Numerade

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Problem 12: A designer wishes to use a stepper motor coupled to a gearbox to drive an indexed conveyor belt to achieve a linear resolution of 1 mm. The gearbox is a speed reducer with a gear ratio of 3 to 1, and the conveyor is driven by a 10-cm diameter drum attached to the output shaft of the gearbox. What is the minimum resolution required for the stepper motor? (Hint: Please note that the angular displacement of the drum (the output of the gearbox) is equal to the linear displacement of the conveyor belt divided by the radius of the drum. Also, the minimum required resolution of the stepper motor is equal to the minimum required number of steps per revolution.)

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Consider the function $f(x) = x^2 - 3x + 2$ and the function $g(x)$ given by the values in the table. Which statement is true? | $x$ | $g(x)$ | |---|---| | -4 | -2 | | -3 | $-\frac{1}{2}$ | | -2 | 0 | | -1 | $-\frac{1}{2}$ | | 0 | -2 | Select one answer A When $x = 0$, then $f(x) = g(x) = 2$ B Both functions have a maximum value. C The functions share a vertex. D There are no $x$-values such that $f(x) = g(x)$.

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The combustion of 5 g of carbon raised the temperature of water from 10°C to 47°C. If 1 kg of water was heated. Calculate the heating value of carbon energy (J) / g

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Problem 8. (a) Show that the product of an even function and an odd function is an odd function. (b) Show that the product of two even functions is an even function. (c) Show that the product of two odd functions is an even function. (d) Show that the definite integral of an odd function over a symmetric interval about zero ($[-L, L]$ for example) is zero.

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S86. The gorilla is flying kite B. Kite C's string has broken so it is blown freely by the wind. The two kites collide and become entangled meaning that they move together as if point C was on top of point B. Determine (a) the velocity of the kites after they collide and (b) the linear impulse that kite B imparts to kite C. Report all answers in the x-y coordinate system shown. ANSWER: $v_2 = (-9.57 \hat{i} - 3.48 \hat{j})$ ft/s and $Imp = (-0.228 \hat{i} - 0.273 \hat{j})$ lb-s • Each kite weighs w. • Immediately before the collision kite C has velocity $\vec{v_c}$. • Immediately before collision kite B is rotating around the z axis through stationary point A. The string from A to B is of constant length, d. At the moment of the collision, it makes an angle of $\psi$ with respect to the y axis. It has angular velocity $\omega$ and angular acceleration $\alpha$ around the z axis. • You may ignore the effects of gravity during the collision. Possibly Important Parameters w = 0.5 lb d = 100 ft $\psi$ = 20° $\vec{v_c} = (5.13 \hat{i} + 14.1 \hat{j})$ ft/s $\omega$ = 0.3 rad/s (CCW) $\alpha$ = 1 rad/s² (CCW)

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16) [1 point] There are many differences between a market served by a monopoly and a market that is perfectly competitive. Which of these followings are true for monopoly only? a. The price is higher than in other market structures. b. An efficient quantity is produced. c. Firms can earn positive economic profit in the long run. d. There are significant barriers to entry. e. Firms have no market power. f. A firm is a price maker. g. A firm is a price taker. A) a, c, f B) c, d, f C) b, c, d, f D) a, b, d, f E) a, c, d, f 17) [1 point] Suppose the GoLogos logo monopoly is broken up, and the logo industry becomes perfectly competitive. We would expect A) consumer; producer and total B) producer; consumer and total C) consumer and total; producer D) producer and total; consumer E) total; consumer and producer surplus to increase and surplus to decrease after the breakup. The graph below depicts the market for electricity in Ohio which is operated by a monopolist. Use this graph to answer questions 18-20. Price, marginal revenue, marginal cost, average total cost MC ATC Z DEF B U H Demand MR 0 W JKL N Quantity (per period) 18) [1 point] When the firm is maximizing its economic profit, its total cost is represented by: A) OIHJ. B) IPDH. C) OPDJ. D) OSBJ. E) OSUK.

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3mA 4K? 2K? 12K? 1mA 6V 4K? 2K? V?

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24 2 points The release of one quantum of neurotransmitter would result in a: inactivating current MEPP EPP action potential

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Construct Nz, Qx, Qy, Mx, My, Mz diagrams Given: $L_1 = L_2 = 1$ m; $P_1 = 2$ T; $P_2 = 4$ T; $M = 2$ T*m; $q = 2$ T/m

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1 B 1 A C 1 E

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ruth n.