# problem

1. ### Binary relation

Hello, i've been given this problem at University and I need some help with the formulas. From already thank you very much. Let A = {1,2,3, ..., 365} be the set of the days of the year 2018, numbered from 1 (January 1, 1018) to 365 (December 31, 2018). Let R be the binary relation in A given by...

3. ### Integral of 1/(1-x)

Yeah so basically we all know that the integral of 1/(1-x) is -ln(1-x)+c, but if I factor out -1 from the denominator before integration I seem to get -ln(x-1)+c. Can someone explain where the mistake is?
4. ### Graph Theory Optimization Problem

Hi everyone, I'm currently working on an algorithm aiming to find the best route between two vertices (the best, not the shortest...(Nod)) My hypothesis : - G a graph - each vertex is graded (a grade out of 10 for example) - the edges are also weighted - we call "mean of a path" the...
5. ### Integral problem with A and c. im very confused, help would be welcomed :)

This is the question and I'm not entirely sure where to go from here. Thanks! Assume c>0 and A>0, and compute the volume of the solid obtained by revolving the region bound by the graph of f(x)=Ax^2, the vertical line x=c, and the x-axis about the x-axis. Your answer should be in terms of A and...
6. ### cylindrical coordinate problem

find the volume bounded by cylinder (y^2 0 + (z^2 0 =1 , plane y = x and y-z plane in first octant... I'm not sure to let my y = rcos theta or r sin (theta) , but i do know that volume must be positive.... I'm not convinced that why should i use y = r sintheta
7. ### simple computation problem?

Another question from sosmath.com: f(x) = x^2 - 2x +3; find [f(a-b) - f(a)]/b And the answer given is 2a + b -2. I keep getting b - 2a + 2. I get it like this: ( (a-b)^2 -2(a-b) + 3 - [a^2 -2a + 3] ) / b ... ( a^2 -2ab +b^2 -2a + 2b + 3 - [a^2 -2a +3] ) / b ( a^2 -2ab +b^2 -2a + 2b +...
8. ### Optmization Problem

Determine the value of the constant k which best approximates a specified function f(x) on the interval ≤≤. Use as a cost function to be minimized: Verify that a minimum is achieved by checking the 2nd order optimality condition. I rewrote L(k) and then tried to find the value of k such that...
9. ### Optmization Problem

Determine the value of the constant k which best approximates a specified function f(x) on the interval ≤≤. Use as a cost function to be minimized: Verify that a minimum is achieved by checking the 2nd order optimality condition. I rewrote L(k) and then tried to find the value of k such that...
10. ### Homogeneous DE's - Wronskian problem with algebra

Hi I am not sure what forum this thread properly belongs to so I apologise in advance if it is in the wrong place. It is related to DE's however is to do with the algebra involved. I have attached a page with two examples from the text "Differential Equations with Boundary Value Problems"...
11. ### Coupons collector problem

Coupon collectors problem Suppose that there are N distinct types of coupons and each time one obtains a coupon it is, independent of prior selections, equally likely to be any one of the N types. One random variable of interest is T, the number of coupons that needs to be collected until...
12. ### Set problem help

Hello, I am really struggling with this problem below: Let A, B, and C be sets in a universal set U. We are given n(U) = 77, n(A) = 39, n(B) = 40, n(C) = 23, n(A ∩ B) = 22, n(A ∩ C) = 14, n(B ∩ C) = 13, n(A ∩ B ∩ CC) = 13. Find the following values.(a) n((A ∪ B ∪ C)C) (b) n(AC ∩ BC ∩...
13. ### Trying to solve a set problem given several sets

Hello, I've been trying to figure out how to solve this question below: Let A, B, and C be sets in a universal set U. We are given n(U) = 82, n(A) = 46, n(B) = 41, n(C) = 42, n(A ∩ B) = 25, n(A ∩ C) = 18, n(B ∩ C) = 23, n(A ∩ B ∩ CC) = 13. Find the following values.(a) n(AC ∩ B ∩ C) (b)...
14. ### Lotka - Volterra problem - Critical Points of the system.

Hi, I'm trying to solve the following Lotka - Volterra model for its critical points but I am encountering some difficulty. This is the problem. I know I have to set both equations to 0, I can do this for the first one and I get x=0 and y-1 = 0, but from here I am lost. Do I sub these...
15. ### Hyperbola problem

Hello everyone! Can anyone please help me with a specific hyperbola problem? it is giving me the vertices and perimeter of rectangle but I don't know how to solve using the perimeter of rectangle
16. ### Optimisation problem

Hi guys. This question has been bothering me because I'm unsure how to go about it. Could someone help me out? An ironman has drifted 1 km along the beach from the finish of the swim stage. He is 400 m from shore and can swim at 4 km/h and run at 12 km/h. At what angle to the shore should he...
17. ### inscribed triangle problem

'ABC is an acute-angled triangle inscribed in a circle and P, Q, R are the midpoints of the minor arcs BC, CA, AB respectively. Prove that AP is perpendicular to QR.' I know that the lines from the midpoints to the centre of the circle are perpendicular bisectors of the sides of the triangle but...
18. ### Word Problem: Systems of Linear Equations

Hi all, I have been trying to solve the following word problem for a few hours now. I think it's time to step in and ask for help after exhausting all of my resources to no avail. Three siblings Tommy, Susie, and Roland are 42 years old together now. When Susie was of Tommy's age, Roland was...
19. ### Linear algebra Gauss-jordan elimination problem

Hi. I've been working on this problem. Show that the following non-linear system has 18 solutions if { 0 <= a, b, c <= pi } sin(a) + 2cos(b) + 3tan(c) = 0 2sin(a) + 5cos(b) +3tan(c) = 0 -sin(a) - 5cos(b) + 5tan(c) = 0 So I substituted sin(a), cos(b), and tan(c) for x, y, and z and then used...
20. ### Equation to solve a basic problem

Hi, Not sure if I'm at the right place but I need an equation if possible. a – c = 44 (variable) a + b + c is always 100 b is always 53% of b + c what is the formula to calculate the values of a, b & c when the 44 changes? Any help would be much appreciated. Thanks.