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Maths... 29 May 2007 Mathematics Prove the quadratic formula by completing the square. The quadratic equation has the solutions
To prove this, we will complete the square.
Consider the general quadratic equation
with a 0. First divide both sides of the equation by a to get
which leads to
Next complete the square by adding to both sides
Finally we take the square root of both sides:
or
We call this result the Quadratic Formula and normally write...

2 Pages(500 words)Essay

Maths coursework...**Math** work Faculty Figure Graph for the given values Sr. No. Times in hours, t Amount of drug in µg, y k= -(ln(y/a))/t and a=10
0
0.0
10.0
--
k = 0.17491
≈ 0.175
1
1.0
8.3
k1 = 0.1863
2
2.0
7.2
k2 = 0.1643
3
3.0
6.0
k3 = 0.1703
4
4.0
5.0
k4 = 0.1733
5
5.0
4.4
k5 = 0.1642
6
6.0
3.8
k6 = 0.1613
7
7.0
2.8
k7 = 0.1819
8
8.0
2.5
k8 = 0.1733
9
9.0
1.9
k9 = 0.1845
10
10.0
1.5
k10= 0.1897
Table1: Amount of drug in the Bloodstream
Part A
1) Use this information to help you find a suitable function to model this data.
Since the rate of decrease of the drug is directly (approximately) proportional to the amount remaining, so let assume that the function is of type y=ae^ (-kt).
Now when value of t is equal to 0 in that case y is...

4 Pages(1000 words)Essay

Maths...**MATH** PORTFOLIO: CREATING A LOGISTIC MODEL A geometric population growth model takes the from where r is the growth factor and is the population at year n. For example, if the population were to increase annually by 20%, the growth factor is r = 1.2, and this would lead to an exponential growth. If r = 1 the population is stable. A logistic model takes a similar form to the geometric, but the growth factor depends on the size of the population and is variable. The growth factor is often estimated as a linear function by taking estimates of the projected initial growth rate and the eventual population limit.
METHOD:
1. A hydroelectric project is expected to create a large lake into which some fish are to be placed. A...

10 Pages(2500 words)Essay

Business Maths...Q1) b) EMV of investing in stocks: = 0.6*2500 + 0.2*500 + 0.2*(1000) =1500+100-200 =$1400 EMV of investing in fixed interest= $1200 Since investing in stocks has a higher EMV of $1400, a risk-neutral investor will choose the option of investing in stocks.
c) In this case the $1200 that the investor can earn is fixed and will get it no matter what the state of the economy is whereas if the investor invests in stocks, his investment return will depend on lot of other factors and hence will be uncertain. An investor has to be compensated with a certainty equivalent to take on the additional risk to invest in stocks. In this case $1200 is the certainty equivalent.
d) An investor is an risk-averse investor if his certainty equivalent...

2 Pages(500 words)Assignment

Maths project...**MATH** PROJECT By PART 2: Assessment criteria for this unit 1 Objectives……………………………………………………………3 2 Manageable task………………...........................................................3,4
2.2 Appropriate methods for undertaking the task……………………….4
3.1 Collect relevant information………………………………………….4, 5
3.2 Performance of variety of calculations………………………………. 6, 7
3.3 Mathematical language notations……………………………………..6, 7
3.4 Use of diagrams, tables and graphs…………………………………...7, 8
3.5 Monitor & making adjustments……………. …………………………8
4.1 interpretation of results………………………………………………. 9
5.1 Conclusions……………………………………………………………10
5.2 Comments of improvements …………………………………………..11
PART 3: My comments on the assignment
I devised questionnaire for...

5 Pages(1250 words)Coursework

Maths Exam...**Math** 012 Final Examination Spring Answer Sheet **Math** 012 Intermediate Algebra ______________________________ Final Examination: Spring, 2014
Instructor __________________________
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam and you may use a calculator. Record your answers and show your work on this document. You must show your work to receive credit: answers given with no work shown will not receive credit. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. If you choose to scan your work, note that most scanners have a setting that will allow you to...

3 Pages(750 words)Speech or Presentation

MATHS... CHAPTER 3 Solve inequality. Write the answer in interval notation (65) 5(2b -3) – 7b > 5b + 9 Then the variable is divided by a negative sign the symbol of inequality changes (Haighton, Haworth and Wake 59)
The solution for b is (-
Solve inequality. Graph the solution set and write the answer in interval notation.
(31) 6(7y + 4) – 10 > 2(10y + 13)
The solution for
CHAPTER 4 10. Complete the table of values for each equation:
4x – 6y= 8
x
y
2
0
0
-4/7
3
2/3
-4
-4
19. Graph each equation by finding the intercepts and at least one other point.
y = -1/6x + 4
x
0
24
6
12
-6
y
4
0
3
2
5
31. Use the slope formula to find the slope of the line containing each pair of point.
(-2, 5) and (3, -8)
=
The slope is
48. Identify... CHAPTER 3...

2 Pages(500 words)Speech or Presentation

Maths Report...Relationship between Engine Size and MPG (**Math** Report) By Relationship between EngineSize and MPG
Abstract
Introduction
The aim of this report was to investigate the relationship between the engine size and MPG (miles per gallon) of the cars using the car sales data containing 99 car data for make, model, price (new), price (used), age, engine size and MPG.
Method
Random sampling method was used for selecting a sample of 30 cars data. A car with an engine size less than 1.8L considered as the small engine size car and a car with an engine size greater or equal to 1.8L considered as the bigger engine size cars.
Results
The results indicated that there is a strong negative linear relationship between cars engine size and...

4 Pages(1000 words)Math Problem

Maths...**Maths** Assignment Number 3 Siobhan O’Connor Question Lo3 LO3.2 a) Histogram to show each distribution scaled such that the area of each rectangle represents frequency density and find the mode.
Data
Revenue
January
July
<5
27
22
5>10
38
39
10>15
40
69
15>20
22
41
20>30
13
20
30>40
4
5
For January
Mode: 40 for 10 and less than 15
For July
Mode: 69 for 10 and less than 15
b) Produce a cumulative frequency curve for each of the distribution and find the median and interquartile range
Revenue
January
Cumulative Frequency
July
Cumulative Frequency
<5
27
27
22
22
5>10
38
65
39
61
10>15
40
105
69
130
15>20
22
127
41
171
20>30
13
140
20
191
30>40
4
144
5
196
Median: (144/2)=72= Approximately 11.5
Interquartile Range: (3/4*144)-(1/4*144)=108 th... Assignment Number 3 Siobhan ...

1 Pages(250 words)Assignment

Maths... Statistics Samples The interest is to determine whether the new program established to aid in improving the performance of students has an impact. As such, the sample score is 40 pairs of students. The first sample is the pretest where 40 students who are not involved in the program participate. The second sample is the posttest where 40 students are involved in the program participate. The relationship of these samples is that the pretest has corresponding posttest of the students.
Problem
The problem involves determination of the performance of the students in terms of scores. Thus, when each student (ith) score prior and after participation in the program is xi and yi respectively, it is clear that the pair (xi, yi) gives... Statistics...

1 Pages(250 words)Speech or Presentation