My dashboard moodle.lsbu Question 16 Not yet answered Marked out of 18 P Flag question The temperature T, in a certain office can be modelled by the differential equation, dT +0.018T = K, dt where K = 0.32 when the heater in the office is off and K = 0.46 when the heater is on. The temperature T, is measured in Celsius ( C) and time t is measured in seconds. 1. Find the complementary function for the equation. (3 marks)} ii. Find the particular solution when the heater is off. (3.5 marks) iii. Find the particular solution when the heater is on. (3.5 marks) iv. Initially, when t = 0, the temperature in the office is T = 10C. At this time the heater is turned on. Find the model for the temperature in the office as a function of time t. Also find how long it will take for the temperature in the office to reach 20C. (5 marks} v. When the temperature in the office reaches 20C the heater is turned off. How long will it take for the office to cool from 20C to 18C? You may assume here that the time is reset to o when the heater is turned off. (2.5 marks) Question 17 Not yet answered Marked out of 18 P i. Let z=1+j21),computethecomplexnumbers(zz and z+z. (2.5 marks) ii. Solve the quadratic equation, \[z^2- 22+5=0,] for the unknown complex number \(\). (3 marks) iii. Convert the complex number (\displaystyle \frac{1}{1+j2}\) to rectangular form. That is, write the number in the form a+jbl).(3marks)iv.Findtherectangularformofthecomplexnumber(1+z1+z where \(z=1 +j21). (3 marks) v. Find the modulus and argument of the 1 + z complex number where 1 + 2 z = 1+ 32. (3 marks) vi. Suppose that z is an arbitrary complex number. Show that the product (1 + x)(1+z) is a real number. (3 marks) Question 18 Not yet answered Marked out of 18 P Flag question Consider the vectors 1 1 3 --0--0) -- 2 1 . i. Compute the three vector products axb, b x c and c xa (4.5 marks) ii. Compute the scalar triple product a:(b x c). (2.5 marks) iii. Let M be the 3 x 3 matrix whose columns are the three vectors a, b and c. That is, 1 -1 3 M 0 2 2 1 0 -5 Also, let N be the 3 x 3 matrix with columns b x C, C x a and a x b, in that order. Compute the matrix product, MTN. (4.5 marks) iv. By using the results found above or otherwise solve the equation, 1 0 1 -1 2 0 .) C :) - 0 3 2 -5 for the unknowns X, y and z. (6 marks) Question 19 Not yet answered Marked out of 18 P Flag question A class of students take a multiple choice test consisting of ten questions. For each question students are awarded one or zero marks. The results of the test are summarised in the table given below, the first column gives the test score and the second column is the number of students in the class achieving that score. Marks Number of students 0 1 1 2 2 3 3 5 4 7 5 5 6 6 7 5 N 8 9 2 10 1 1. How many students took the test? That is, how many scores were recorded? (2 marks) ii. Find the mean score of the class. (5 marks) iii. Find the variance and standard deviation of the data. (7.5 marks) iv. What is the median test score
