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Mathematics Project
 * Grade 12 **

Student Name: Omar Abdulla Khamis ID#: 1021090006

 Student Name: Omar Ibrahim Saleh ID#: 1021090167 Section:12.14 Teacher: Ahnaf Chehade Abbas

Ahmed,who is a grade 09 student, is planning to save money while he is studying at ATHS. Ahmed has 5,000 Dhs to start with, and he is planning to save 500 Dhs per month. a. What is the type of the sequence at which the money will grow?  Arithmetic sequence b. How much money will he save after 4 years? an = a1 +(n-1)d a48 = 5000 +(48-1)500 a48 = 28500 AED c. His brother has borrowed from him some money, his brother agreed to pay 50 Dhs in the first month and 25 Dhs more in each of the following months; how much did Ahmed’s brother borrow knowing that it took him 1 year to pay his debt? an = a1 +(n-1)d <span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">a12 = 50 + (12-1)25 <span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">a12 = 325 AED <span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">So his brother borrowed from him 325 AED.
 * __<span style="font-family: 'Times New Roman',serif; font-size: 14pt;">The Goal __**
 * <span style="font-family: 'Times New Roman',serif; font-size: 14pt;">Students will work with financial concepts to find the amount of investment that an individual can do over an amount of time. **
 * __<span style="font-family: 'Times New Roman',serif; font-size: 14pt;">Part I: __**

<span style="font-family: 'Times New Roman',serif; font-size: 14pt;">d. Let the amount saved at the end of the first year be and the amount that was saved at the second year, and the amount that was saved at the end of the fourth year, find a relation between <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">a12 = a -- a1+11d=a <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">a24 = b -- a1+23d=b <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">a48= c -- a1+47d=c

<span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">d=(a-b/-12) <span style="color: #00b050; font-family: 'Times New Roman',serif; font-size: 14pt;">a1+11d=a <span style="color: #00b050; font-family: 'Times New Roman',serif; font-size: 14pt;">a1+11(a-b/-12)=a <span style="color: #00b050; font-family: 'Times New Roman',serif; font-size: 14pt;">a1- (11/12) (a-b)=a <span style="color: #00b050; font-family: 'Times New Roman',serif; font-size: 14pt;">a1= (11/12) a –(11/12) b +a <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">a48= c =a1+47d <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;"> = (11/12) a –(11/12) b +a +47(a-b/-12) <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;"> = (23/13) a –(11/12) b -(47/12) a+(47/12) b <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">C=-2a+3b <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">C=3b-2a

<span style="font-family: 'Times New Roman',serif; font-size: 14pt;">Ahmed wanted to invest his savings; he bought shares in a company, the company will offer an interest rate of 8% annually. <span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">A=p(1+r/n)n.t
 * __<span style="font-family: 'Times New Roman',serif; font-size: 14pt;">Part II __**
 * 1) <span style="font-family: 'Times New Roman',serif; font-size: 14pt;">a. How much money will be in the account in 4 years?

<span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">A=28500(1+0.08/12)12(3)

<span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">A=36201.75 AED <span style="display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">b. After 4 years the shares were decreased by 20% each year, after how many years Ahmed will lose all of the profits?

<span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">In the first year = 36201.75(0.8) = 28961.4

<span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">In the second year = 28961.4(0.6) = 17376.8

<span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">In the third year = 17376.84 (0.4) = 6950.73

<span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">In the fourh year = 6950.736(0.2) = 1390.1

<span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">In Fifth year = 1390.1472(0.0) = 0

__<span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">So he will lose all of the profits in 5 years. __

<span style="font-family: 'Times New Roman',serif; font-size: 14pt;">1. Ahmed has started his own company. He plans to hire 8 new employees. He wants to hire males and females, knowing that there are an equal number of males and females applying for the job, use the binomial theorem to find the all combinations of males and females that could be hired.
 * __<span style="font-family: 'Times New Roman',serif; font-size: 14pt;">Part III __**

<span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">m8+8m7f+28m6f2+56m5f3+70m4f4+56m3f5+28m2f6+8mf7+f8

<span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">By adding the coefficients of the polynomial, we determine that there are 256 combinations of males and females that could be hired <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">70m4f4 represents the number of combinations with 4 males and 4 females

<span style="font-family: 'Times New Roman',serif; font-size: 14pt;">2. Ahmed established a phone chain in which every staff member calls two other staff member to notify them about company events, the first round of calls begins with Ahmed calling two members. If there are 94 total staff members, how many rounds of calls are there to pass the information to all employees? <span style="color: red; display: block; font-family: 'Times New Roman',serif; font-size: 14pt; text-align: center;">an = a1 +(n-1)d <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">94= 1(2)n-1 <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;"> 94=2n-1 we have to plug in till we reach 94. <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">When n=7 è <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;"> the answer will be 64 <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;"> When n=8 è <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;"> the answer will be 128

<span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">So, there will be 8 rounds.

<span style="font-family: 'Times New Roman',serif; font-size: 14pt;">
 * 1) <span style="font-family: 'Times New Roman',serif; font-size: 14pt;">1. Those employees will be seated around tables attached end-to-end for an event, How many tables are required to seat all the employees?

<span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">a1=4 an = a1 +(n-1)d <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">a2=6 94 = 4 +(n-1)2 <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">a3=8 94 = 4 +2n-2 <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;"> 92 = 2n <span style="color: red; font-family: 'Times New Roman',serif; font-size: 14pt;">d=2 n= 46 Tables



Java Program public class Math_Proj {

/** public static void main(String[] args) { // TODO Auto-generated method stub
 * @param args

float x1 = 0.9f; float x2 = 0.99f; double x3 = 0.999; double x4 = 0.9999; int x5 = 1; double x6 = 1.0001; double x7 = 1.001; float x8 = 1.01f; float x9 = 1.1f;

System.out.println((Math.pow(x1,2)+(-x1-2))/(x1-1)); System.out.println((Math.pow(x2,2)-x2-2)/(x2-1)); System.out.println((Math.pow(x3,2)-x3-2)/(x3-1)); System.out.println((Math.pow(x4,2)-x4-2)/(x4-1));

System.out.println((Math.pow(x5,2)-x5-2)/(x5-1));

System.out.println((Math.pow(x6,2)+(-x6-2))/(x6-1)); System.out.println((Math.pow(x7,2)-x7-2)/(x7-1)); System.out.println((Math.pow(x8,2)-x8-2)/(x8-1)); System.out.println((Math.pow(x9,2)-x9-2)/(x9-1)); } }

20.9 200.99 2000.999 20000.9999 -Infinity -19998.9999 -1998.999 -198.99 -18.9