Numerade

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The polynomial of degree 3, P(x), has a root of multiplicity 2 at x=2 and a root of multiplicity 1 at x=-2. The y-intercept is y=-4.

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P D.2 (pg 1 of 3) Ideal Gas Law & Density Please note that both mm Hg and atm are used as units of pressure. It is a simple conversion: 760 mm = 1 atm 1. Given 3.43 g of gas in a 2.00 L container at 25.0°C and a pressure of 1140 mm Hg: a. Determine the number of moles of gas in the container. b. Recalling that molar mass (molecular weight) is nothing more than a quotient of grams per mole (mass/moles), determine the molar mass of this gas. c. What might be the identity of this gas?

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Question 3 The \_\_\_\_\_\_ system was based upon the principle that isolation and silence are needed for rehabilitation and reformation. Auburn Ohio New York Pennsylvania 2 pts

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The standard price and quantity of direct materials are separated because a. GAAP and IFRS reporting requires separation b. standard prices are more difficult to estimate than standard quantities c. standard quantities change more frequently than standard prices d. direct materials prices are controlled by the Purchasing Department and quantity used is controlled by the Production Department

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Given a stated future value in Year 5 and an annual percentage rate of 10 percent, ____________________ compounding will yield the lowest effective annual rate

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11-18. Prove, by induction, the following results for all n ? P. 11. 1² + 2² + 3² + ... + n² = \frac{n(n+1)(2n+1)}{6} 12. 1³ + 2³ + 3³ + ... + n³ = \left[\frac{n(n+1)}{2}\right]² 13. 1? + 2? + 3? + ... + n? = \frac{n(n+1)(6n³ + 9n² + n - 1)}{30} 14. 1² + 3² + 5² + ... + (2n - 1)² = \frac{n(2n - 1)(2n + 1)}{3} 15. 1 \cdot 2 + 2 \cdot 3 + 3 \cdot 4 + ... + n(n+1) = \frac{n(n+1)(n+2)}{3} 16. \frac{1}{2} + \frac{2}{2²} + \frac{3}{2³} + ... + \frac{n}{2?} = 2 - \left(\frac{n+2}{2?}\right) 17. A set with n elements contains 2? subsets (including the set itself) 18. 6(2n³ + 3n² + n)

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2. (4 points) If an electric scalar potential is given by $V = r^2(z + 1)\sin\phi$ (V), what is the corresponding electric field?

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4. One example of tunneling is the cold emission of electrons from a metal by the application of an external field. In this case, as shown in the diagram below, the electrons at the Fermi energy $\varepsilon_f$ located $\Phi$ below the vacuum level (where $\Phi$ is the work function of the metal) tunnel out of a triangular potential barrier of the form $-eEx$, where $E$ is a applied field. $\varepsilon_f$ Electrons in metal $-eEx$ $\Phi$ Tunneled electron Prove that the transmission probability through the \"thick\" barrier for electrons of mass $m$ at the Fermi energy $\varepsilon_f$ is given by the Fowler-Nordheim formula; $|T|^2 = \exp\left[ - \left( \frac{4\sqrt{2}}{3} \right) \frac{\sqrt{m\Phi}}{\hbar} \left( \frac{\Phi}{eE} \right) \right].

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A MOSFET layout is illustrated in the diagram. Given: For substrate, NA = 10^15 cm^-3 and Np = 5x10^18 cm^-3 for the source and drain wells. The bias voltages are: Vsp = 1V, VGB = 3V, and Vps = 4V. Assume V = 1V. a) If the lateral diffusion under the gate is 0.2 um and the oxide thickness is tor = 30 nm, what is the total gate capacitance, Cor? b) What is the MOSFET transconductance, gm, under the given bias? c) Explain the source of the three types of capacitance in MOSFETs. d) If Cdep = 5 x 10^-11 F/cm and Cdep = 1 x 10^-9 F/cm^2, calculate the total source and drain depletion capacitances. Assume the grading coefficient to be 0.5. e) Based on the lateral diffusion value of part a) and assuming CGB,ovt = 1 x 10^-12 F/cm, estimate the three extrinsic MOSFET capacitances. f) The intrinsic capacitances, Ces and Ceo, change with biasing condition. What are their values under the given bias conditions? g) Draw the high-frequency, small-signal representation of this MOSFET device at the given DC bias. Ignore ro.

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3) In Figure, a stone is projected at a cliff of with an initial speed $V_0$ directed at angle $\theta_0$ above the horizontal. The stone strikes at A at time $t_a$ after launching. Find the followings by using the known values (initial speed $V_0$, angle $\theta_0$, time $t_a$, and gravitational acceleration $g$). a. the height h of the cliff, b. the speed of the stone just before impact at A, and c. the maximum height H reached above the ground

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jose b.