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diane cantu

diane c.

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Soru 6 Bonus Problem 5 (20 points) The figure shows a box of mass $m_2$= 1.0 kg on a frictionless plane inclined at angle $\theta$ = 30°. It is connected by a cord of negligible mass to a box of mass $m_1$ = 3.0 kg on a horizontal frictionless surface. The pulley is frictionless and massless. (a) Draw free body diagrams for each block. [7 pts] Solution: $m_1$ $N_1$ T F $m_2$ $N_2.cos30$ T+F T. sin(30) $m_1g$ (3x9.8) $m_1g$ Answer: $m_2g$ 0/10 p. --- OCR End ---

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(1 point) Use part I of the Fundamental Theorem of Calculus to find the derivative of g(y)=int_6^y t^(13)sintdt (1 point) Use part I of the Fundamental Theorem of Calculus to find the derivative of sin t dt

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A layered composite panel is loaded as shown below. The composite is composed of equal parts of two different materials. The light colored layer is made of drawn fibers with a Young's modulus of 136GPa, while the darker layer is a soft thermoset with E=3.6GPa. Calculate the Young's modulus of the composite.

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Part A The molar solubility of lead iodide is 1.45 x 10^-2 M at 20°C and 6.85 x 10^-2 M at 80°C. PbI2 → Pb2+ + 2I- Assume that H and S° are independent of temperature. Enter your answers numerically separated by a comma. H° = kJ/mol, S° = J/(K·mol)

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An inventor claims to have developed a refrigeration cycle that requires a net power input of 0.7 horsepower to remove 12,000 Btu/h of energy by heat transfer from the cold reservoir at 0 °F and discharge energy by heat transfer to a hot reservoir at 70 °F. There are no other energy transfers with the surroundings and operation is at steady state. Evaluate this claim to see if it is valid. You can use any of the following information if you find relevant to solve the problem. (1hp=2545 Btu/h, °R=460+°F) $\beta = Q_c/W_{cycle} = Q_c/(Q_H - Q_c)$ $\gamma = Q_H/W_{cycle} = Q_H/(Q_H - Q_c)$ $\beta_{max} = T_c/(T_H - T_c)$ $\gamma_{max} = T_H/(T_H - T_c)$

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8:07 Find the exact value of each product. 9. $\sin(52.5^\circ)\sin(7.5^\circ)$ 10. $\cos(105^\circ)\cos(75^\circ)$ 11. $\sin(\frac{13\pi}{24})\cos(\frac{5\pi}{24})$ 12. $\cos(\frac{5\pi}{24})\sin(-\frac{\pi}{24})$ Use the sum-to-product identities to rewrite each expression. 13. $\sin 12^\circ - \sin 8^\circ$ 14. $\sin 7^\circ + \sin 11^\circ$ 15. $\cos 80^\circ - \cos 87^\circ$ 16. $\cos 44^\circ + \cos 31^\circ$ 17. $\sin 3.6 - \sin 4.8$ 18. $\sin 5.1 + \sin 6.3$ 19. $\cos(5y - 3) - \cos(3y + 9)$ 20. $\cos(6x^2 - 1) + \cos(4x^2 - 1)$ 21. $\sin 5a - \sin 8a$ 22. $\sin 3s + \sin 5s$ 23. $\cos(\frac{\pi}{3}) - \cos(\frac{\pi}{5})$ 24. $\cos(\frac{1}{2}) + \cos(\frac{2}{3})$ Find the exact value of each sum. 25. $\sin(75^\circ) + \sin(15^\circ)$

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3- Firms Kaka and Nana serve the same market. They have constant average costs of 2\$ per unit. The firms can choose either a high price (10\$) or a low price (5\$) for their output. When both firms set a high price, the total demand equals 10,000 units, which is split evenly between the two firms. When both set a low price, the total demand is 18,000 units, which is again split evenly. If one firm sets a low price and the second a high price, the low-priced firm sells 15,000 units, the high-priced firm only 2,000 units. Analyze the pricing decisions of the two firms as a non-cooperative game. A- In the normal form representation, construct the pay-off matrix, where the elements of each cell of the matrix are the two firms' profits. B- Derive the equilibrium set of strategies. C- Explain why this is an example of the prisoners' dilemma game.

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30 Points 2. Determine built-in-potential $\Phi_b$ of the $p-n$ diode shown in Figure 1. Show step-wise calculations. $\Phi_b$ $N_a = 6 \times 10^{16}/cm^3$ $p$ Figure 1. $p-n$ diode. $N_d = 6 \times 10^{16}/cm^3$

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Problem 3. In class I gave you the final expression for the 1<sup>st</sup> order fine structure energy correction, which is a sum of the relativistic and the spin-orbit contributions. Derive that formula starting with individual expressions for $E_r^1$ and $E_{so}^1$.

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Problem-1 (50 Points) Three parallel single-phase loads are supplied from a 440-V rms, 60 Hz single-phase supply. The load data is given below Load 1: 24 kW, 0.866 pf lagging Load 2: 32 kW, 0.85 pf leading Load 3: 30 kvar, 0.866 pf lagging Answer the following questions (a) [20 Points] Determine the total active power, reactive power, apparent power, and complex power delivered by the source. (b) [10 Points] Determine the supply current and the load power factor. (c) [5 Points] Calculate the kvar rating of the capacitor required to improve the power factor of the load to unity. (d) [5 Points] Determine the supply current when the capacitor in part (c) is connected across the loads. (e) [5 Points] Compare the current magnitude in part (b) and part (d). Does the supply current increase or decrease? State valid reasons. (f) [5 Points] What are the advantages of improving the power factor?

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