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Your colleague is working on two algorithms, \(X\) and \(Y\), that determine whether two people are a certain distance apart. They use a number of different inputs, \(n\). They are seeking your advice.

If they tell you that algorithm \(X\) has a worst-case runtime complexity of \(O(n^2)\) and algorithm \(Y\) has a worst-case runtime complexity of \(O(n^3)\), which algorithm would you recommend and why?

Your colleague then adds that the average-case time complexity for \(X\) is \(Θ(n^2)\) and for \(Y\) is \(Θ(n)\). Does this change your advice at all, and why? Your answers should be no longer than a sentence or two.

What would you expect to be the electron-group arrangement around atom A in each of the following cases? For each arrangement, give the ideal bond angle and the direction of any expected deviation:

The 15-kg block A and 25-kg cylinder B are connected by the light cord that passes over a 5-kg pulley with I_{G} = 0.025 kg.m^{2}. If the system is released from rest, (with coefficient of friction between the block and ground of 0.3) calculate the angular acceleration of the pulley.

This problem illustrates that the factor of safety for a machine element depends on the particular point selected for analysis. Here you are to compute factors of safety, based upon the distortion- energy theory, for stress elements at A and B of the member shown in the figure. This bar is made of AISI 1006 cold-drawn steel and is loaded by the forces F = 0.55 kN, P = 4.0 kN, and T = 25 N ∙ m.

According to the U.S. National Electrical Code, the copper wire used for interior wiring of houses, hotels, office buildings, and industrial plants is permitted to carry no more than a specified maximum amount of current. The table below shows the maximum current Imax for several common sizes of wire with varnished cambric insulation. The“wire gauge” is a standard used to describe the diameter of wires. Note that the larger the diameter of the wire, the smaller the wire gauge.

Wire gauge

Diameter (cm)

Imax (A)

14

0.163

18

12

0.205

25

10

0.259

30

8

0.326

40

6

0.412

60

5

0.462

65

4

0.519

85

What considerations determine the maximum current-carrying capacity of household wiring?

A total of 4200 W of power is to be supplied through the wires of a house to the household electrical appliances. If the potential difference across the group of appliances is 120 V, determine the gauge of the thinnest permissible wire that can be used.

Suppose the wire used in this house is of the gauge found in part (b) and has a total length of 42.0 m. At what rate is energy dissipated in the wires?

The house is built in a community where the consumer cost of electric energy is $0.11 per kilowatt-hour. If the house were built with the wire of the next larger diameter than that found in part (b), what would be the savings in electricity costs in one year? Assume that the appliances are kept on for an average of 12 hours a day.

Assume you have two analog-to-digital converters with the following characteristics: ADC1: 8 bit, nominal input range 0→5 volts, ADC2: 12 bit, nominal input range 0→10 volts

What is the resolution of each of these ADCs (smallest step in voltage that you can measure, i.e. step size)

If ADC1 created a binary code (1110 0010)_{2}, what is the range of input voltages that could have produced this code?

If ADC2 created a binary code (0000 1110 0010)_{2} what is the range of input voltages could have produced this code?

Find the codes produced by the two ADCs when the input voltages are: (i) 3.5V (ii) 2.35 V (iii) 6.35 V