Help ISOKA CAMPUSDIPLOMA IN ENVIRONMENTAL HEALTH SCIENCESMATHEMATICS: MAT 111Assignment 2INSTRUCTIONS1. Answer all the questions in this assignment.2. Show all the essential working.3. Be neat and orderly in your workingQuestion 1(a) Given that P is a point (6, 8),(i)write P as a position vector,(ii)find JOPJ.(b) A, B and C are points with position vectors 2i - 3j, i + 2j and 4i - j respectively. Find in terms ofi and j the vectors AB, BC and CA.(c) The position vectors of A and B are 4i + 3j and 7i – j respectively. Show that OA isperpendicular to AB and find < AOB.Question 2(a) Differentiate y = x² – 2 from first principles.(b) Differentiate the following with respect to x:1-x(i)y = -x3 - 4x + 28(ii) y =1+x(iii) y = xsin³xdy(c) (i) A Curve has gradient function given by(-1, 5). Find the equation of the curve.= 4x + and passes through the pointx2(ii) The diagram below shows a first aid box in form of a closed rectangular boxmeasuring ycm by xcm and 2xcm.y cmx cm2xcm(a) Given that the volume of the box is 72cm³, express y in terms of x.(b) Show that the total surface area, Acm2 of the first aid box is given by A = 4x +2161 (c) Find the value of x for which A is a minimum.(d) Calculate the dimensions of the first aid box.Question 3(a) A small body moves in a straight line so that its velocity vm/s-1 at time t seconds isgiven by v = t³ – 6t2 + 9t + 2. Find:(a) the times when its acceleration is zero,(b) its distance form a fixed point on the line when t = 2 given that it started from this point.(c) for how long was its acceleration negative?(b) In the diagram below, the curves y = 3x - x² and y = x? – 4x + 5 intersect at A and B.y =x2 - 4x+5y = 3x-r?(i)Find the x coordinates of A and B.(ii)Calculate the area of the shaded region.Question 4The number of people in a small town increases by 3.2% per year. If the population at the start of yeone was 9 567, at the start of which year will the population have grown to 43 391? Given the formuPn = P1 (1+ where p, is the population at the start of year n, P, is the population at the startyear 1, r is the population growth rate, and n is the number of years from year 1 to year n.100,Question 5The following figures show the number of patients admitted with malaria at a certain district hospitafrom day 1 to day 60.41 42 46 49 52 54 41 43 46 49 52 55 42 43 4650 52 55 42 44 47 50 52 57 42 44 47 51 52 5742 44 47 51 52 57 42 45 48 51 53 57 42 45 4851 53 59 42 45 48 53 59 60 42 45 49 52 53 60(a) Using a class interval of 3 and starting at 40, construct a frequency table,(b) Draw the bar chart using the information in the frequency table constructed in (a),(c) What is the modal class interval of the number of patients?(d) Calculate the mean number of patients per day.DUE DATE: 5th April, 2021Lecturer: Mr. Mubanga, S. (0967223034/0979223034), muhar

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Description: Help ISOKA CAMPUSDIPLOMA IN ENVIRONMENTAL HEALTH SCIENCESMATHEMATICS: MAT 111Assignment 2INSTRUCTIONS1. Answer all the questions in this assignment.2. Show all the essential working.3. Be neat and orderly in your workingQuestion 1(a) Given that P is

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Question 1 (a) Given that P is a point (6, 8), (i) write P as a position vector, find JOP. (ii) (b) A, B and C are points with position vectors 2i - 3j, i + 2j and 4i -j respectively. Find in terms of i and j the vectors AB, BC and CA. (c) The position vectors of A and B are 4i + 3j and 7i - j respectively. Show that OA is perpendicular to AB and find < AOB.

Question 1 (a) Given that P is a point (6, 8), (i) write P as a position vector, find JOP. (ii) (b) A, B and C are points with position vectors 2i - 3j, i + 2j and 4i -j respectively. Find in terms of i and j the vectors AB, BC and CA. (c) The position vectors of A and B are 4i + 3j and 7i - j respectively. Show that OA is perpendicular to AB and find < AOB.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter8: Applications Of Trigonometry

Section8.4: The Dot Product

Problem 48E

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(c) Find the value of x for which A is a minimum.
(d) Calculate the dimensions of the first aid box.
Question 3
(a) A small body moves in a straight line so that its velocity vm/s-1 at time t seconds is
given by v = t³ – 6t2 + 9t + 2. Find:
(a) the times when its acceleration is zero,
(b) its distance form a fixed point on the line when t = 2 given that it started from this point.
(c) for how long was its acceleration negative?
(b) In the diagram below, the curves y = 3x - x² and y = x? – 4x + 5 intersect at A and B.
y =x2 - 4x+5
y = 3x-r?
(i)
Find the x coordinates of A and B.
(ii)
Calculate the area of the shaded region.
Question 4
The number of people in a small town increases by 3.2% per year. If the population at the start of ye
one was 9 567, at the start of which year will the population have grown to 43 391? Given the formu
Pn = P1 (1+ where p, is the population at the start of year n, P, is the population at the start
year 1, r is the population growth rate, and n is the number of years from year 1 to year n.
100,
Question 5
The following figures show the number of patients admitted with malaria at a certain district hospita
from day 1 to day 60.
41 42 46 49 52 54 41 43 46 49 52 55 42 43 46
50 52 55 42 44 47 50 52 57 42 44 47 51 52 57
42 44 47 51 52 57 42 45 48 51 53 57 42 45 48
51 53 59 42 45 48 53 59 60 42 45 49 52 53 60
(a) Using a class interval of 3 and starting at 40, construct a frequency table,
(b) Draw the bar chart using the information in the frequency table constructed in (a),
(c) What is the modal class interval of the number of patients?
(d) Calculate the mean number of patients per day.
DUE DATE: 5th April, 2021
Lecturer: Mr. Mubanga, S. (0967223034/0979223034), muhar

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