Numerade

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32. Sketch a graph of the system of inequalities on a sheet of paper. \[ \begin{array}{l} y \leq-x-6 \\ y \geq 2 x+3 \end{array} \] Determine if the following point satisfies the system: \[ (-10,0) \] yes no

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6. In epidemiology, the basic reproduction number of an infection is the expected number of cases directly generated by one case of the infection. How would you expect the basic reproduction number of an infection to influence the marginal social benefit of research efforts aimed at finding a vaccine against the infection? If the basic reproduction number of COVID-19 increases, then the marginal social benefit of research efforts to find a vaccine would most likely A. decrease B. increase C. not change

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P1: Verify that the Lamé constants are formulated as $\lambda = \frac{\nu E}{(1+\nu)(1-2\nu)}$ and $\mu = G = \frac{E}{2(1+\nu)}$ in the Navier-Space equilibrium relation by substituting them into the 3D LEHI strain-stress formulas. $\begin{bmatrix} \epsilon_{xx} \\ \epsilon_{yy} \\ \epsilon_{zz} \end{bmatrix} = \frac{1}{E} \begin{bmatrix} 1 & -\nu & -\nu \\ -\nu & 1 & -\nu \\ -\nu & -\nu & 1 \end{bmatrix} \begin{bmatrix} \sigma_{xx} \\ \sigma_{yy} \\ \sigma_{zz} \end{bmatrix}$ and $\begin{bmatrix} \epsilon_{xy} \\ \epsilon_{xz} \\ \epsilon_{yz} \end{bmatrix} = \frac{1}{2G} \begin{bmatrix} \sigma_{xy} \\ \sigma_{xz} \\ \sigma_{yz} \end{bmatrix}$ Verify using one normal stress-strain equation and one shear stress-strain equation with $\sigma_{xx} = \lambda(\epsilon_{xx} + \epsilon_{yy} + \epsilon_{zz}) + 2\mu\epsilon_{xx}$ and $\sigma_{xy} = 2\mu\epsilon_{xy}$.

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30. The rate of consumer biomass accumulation in a given area; analogous to NPP for producer a. Egested energy d. Net secondary productivity. b. Respired energy c. assimilated energy 31. Net primary productivity depends on autotrophs for energy. a. True b. False 32. Which of the following is false? a. Tropical rainforests are the most productive terrestrial ecosystems b. Arctic and alpine regions have low productivity c. Temperate open ocean waters tend to have a higher productivity than tropical waters d. The interface between terrestrial and aquatic ecosystems is highly productive e. Productivity of open oceans is generally quite high compared to coastal waters.

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Q4. A system with turpentine at 25°C (with density $\rho$ = 870kg/m³ and dynamic viscosity $\mu$ = 1.37 × 10?³Pas) is flowing at the rate of 0.015 m³/s as shown in Figure 4. The suction line is a standard 4-in Schedule 40 steel pipe, 15m long. The total length of 2-in Schedule 40 steel pipe in the discharge line is 220m. Assume that the entrance from reservoir 1 is through a square-edged inlet (with resistance coefficient K=0.5) and that the elbows are standard. The valve is a fully open globe valve. (Note: The roughness of steel pipe $\epsilon$ = 4.6 x 10??m) (a) Write an expression to represent the energy equation of this system; (1 mark) (b) Find out the velocity at suction line $v_s$ and velocity at discharge line $v_d$; (2 marks) (c) Determine the friction factor at suction line $f_s$ and discharge line $f_d$ respectively; (3 marks) (d) By given the energy loss in valve in the discharge line is 15.76m and in each standard elbow is 1.39m, find out the total loss $h_L$ of overall system; (3 marks) (e) Calculate the power supplied to the pump if its efficiency is 80 percent. (1 mark) 10 m Standard elbow Discharge line 2-in schedule 40 steel Pump ? I Flow 1 Standard elbow Suction line 4-in Fully open globe valve schedule 40 steel Figure 4 2

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11. Solve and check. a) $2^{x+2} - 2^x = 48$ b) $4^{x+3} + 4^x = 260$ c) $2^{x+5} + 2^x = 1056$ d) $6^{x+1} + 6^{x+2} = 7$ e) $3^{x+3} - 3^{x+1} = 648$

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2. What charge is a 100-pF capacitor storing, if it is charged to 100 V? 3. What is the capacitor value that stores 200 pC when charged to 50 V? 4. What voltage is present across a 10-µF capacitor having a charge of 2,000 ?C?

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6.8 From the general equations of motion in cylindrical coordinates, prove that for incompressible, steady and axisymmetric flow $\frac{\partial^2 \phi}{\partial r^2} + \frac{\partial^2 \phi}{\partial x^2} + \frac{1}{r} \frac{\partial \phi}{\partial r} = 0$ $\frac{\partial^2 \psi}{\partial r^2} + \frac{\partial^2 \psi}{\partial x^2} - \frac{1}{r} \frac{\partial \psi}{\partial r} = 0$ State any other assumptions made in the derivation of the above equations.

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$\lim_{n \to -2} (n^3 - 3n + 1)$

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1. [15 pts] Determine whether the set $S = \{x^2 - 2x, -x^2 + x, 2x^2 + 1\}$ spans $P_2(\mathbb{R})$.

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donald s.