"for a first order instrument with a sensitivity of .4 mv/k and a time" constant of 25 ms, find the instrument’s response as a function of time for a sudden temperature increase from 273 k to 473 k. before the temperature increase, the instrument output was a steady 109.2 mv. plot the response y(t) as a function of time. what are the units for y(t)? find the 90% rise time for y(t90) and the error fraction, γ(t90).

A33.1 g copper object is launched from a 1.5 m 30° steel incline positioned on the floor by being pulled up a string attached to a 50.0 g mass suspended vertically over a pulley. the object is projected towards a glass table where it lands when it is at the point along its trajectory with the lowest speed. it comes to a halt when it clears the opposite edge of the table. it then falls and lands on 9 physics texts each 5 cm thick that are stacked on the floor on the opposite side of the table. assume that the table does not have a ledge and the rectangular object experiences 0.05 n of air resistance as it falls towards the books. how far and how long did the object travel and how fast does it hit the books. assume that at the moment the copper object leaves the incline, the massless string and ideal pulley break off

Astone is dropped from a cliff and falls 9.44 meters. what is the speed of the stone when it reaches the ground? a. 13.6 m/sec b. 1.39 m/sec c. 185 m/sec d. 9.80 m/sec

Suppose that f : rn → rm and that a ∈ k, where k is a connected subset of rn . suppose further that for each x ∈ k there exists a δx > 0 such that f(x) = f(y) for all y ∈ bδx (x). prove that f is constant on k; that is, f(x) = f(a) for all x ∈ k