Solve the recurrence relation using back subtitution or recurrence tree : t(n) = t(n/2) + n 3 . t(1)=1

Signal sets company contracts to deliver one hundred 52-inch plasma high-definition television sets to a new retail customer, tuner tv store, on may 1, with payment to be made on delivery. signal tenders delivery in its own truck. tuner's manager notices that some of the cartons have scrape marks. tuner's owner phones signal's office and asks whether the sets might have been damaged as they were being loaded. signal assures tuner that the sets are in perfect condition. tuner tenders signal a check, which signal refuses, claiming that the first delivery to new customers is always for cash. tuner promises to pay the cash within two days. signal leaves the sets with tuner, which stores them in its warehouse pending its "grand opening sale" on may 15. two days later, tuner's stocker opens some of the cartons and discovers that a number of the sets are damaged beyond ordinary repair. signal claims tuner has accepted the sets and is in breach by not paying on delivery. will signal succeed on these claims? explain.

Robots with telescoping arms are sometimes used to perform tasks (e.g., welding or placing screws) where access may be difficult for other robotic types. during a test run, a robot arm is programmed to extend according to the relationship r = 3 + 0.5cos(4θ) and the arm rotates according to the relationship θ=−π4t2+πt , where r is in feet, θ is in radians, and t is in seconds. use a computer program to plot the path of tip a in x and y coordinates for 0 ≤ t ≤ 4s.

Match the feature to the network architecture. expensive to set up useful for a small organization easy to track files has a central server inexpensive to set up difficult to track files useful for a large organization does not have a central server client- server network peer-to-peer network