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17. The membrane that surrounds a living cell has a surface area of 4.2 x 10-9 m² and a thickness of 1.4 x 10-8 m. Assume that the membrane behaves like a parallel plate capacitor and has a dielectric constant of 4.8. (a) What is the capacitance of cell membrane? (b)The potential on the outer surface of the membrane is +75.6 mV greater than that on the inside surface. How much charge resides on the outer surface of membrane? Eo= 8.85x10-12 c2/Nm² $A= 4.2 \times 10^{-9} m^2$ $d = 1.4 \times 10^{-8} m$ $k = 4.8$ $75.6 mV \times 10^{-3} V$ $C = k \epsilon_0 \frac{A}{d}$ $C = (4.8) (8.85 \times 10^{-12}) \frac{(4.2 \times 10^{-9})}{1.4 \times 10^{-8}}$ $C = 1.2744 \times 10^{-11} C$ $q = C.V$ $q = 1.2744 \times 10^{-11} \times 75.6 \times 10^{-3}$ $q = 9.63 \times 10^{-13} C$

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Let $ (S) $ be the part of the elliptic paraboloid $ z=8 x^{2}+8 y^{2}+3 $ lying inside the cylinder $ x^{2}+y^{2}=2 $. Evaluate the surface integral \[ I=\iint_{S} 7 z d S \] Answer: $ \square $

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2. The composite bar consists of a 25-mm-diameter A-36 steel segment AB and 50-mm-diameter red brass C83400 end segments DA and CB. Determine the maximum normal stress developed in the composite bar due to the applied load. The modulus of elasticity of the steel and red brass are $E_{st} = 200$ GPa and $E_{br} = 100$ GPa, respectively. [10 marks] 200 mm 500 mm 200 mm 50 mm 25 mm 75 kN 100 kN D A 75 kN 100 kN B C

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A carnival game at the Fair consists of spinning a wheel with 12 slots, of which 11 are purple and one is golden yellow. If you land on the golden yellow slot you win a prize. Suppose that the prizes. Suppose that the prizes are so terrific that you buy 5 tickets at once to play this game (though you still play one ticket at a time). What is the probability that you will win exactly one prize with your 5 tickets?

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Host factors in the causation of disease include. A. Temperature and humidity B. Chemicals in the air, water, or food C. Genetic factors D. Altitude E. All of the above

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Consider an instance of the Satisfiability Problem, specified by clauses C1 , . . . , C k over a set of Boolean variables x1 , . . . , x n. We say that the instance is monotone

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What compound would result if water were added to the product of a Perkin condensation? Draw the molecule on the canvas by choosing buttons from the Tools (for bonds), Atoms, and Advanced Template toolbars. The single bond is active by default.

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7. A flux of $N_1 = 3.7 \times 10^{10}$ alpha particles every second, with a kinetic energy of 5.5 MeV is incident on a foil of thickness $d = 5 \times 10^{-5} cm$ and surface area of $A_1 = 1 cm^2$. Suppose the beam hits all the surface of the foil. Find the number of particles scattered to a detector of surface $A_2 = 4 cm^2$, which is at a distance $r = 50 cm$ from the foil and at an angle of $\theta = 45^\circ$ respect to the initial beam.

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2. Majan company shared the following data for a number of recent months: Product Returns Warranty Cost April 24 $2,972 May. 23 $2,928 June 27 $3,141 July 39 $3,752 August. 36 $3,569 September 35 $3,551 October 26 $3,071 November 37 $3,636 Required: Estimate the variable cost per product return and the fixed cost per month using high-low method (3 marks)

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1.) A spring (k = 5.00 x 10$^2$ N/m) hangs under the influence of gravity. Affixed to it is a 0.500 g mass. The mass/spring system is displaced from equilibrium and allowed to oscillate. a. Draw a picture of the situation. b. What is the angular frequency of the system? c. Find the period of one complete oscillation. 2.) Consider the system from 1.) above a. The original displacement was 0.30 m prior to release. Find the work done in displacing the mass. b. Using Conservation of Energy determine the speed of the mass as it returns to the equilibrium position.

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