4 marks 2 Which of the regions on this Fe2 Fe3 C phase diagram are solid solutions a 2678910 b 24689 c 47810 d 12679 3SP3 Winter 2024 Solutions 1 9

In-Class Activity 1 PHYS 259 Winter 2024In-Class Activity 1 PHYS 259 Winter 20243 Calculate the values of vecE d vecA for each of the remaining five faces of the cube ( 25 marks) lclll Group Student lticolumn1c Last name lticolumn1c First name lticolumn1c UCID ltirow47 1 Dang Adran 39798985 cline 2 - 5 2 Panaweern Thanindu 30147025 cline 2 - 5 3 Notyen Tason 30209015 cline 2 - 5 4 In the region of space shown in the diagram in Question 1 there is an electric field given by vecE= ft(50-x2 ) +(30) +(40 z) k where the units of the electric field are N/C provided x y and z are measured in units of metres Also shown in the diagram is a Gaussian cube of side length d=20 m Calculate how much charge is contained inside the Gaussian cubeThe parts below walk you through related questions and the steps with which to solve this problem Please show all work in the boxes provided and then choose the correct answer at the bottom from the choices provided1 On the diagram below draw the normal vectors for all six faces of the cube (have the tail of the vector placed at the dots 1 mark) What is the surface area vector for the top (6) and the bottom (5) faces of the cube in terms of k (1 mark)Face 1Face 2Face 3Face 4Face 54 What is the net electric flux E passing through the Gaussian cube How did you determine this (15 marks)2 Calculate the value of vecE d vecA on face 6 (1 mark) Show the steps how this integral simplifies (1 mark) l sindifas vecE d vecA + E2 A=(40 20)(40)=320 N m2 C 6 Choose the answer for the total amount of charge contained inside the Gaussian cube from the options below (1 mark)a) 08 nCb) 01 nCc) 11 nCd) 09 nC

Full marks are not necessarily awarded for a correct answer with no working Answers must be supported by working and/or explanations Solutions found from a graphic display calculator should be supported by suitable working For example if graphs are used to find a solution you should sketch these as part of your answer Where an answer is incorreet some marks may be given for a correct method provided this is shown by written working You are therefore advised to show all working Answer all questions Do not write solutions on this page Answer all questions in an answer booklet Please start each question on a new page 1 Maximum mark 13 The number of people (in thousands) subscribed to a website x weeks after it is launched is modelled by f(x)=x3-6 x2+9 x+4 x qslant 0 a Find the initial number of subscribers when the website launches b Find f((x) c Interpret f f( x) in context d Find all solutions of f (x)=0 e Find the values of x for which f(x) is increasing f Sketch y= f(x) g How long does it take the website to reach 10000 subseribers 2 Maximum mark 12 A fair four-sided dice is rolled twice S is the sum of the scores a Copy and complete the probability distribution of S cccccccc s 2 3 4 5 6 7 8 P(S-s) 116 216 316 416 b Find the expected value of S c Given that the total is more than 4 find the probability that it is more than 6 Eric plays a game where he rolls a fair four-sided dice twice If the score is four or less he loses and pays 1 If he scores 5 or more he receives k d Find the value of k if the game is fair I 2 I 2 2 3 2 2 2 3 5 3 Maximum mark 14 Kwami keeps a record of his best 5000 m time ( y minutes) for each week (x) in the 13 weeks after he starts training for a competition season The results are shown here

Question 5 The function f is given by f(x)= ft(x+ 74 ) The solutions to which of the following equations on the enterval 0 q x q 2 are the solutions to f(x)= 12 on the interval 0 q x q 2 (A) 3 x- x=1 (B) 3 x+ x=1 (C) 3 z- z=1 (D) 3 x+ x=1

Interpret the following phase diagram for a hypothetical substance using the letters in black to identify the various features of the diagram (a) A represents the --- Select--- phase B represents the --- Select--- phase and C represents the --- Select--- phase (b) The phases are separated by lines representing where the phases are in equilibrium with each other The line between regions A and B represents the ---Select--transition The line between regions B and C represents the --- Select-- transition The line between regions A and C represents the --- Select--- transition (c) The ---Select--- transition The line between regions A and C represents the transition (d) The critical point occurs at the critical -- Select--- and marks the end of the line that separates the gas and liquid phases If the pressure and temperature exceed the values at this point the substance becomes -- Select-- where the gas and liquid phases are indistinguishable