Question

Problem (1): Define the variable z as z -4.5; then evaluate (a) 0.4z'+3.12 -162.3z -80.7 (b) (z-23)/V2+17.5 Problem (2): The distance d from a point P(xp, yp,Zp) to the line that passes through two points 4(XA ,y,,2, ) and B(хв, Ув, zs) can be calculated by d-2S / r where r is the distance between the points A and B, given by r |(хв-%). (Yo-yA )4+ (Zg-2, )2 and S is the area of the triangle defined by the three points calculated by Ss+i+sj where Determine the distance of point P (2, 6, -1) from the line that passes through point A (-2,-1.5,-3) and point B (-2.5,6, 4) Problem (3): A Newton's law of cooling gives the temperature T(t) of an object at time t in terms of To, its temperature at t = 0, and T's, the temperature of the surrounding TO-T-exp() A police officer arrives at a crime scene in a hotel room at 9:18 PM, where he finds a dead body. He immediately measures the body's temperature and find it to be 79.5°F. Exactly one hour later he measures the temperature again, and find it to be 78.0°F. Determine the time of death, assuming that victim body temperature was normal (98.6°F) prior to death, and that the room temperature was constant at 69.0°F Problem (4): Consider 1-D heat conduction in the domain -oo <x <oo. If the region -a<x<a is initially at constant temperature To and the region r> a is initially at zero temperature then the temperature distribution T(x,t) is given by: a-x atx If at t-30 second the temperature at the center x 0 is one third of the initial temperature then find the temperature at x-0.5 for t 0:2:100 seconds. Take a -1 and To-100. Note that if erfly) = z then y = erfinv(z). Both erfand erfinv are MATLAB's built-in functions Problem (5): Create the following two row vectors

Answer 1