You must determine the root of the following easily differentiable function: 0.5x5-5x pick the best numerical technique, justify your choice, and then use that technique to determine the root. note that t is known that for positive initial guesses, all techniques except fixed-point iteration will eventually converge. perform iter- ations until the approximate relative error falls below 2%. if you use a bracketing method, use initial guesses of xi =0 and x 2. if you use the newton-raphson or the modified secant method, use an initial guess of xi =0.7. if you use the secant method, use initial guesses of x-0 and xi = 2.

In a vernier instrument the main scale is in 1/2 mm divisions .vernier is made by redividing 19 such divisions into 20 equal parts. calculate the least count of the instrument.

Which is an example of gaining a static charge by conduction? a) rubbing a balloon against your hair. b) shuffling your shoes across a carpet. c) bringing a charged rod near an electroscope. d) touching your car on a cold day and getting a shock.

As you are trying to move a heavy box of mass m, you realize that it is too heavy for you to lift by yourself. there is no one around to , so you attach an ideal pulley to the box and a massless rope to the ceiling, which you wrap around the pulley. you pull up on the rope to lift the box. use g for the magnitude of the acceleration due to gravity and neglect friction forces. once you have pulled hard enough to start the box moving upward, what is the magnitude f of the upward force you must apply to the rope to start raising the box with constant velocity? express the magnitude of the force in terms of m, the mass of the box.