1. B

    Complex domain coloring - a form of art

    Hello all, I hope you guys don't mind a little bit of self-promotion, but I recently introduced an advanced complex function plotting feature to Grapher Pro for Android. In short, I would like to share with you the fact that a myriad of undiscovered opportunities exist here, not just for...
  2. N

    Optimization Problem with Exponential Form (double terms)

    Hello, Could anybody help me with this optimization problem? I want to minimize sum(s=1,S) a_s * exp(b_s*x_s) + c_s * exp(d_s*x_s) subject to the constraint: sum(s=1,S) x_s = A I am supposed to find x_s which makes the statement minimized. a_s, b_s, c_s, d_s, and A values are constants in...
  3. A

    Functions in function - synthesis of a general form

    Hi All, I've one problem related to defining general form of fuction f(x) which is constructed by using functions inside of it. Let we say, that f(x) is defined as follows: f(x)= \frac{c \cdot a_{0}+ f_{1}(x) }{ a_{0}+ c \cdot f_{1}(x)} and the two next functions are: f_{1}(x)= \frac{c...
  4. A

    Functions in function - synthesis of a general form

    Hi All, I've one question related to a function, which can be defined by using other functions. Let we say, that such situation can be defined as follows: f_{0}(q)= \frac{a_{0}+c \cdot f_{1}(q)}{c \cdot a_{0}+ f_{1}(q)} f_{1}(q)= \frac{a_{1}+c \cdot f_{2}(q)}{c \cdot a_{1}+ f_{2}(q)}...
  5. G

    How to represent this statement in graph form?

    How to represent this statement in a diagram? Statement: My friend represented this sentence "Two forces have magnitude of 3N and 5N, and have an angle of 60 between them" into this diagram: But why didn't he represent like this?:
  6. H

    Show these point form a square

    Show ACDE is a square C=10,2 A=4,2 E=8,-8 D=14,-4
  7. J

    How to rewrite these formulas in the opposite form?

    I want to know how I can write from some predicate formula its negative form. For example ∀x∃y(x R y) then not(∀x∃y(x R y)) is equal to ∃x,not ∃y(x R y)))(not exist y) How do these formula work with conjunction implication and disjunction? Bellow are examples of some formulas but...
  8. D

    Put these in the form y=mx+c?

    Put these in the form y=mx+c as not sure how to do this? 6x-5=2y 4x+2y=7 3y=4x+6 000 3x-7=6y 3x+3y=6 7y+6x=60 000 Many thanks xx
  9. R

    Number of steps to form 1 fluid oz

    Jane wants to have two separate 1 fluid ounce measures of water at the same time. However the only measures she has are for six, ten and fifteen fl oz. Show how this could be done in the smallest number of steps without marking the measures or using any container other than the original large...
  10. C

    Leave in the form x^p - x^q

    Please Help, Been at this for hours: Leave in the form x^p - x^q: 1-x^2/∜x^3 Thanks.
  11. C

    Row reduced echelon form and its meaning

    Hey. I have the following question to solve: * Given a matrix A that is size m x n and m>n. Let R be the RREF that we get by Gaussian elimination of A. Prove that the system equation Ax=0 has only one solution iff in every column of R there is a leading element. I have some answer...
  12. B

    Factor Trinomials Of The Form Ax2 + Bx + C Using Trial And Error.

    In the OpenStax Elementary Algebra book in the section on factoring using Trial and Error, there is the following paragraph. "When we factor an expression, we always look for a greatest common factor first. If the expression does not have a greatest common factor, there cannot be one in its...
  13. T

    WolframAlpha syntax to convert cartesian equation to parametric form

    Does anyone know how to do that? I tried it with Wolfram|Alpha: Computational Intelligence but it just won't show x=5cos t & y=4sin t
  14. P

    Form of an operator

    Please help with this problem. Let x be a vector in a three-dimensional space R^3 and c be a constant vector and let A be an operator acting on R^3 with values ​​in R^3, then I'm looking for the form of the operator A such that A(x + c) = c + A^2(x) Thank you for your reply.
  15. M

    Primes of the form Sigma(Sigma(x))

    Hi, I checked for the primes of the form sigma(sigma(x)). (Sigma(x) : sum of divisors of x) and it is prime for the x values x>1; x=3, 2667, 3937,57337,172011,253921 and all the primes of this form I found are Mersenne primes. sigma(sigma(3))=7 ......... ............(2667)=8191 :2^13-1...
  16. N

    I don't know how to transcribe these propositions into the symbolic form

    b) There exists x such that x² is even and divisible by 3 d) There is no integer x such that x² is prime or x² is negative.
  17. E

    Write in the form ca^pb^q

    Hey, if anyone could help me with a few of these calculus problems, I'd greatly appreciate it. I'm supposed to write each expression in the form ca^pb^q where c, p, and q are numbers. The first problem is: a(2/b)/(3/a)
  18. M

    Primes of the form (4n-1)

    I would like help to prove that primes of the form (4n-1) or (6n-1) are not finite in number. I'll try to assume that primes of the form (4n-1) are finite so there is k in N where (4k-1) is the largest prime of this form. So for any m in N larger than k, (4m-1) is not prime. So there is a prime...
  19. G

    Basis for a degenerate quadratic form

    Hello, I have this quadratic form q(x,y,z)= x²-z²-4xy-4zy I have reduced this form using the Gauss algorithm into q(x',y',z') = x'² -y'² with x' = x-2y and y' = 2y+z , z=? The problem statement wants me to find the reduced form (which I already did) and to find THE basis on which q...
  20. V

    Simplest form of curve equation

    I'm kind of confused with this excercise: In 2d space and in respect to an orthonormal system Oxy we are given the curve with equation: x^2-10\sqrt{3}xy+11y^2+64=0 Find an orthonormal system for which the equation takes the simplest form. What is that form? I'm confused as to what...