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ruben serrano

ruben s.

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Given the wave function psi (x) = A * e^(-x^2/2), what is the value of A that normalizes the function on the interval (-infty , infty )?

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Q1\ Fill in the blank spaces of the following table: Q VC TC AFC AVC ATC MC 0 $100 1 20 $20 $120 $20 2 60 160 3 33.33 40 73.34 60 4 200 300 25 75 5 300 60 6 420 520 16.66 70 86.66 160 Q2\ On a separate paper do the following: 1- Graph the situation of profit maximization in the perfectly competitive market, (When P > ATC) 2- Graph the situation of loss minimization in the perfectly competitive market, (When P < ATC) 3- Graph the situation of breakeven in the perfectly competitive market, (When P = ATC)

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12.11 3 Data water-cooled (122°C; 6.23 m³/kWh; 87.6%) A single-cylinder, single-acting reciprocating air compressor supplies a receiver from which the air is drawn off for process work. Taking the polytropic index of.compression and re-expansion as 1.3, and using the data below, calculate: (i) the pressure in the receiver; $Q_{rej}$ (ii) the rate of heat rejection from the receiver; (iii) the volumetric efficiency of the compressor; $\eta_v$ (iv) the required power input to the compressor. Cylinder bore, 200 mm; stroke, 250 mm; rotational speed, 440 rev/min; clearance volume, 5% of swept volume; ambient pressure and temperature in compressor house, 1.01 bar and 10°C; average pressure and temperature during the induction stroke, 1 bar and 273 83k 20°C; volume flow rate of air drawn off for process work, 0.6 m³/min at 17°C. Note: Use a trial-and-error method for part (i). 200 3k (5 bar; 8.14 kW; 83.9%; 9.85 kW) of 3 in to 175 har

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There is uniform Euler beam of length L and both sides have pinned (hinged) boundary condition a) Harmonic force $f(x,t) = f_0 sin\omega t$ at Euler beam $x = L/2$ Find forced response $w(x,t)$ of beam bending vibration b) What are the modes that are not excitation from the result of a?

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Given the function f defined as: f: R?R f(x) = 2x²+1 Select the correct statements 1.f is bijective 2.f is a function 3.f is one to one 4. f is onto 5. None of the given statements Moving to the next question prevents changes to this answe

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2. Write down the path of urine from the point of origin to secretion. (0.5 point)

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Sketch the graph of the function. Identify any local extrema and points of inflection. $f(x) = \frac{x^2 + 4}{4x}$ What are the coordinates of the relative maxima? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no maximum. What are the coordinates of the relative minima? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There is no minimum. What are the coordinates of the points of inflection? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. (Simplify your answer. Type an ordered pair. Use integers or fractions for any numbers in the expression. Use a comma to separate answers as needed.) B. There are no inflection points. Choose the correct graph below. A. B. C. D.

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5. Find \mathcal{L}\{f(t)\}, if $f(t) = \begin{cases} 1, & 0 \le t < 2; \\ e^{-(t-2)}, & t \ge 2 \end{cases}$

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Question 1 (Forces in structural frameworks) A tripod is constructed having three 9-metre-long legs. The base of the legs forms an isosceles triangle on the ground of AB & AC = 7 m, BC = 6 m. A load of 70 kN is suspended from the apex "O". Use the following scales; Legs: 1m = 1 cm Force: 1 kN = 1 cm Graphically determine the forces in the legs. Question 2 (Thick cylinders) During the American civil war, it was noted that the Parrot gun had a fatal flaw. The 35 MPa radial pressure induced during firing was so violent that the screw-on end cap occasionally popped off due to the radial expansion of the barrel. This caused unexpected fatal injuries. This dangerous situation was overcome by shrink fitting an outer cylinder with an outside diameter of 240 mm onto the barrel having inner and outer diameters of 150 mm and 200 mm respectively. The barrel was cooled and the outer ring was heated during fitting, inducing a 7 MPa shrinkage pressure after the temperatures were normalised. E = 200 GPa. Calculate the hoop maximum hoop stresses in both cylinders during firing. Question 3 (Deflexion of beams) A hollow rectangular section having a wall thickness of 20 mm is used as a 5,5-meter-long beam supporting a point load in its centre. The point load is limited as the beam must not exceed a stress of 120 MPa and a slope must not be more than 1". Take the density of steel as 7 500 kg/m³, E = 210 GPa Calculate the safe load that can be supported by the beam.

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A three-phase 50 Hz source supplies three loads: LOAD-1: A delta connected three-phase 45 kW Induction motor load operating at \(\frac{3}{4}\)^{th} of rated output with an efficiency of 90% and power factor of 94%. LOAD-2: A wye connected 3-phase 56 kW Induction motor operating at half of its rated output with an efficiency of 88% and a power factor of 74%. LOAD-3: A delta connect resistive heater drawing 20 kW. Calculate (i) total active, reactive and apparent power supplied by the source (ii) the power factor of the combined loads (iii) the magnitude of the line current (iv) the capacitance and voltage rating for a star connected capacitor bank that will correct the system power factor to 0.95 lagging. (7 Marks) (1 Mark) (2 Marks) (5 Marks)

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