Suppose we want to prove the statement S(n): "If n ⥠2, the sum of the integers 2 through n is (n+2)(n-1)/2" by induction on n. To prove the inductive step, we can make use of the fact that 2+3+4+...+(n+1) = (2+3+4+...+n) + (n+1) Find, in the list below an equality that we may prove to conclude the inductive part. a. If n ⥠3 then (n+2)(n-1)/2 + n + 1 = (n+3)(n)/2
b. If n ⥠1 then (n+2)(n-1)/2 + n + 1 = (n+3)(n)/2
c. If n ⥠2 then (n+2)(n-1)/2 + n + 1 = (n+3)(n)/2
d. If n ⥠1 then (n+2)(n-1)/2 + n + 1 = n(n+3)/2

Let r be a robotic arm with a fixed base and seven links. the last joint of r is a prismatic joint, the other ones are revolute joints. give a set of parameters that determines a placement of r. what is the dimension of the configuration space resulting from your choice of parameters?

Given a link with a maximum transmission rate of 32.8 mbps. only two computers, x and y, wish to transmit starting at time t = 0 seconds. computer x sends filex (4 mib) and computer y sends filey (244 kib), both starting at time t = 0. statistical multiplexing is used, with details as follows packet payload size = 1000 bytes packet header size = 24 bytes (overhead) ignore processing and queueing delays assume partial packets (packets consisting of less than 1000 bytes of data) are padded so that they are the same size as full packets. assume continuous alternating-packet transmission. computer x gets the transmission medium first. at what time (t = ? ) would filey finish transmitting? give answer in milliseconds, without units, and round to one decimal places (e. g. for an answer of 0.013777 seconds you would enter "13.8" without the quotes)

How are stop motion special effects in animated films created