree (like the lec2.pdf slides from class) Total = n + 2(n/2) + 4(n/4) + ... [Hint: There is a geometric series similar to the lecture example)

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The green arrow is indicating the ______ lobe of the liver.

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kevin p.