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Find the coordinates of the vertex and the focus for the parabola given by the following equation: $$x^2 + 8x - 16y - 80 = 0$$ Round all answers to 2 places after the decimal point, if necessary. Coordinates of the vertex: Coordinates of the focus:

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Required information [The following information applies to the questions displayed below.] At the end of June, the job cost sheets at Ace Roofers show the following costs accumulated on three jobs. At June 30 Direct materials Direct labor Overhead applied Job 5 $ 17,400 Job 6 $ 34,200 Job 7 $ 28,200 10,400 16,600 23,400 5,200 8,300 11,700 Additional Information a. Job 5 was started in May, and the following costs were assigned to it in May: direct materials, $7,200; direct labor, $3,000; and applied overhead, $2,100. Job 5 was finished in June. b. Job 6 and Job 7 were started in June; Job 6 was finished in June, and Job 7 is to be completed in July. c. Overhead cost is applied with a predetermined rate based on direct labor cost. The predetermined overhead rate did not change across these months. 4. What is the total cost transferred to Finished Goods Inventory in June? Total transferred cost

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Find the one-sided limit (if it exists). (If the limit is infinite, enter '$\infty$' or '$-\infty$', as appropriate. If the limit does not otherwise exist, enter DNE.) $$ \lim_{x \to (-1/2)^+} \frac{6x^2 + x - 1}{8x^2 - 2x - 3} $$

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If the reaction is 1 st order in NO and zero order in Cl 2 , what are the units for k?

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The cell body of the third order neuron is in the: sensory ganglion cerebral cortex thalamus brainstem or spinal cord

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Maths for Economics Spring 2021 - EX9 1. Consider this set of national accounts: Buying sector IT goods Services Transport Final demands Total Selling sector IT goods £25m £20m £10m £25m Services £40m £5m £30m £125m Transport £0m £80m £40m £40m Primary inputs £15m £95m £80m £60m Total (i) How much does the transport sector buy from the service sector? (ii) How much does the service sector sell to itself? (iii) Fill in the total rows and columns. (iv) Hence construct an input coefficients matrix, A, for the IT, Services and Transport sectors and the matrix I-A 2. (i) Find the 7 principal matrices for (I-A) constructed in the previous question. (ii) Hence calculate the principal minors. (iii) Are the Hawkins-Simon conditions satisfied for this economy?

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Texts: 2.3. Consider Equation 2.6, and now suppose that we wish to use a combination of feedback and feedforward control in the form qe=q*+Kbh -h*)+KQ(1. a. Show that you obtain perfect control (h = h* at all times) for Kfr = 1. Show that steady-state offset is reduced for K < 1. (Why should K never be greater than unity?) b. Now suppose that some input disturbances are unmeasured, or there is unknown measurement error, in which case the controller then has the form qe=q+ Kh -h*+ KQmt. Obtain the equation for the response of the controlled system. How should K be chosen if Kfr = 1? If Kff < 1? c. In your physics course, you may have studied the damped harmonic oscillator. If so, consider the case in which the feedback controller is proportional plus integral, or PI, control: qe=q*+ Kfb(h-h*)+ Ki [h(t)] Show that the equation for the flow in the tank becomes identical to the equation for the damped harmonic oscillator, and that steady-state offset is eliminated for O(t) = constant.

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1) This is a solution to the bounded-buffer problem for a Coke machine (Producer-Consumer Problem) using three semaphores (mutex, emptyBuffers, and fullBuffers): Producer () { } emptyBuffers.P(); mutex.P(); put 1 coke in machine; mutex.V(); fullBuffers.V(); Consumer() { fullBuffers.P(); mutex.P(); take 1 coke from machine; mutex.V(); emptyBuffers.V(); Given each of the following variations, Consider the case where the coke machine is initially full, say whether it is correct or incorrect. If you say correct, explain any of the advantages and disadvantages of the new code. If you say incorrect, explain what could go wrong (i.e., trace through an example where it does not behave properly). a) (5 points) Producer () { mutex.P(); emptyBuffers.P(); put 1 coke in machine; fullBuffers.V(); mutex.V(); Consumer () { mutex.P(); fullBuffers.P(); take 1 coke from machine; emptyBuffers.V(); mutex.V(); b) Producer () { emptyBuffers.P(); mutex.P(); put 1 coke in machine; fullBuffers.V(); mutex.V(); Consumer() { } fullBuffers.P(); mutex.P(); take 1 coke from machine; emptyBuffers.V(); mutex.V();

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A monopolist operates in an industry where the demand curve is given by Q = 1,800 - 4P 4.1 Suppose that the monopolist's constant marginal cost is $240. Calculate the profit- maximizing monopoly quantity and compute the monopolist's total revenue at the optimal price. 4.2 Now, assume that the monopolist's marginal cost increases to MC = $360. Calculate the profit-maximizing monopoly quantity and compute the monopolist's total revenue at the optimal price and verify that the monopolist's total revenue goes down. 4.3 Given [4.1], suppose that all firms in a perfectly competitive equilibrium had a constant marginal cost MC = $240. Find the long-run perfectly competitive industry price and quantity.

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Find the total weight of a 280 liter tank of oxygen if the oxygen is pressurized to 3.5 MPa, the tank itself weighs 68 kgf, and the temperature is 295 K?

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