# operations

1. ### Operations with Positive Fractions

Sorry if this problem is very basic I just know the right procedure. This questions are from a placement test I will be taking, so expect to see similar ones. If you have four quarters, three dimes, two nickels, and two pennies, what fraction of the whole coin collection is in dimes? My...
2. ### Problem with Elementary row operations and rank theorems.

Ok, so I am taking my first course in linear algebra, and even though I am not a math major (physics major actually), I can't help but wish my teacher and text were more rigorous. So let me start by telling you all the problem I am having: (First question) My book states the following rank...
3. ### Rational function operations

\frac{x-4}{6x-24}÷\frac{1}{4-x} = ? Result: \frac{(x-4)(4-x)}{6x-24} I do not know if I should simplify this...
4. ### Thomas algorithm number operations

I have to find the number of operations needed by Thomas algorithm for an nxn tridiagonal matrix. The Thomas algorithm is divided into two parts, the forward sweep and the back substitution. The forward sweep is: c(i)' = c(1)/b(1) for i = 1 and c(i) / ((b(i) - c(i-1)' * a(i)) for i=2 to...
5. ### Set Operations

Hi All, hope I have the correct forum first of all. I have the following set expression: (Y \cap X) \cap (X \cap Y) I want to simplify the expression further. However I need to show full workings out. Could I simply just use the idempotence operation so it would become the following...
6. ### a "basis" in {0,1}^n with operations induced from the boolean algebra {0,1}

Let u_1,...,u_n\in\{0,1\}^n. Can we impose a condition on these vectors so that every vector s\in\{0,1\}^n has a unique decomposition s=\alpha_1\cdot u_1\vee ... \vee\alpha_n\cdot u_n, where \alpha_i\in\{0,1\}, and by definition \alpha\cdot...
7. ### Simple Binary Operations Question

Problem: Let S be a set having exactly one element. How many different binary operations can be defined on S? Answer the question is S has exactly 2 elements, exactly 3 elements, exactly n elements. ---------- I think I'm getting a little confused with the term "element", because it seems...

\frac{{\sqrt 3 }}{{\sqrt 2 }} + \frac{3{{\sqrt 2 }}[/}[/{{\sqrt 2 }}
9. ### Checking validity of defined operations

I truly do not know where to begin to start checking these answers, as I do not understand how the symbol applies to a and b. However, the answer is that all 3 of these definitions for a and b are true.
10. ### Aren't derivative and integral inverse operations?

Hey what's going on here. I thought if you take the derivative of a function, then integrate that derivative, you get the original function back. But when I perform this routine on the function below I get a different function from the original. I'd appreciate it if someone could point out...
11. ### Finding the derivative of a large function. Help with the order of operations.

Differentiate (9x -3x^2)^3 cos(4x^3 – 3x) e^(7-12x) ln(-x^2 + 3) With respect to x I don't want the solution, what i'm after is some help in how to tackle this differentiation question. This is what i plan to do: Find dy/dx for (9x-3x^2)^3 [make this part A] find dy/dx for cos(4x^3...
12. ### Commutative and Associative relations of binary operations

Hi I've got some problems and just need a bit of reassurance that I'm doing them right! a) For each of the following binary operations on z^+ say whether or not it is associative, commutative i) a*b=a+b^2 This is neither commutative nor associative ii)a*b=a+1 Is again neither commutative...
13. ### another operations problem

perform the indicated operations and simplify. write answers in descending order. (xy-ab-8) -(xy-3ab-6)
14. ### operations

perform the indicated operations and simplify. Write answers in descending form. (x-5)^2
15. ### Order of Operations

I have a question about rearranging equations to solve for variables. What is the order of operations? Is it reversed? PEM DAS. When do I use SAD MEP. Can you give me a simple example of this or perhaps somewhere to practice this?
16. ### Continuity of vector space operations

Dear Colleagues, I need the solution of the following problem: Show that in a normed space X, vector addition and multiplication by scalars are continuous operations with respect to the norm; that is, the mappings defined by (x,y)\longmapsto x+y and (\alpha,x)\longmapsto \alpha x are...
17. ### What if Order of Operations was reverse?

What if you reversed the order of operations? Instead of PEMDAS it was SADMEP. At first glance you would think the order of operations is arbitrary. A convention we agree upon for no reason other than that having a convention ensures (or at least tries to ensure) that expressions will evaluate...
18. ### How to get 14 from 5 3's and only using the four basic operations and brackets

Hey, I was just trolling the web and saw this question of how to make 14 from 5 3's and it got me puzzled. You can only use +,-,x,/ and brackets but I just can't seem to get it. According to where this question is asked here I have 5 lots of 3's, using any of the plus, minus, times or divide...
19. ### vector operations word problem.

suppose you manage a mutual fund that invests in 1000 companies. Let S be the vector in Rn whose ith component is the number of shares of company i that you've today. Let P be the vector in R^1000 whose ith component is today's price per share of company i's stock. Express the total value of...
20. ### [Discrete math]Help with a relation involving modular arithmatic and set operations

1. The problem statement, all variables and given/known data Let R1 and R2 be the "congruent modulo 3" and "congruent modulo 4" relations on the set of integers. 2. Relevant equations Find: a) R1 U R2(or R1 union R2) b)R1 intersects R2 There is also problem c, d but I won't write these here...