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thematics Page 156 Question 4 b. n3+(n+1)3+(n+2)3Is divisible by 9 for all n≥1Proof The base case in this situation is n=0 which implies that n3+(n+1)3+(n+2)3=03+13+23=9 This is divisible by 9. Therefore, the basis holds true for n=0The inductive hypothesis becomes n=k≥0, k3+k+13+(k+2)3 is also divisible by 9 → k3+k+13+(k+2)3=9p…(i)By inductionn=k+1, equation (i) becomes (k+1)3+(k+2)2+(k+3)3=9p-k3+k+33…(ii) Simplifying (ii) we have =9p-k3+k+33=9p-k3+k3+9k2+9k+27=9p+9k2+k+3=9(p+k2+k+3)This implies that (k+1)3+(k+2)2+(k+3)3 is also divisible by 9 therefore, n3+(n+1)3+(n+2)3is divisible by 9 for all n≥1 d. 83 – 3n Is divisible by 5 for all n≥1Proof If n=1 then, 8n-3n= 81+31=5 this can be...
The different materials used include: Round seals Clay Small stamps; which progressed to large blocks Papyrus paper Clothes e.g. silk cloth 2. Medium times There was progression to printing on books, magazines and newspapers, but with little efficiency. A bulk of printing was possible, but would take a lot of time. A pattern had to be duplicated; hence, similar images. Modern printing Digital technology has influenced printing such that it is possible to produce massive work efficiently. It is also possible to print varied patterns without necessarily duplicating an image on the same...
them, it is a state in which human beings are in line with what the law has provided for. In basic terms even from the nonprofessional perspective, this is what compliance and should be. It is the state in which people get to go in line with what the law has provided. It does not necessarily mean that the parties have to blindly follow the provisions of the law but rather that they have to follow what has been provided under the law either expressly or even if it is impliedly (Koh, 1998). It must not be word to word as it has been prescribed in the statute, but even in cases where the aspect is close to what the law does expect, then we do assume that such is also compliance as well. I am of the...
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the target to get a total of $ 1000 after three years, less money will be deposited for an interest rate of 4 % as compared to a 3% interest rate. An interest rate shows the amount of earning in terms of profit per dollar per month or per year. Thus, a 4 % interest rate per annum will imply that for each dollar deposited, the earnings will be four dollars per annum. Thus, making a deposit of say $ 100 with an interest rate of 4 % per annum means that my money will earn me exactly four dollars for each financial year. Given that the rate of interest is lowered to three, for $ 100, it implies that for each year that my money will be in the saving account, I will receive exactly three dollars (Koller,...
the top-rated gyms in the Northwest. 3To continue to provide you with the best equipment and programs, your feedback is needed. 5However, more individual attention could be given by us to our customers if our peak usage time could be extended. 11To encourage you to stay later, security cameras for our parking area are being considered by my partner and me. 12Cameras for some inside facilities may also be added. 13This matter has been given considerable thought. 17By completing this questionnaire, your workouts and training sessions can be better planned so that you can enjoy exactly the equipment and trainers you prefer. Fragment sentences 11To encourage you to stay later, security cameras for our...
then the f(x) = -(-2)2-4(-2)+3=7Question 2) 3(x-2)=-4(x+8)+103x-6= -4x-32+107x=-16X=-167Question 3) F(x) = xx-4All values would be real except when the value of x=4 hence the domain is D: allR: x≠4Question 4 Slope (m) = -3/7, y-intercept(c) =-4Y=mx+cHence, y=-37x -4Question 5 Slope(m) = -2, passes through (-1,6) hence the y intercept is Taking a point (x,y) where the line passes then Gradient is ∆y/∆x = y-6x-(-1)=-2y-6x+1=-2Hence y=-2x+4Question 6 (2x-7)(x+4)=02x(x+4)-7(x+4)=02x(x+4)=7(x+4)2x2+8x=7x+28 hence 2x2+x-28=0Using the factor method the values of X=7/2 , -4Question 7 Vertex f(x) =3x2-6x+8f(x) = a(x - h)2 + k, where (h, k) is the vertex hence f(x) =3(x-1)2+5the vertex =(1,5)Question 8 Y...
the security of the database. However, it is essential to understand the basic controls for the creation of the database tables and the fields. The AUTOTRACE command is a critical element in database administration. In the Oracle database, the AUTOTRACE executes the query and queries the plan table automatically. For the user to use the AUTOTRACE, the user must have the PLUSTRACE role which has its location in ORACLE_HOME/sqlplus/admin directory. Creating a Table called Students The script creates the table Students with fields such as StudentId, LastName, FirstName, AdvisorName and the Faculty. CREATE TABLE Students ( StudentID int, LastName varchar(200), FirstName varchar(200), AdvisorName...
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