An analogue sensor has a bandwidth which extends from very low frequencies up to a maximum of 14.5 kHz. Using the Sampling Theorem, what is the minimum sampling rate (number of samples per second) required to convert the sensor signal into a digital representation? If each sample is now quantised into 2048 levels, what will be the resulting transmitted bitrate in kbps?

Give your answer in scientific notation to 1 decimal place.

Hint: you firstly need to determine the number of bits per sample that produces 2048 quantisation levels

Show that there is a language a ⚆ {0, 1} â— with the following properties: 1. for all x â a, |x| ≤ 5. 2. no dfa with fewer than 9 states recognizes a. hint: you don’t have to define a explicitly; just show that it has to exist. count the number of languages satisfying (1) and the number of dfas satisfying (2), and argue that there aren’t enough dfas to recognize all those languages. to count the number of languages satisfying (1), think about writing down all the strings of length at most 5, and then to define such a language, you have to make a binary decision for each string about whether to include it in the language or not. how many ways are there to make these choices? to count the number of dfas satisfying (2), consider that a dfa behaves identically even if you rename all the states, so you can assume without loss of generality that any dfa with k states has the state set {q1, q2, . . , qk}. now think about how to count how many ways there are to choose the other four parts of the dfa.

Jason, samantha, ravi, sheila, and ankit are preparing for an upcoming marathon. each day of the week, they run a certain number of miles and write them into a notebook. at the end of the week, they would like to know the number of miles run each day, the total miles for the week, and average miles run each day. write a program to them analyze their data. your program must contain parallel arrays: an array to store the names of the runners and a two-dimensional array of five rows and seven columns to store the number of miles run by each runner each day. furthermore, your program must contain at least the following functions: a function to read and store the runners’ names and the numbers of miles run each day; a function to find the total miles run by each runner and the average number of miles run each day; and a function to output the results. (you may assume that the input data is stored in a file and each line of data is in the following form: runnername milesday1 milesday2 milesday3 milesday4 milesday5 milesday6 milesday7.)

Draw the resistor’s voltage and current phasors at t=15ms. draw the vectors with their tails at the origin. the orientation of your vectors will be graded. the exact length of your vectors will not be graded.