Use this tag when you want to determine the thinking that is needed to solve a certain type of problem, as opposed to looking for a specific answer to a question.

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2
votes
0answers
27 views

Rank of a symmetric matrix. (ISI Sample Paper)

Here, $\langle v,w\rangle=v^tw$ is the usual dot product. Let $A$ be an $n \times n$ symmetric matrix. Let $l_1, l_2, \ldots , l_{r+s}$ be $(r + s)$ linearly independent $n\times 1$ vectors such ...
-4
votes
1answer
31 views

Problem solving using quadratic equations [on hold]

A right triangle has a hypotenuse that is 1 cm more than double the length of its shortest side, and the other side is 1 cm less than twice the shortest side. Find the dimensions of the triangle.
5
votes
0answers
26 views

How to find a list of summands and factors adding up to a total?

I am neither a mathematician nor do I have an idea on how to write down my problem in accurate mathematic formulas. Please feel free to edit my question into shape and remove this paragraph. Also I am ...
0
votes
2answers
36 views

Homework Problem About Finding a Value of $k$ for Which the Given System of Equations Has No Solutions

While working through the third of three packets I'm going through to review for a pre-test for an independent-study calculus class, I came across the following problem: For what value of $k$ ...
2
votes
1answer
35 views

mod operation proof [on hold]

Prove: $ ab\,\bmod\,d = ((a\,\bmod\,d)\,(b\,\bmod\,d))\,\bmod\,d $ where $a$, $b$ and $d$ are non-negative integers. Reference : http://en.wikipedia.org/wiki/Modulo_operation#Equivalencies Context ...
0
votes
1answer
46 views

Find all continuous functions $f:\mathbb{R}\to\mathbb{R}$ satisfying $\frac{f(x+3)}{3+f(x)}=\frac{4+x^2}{x^2}$

Find all continuous $f:\mathbb{R}\to\mathbb{R}$ satisfying $$\frac{f(x+3)}{3+f(x)}=\frac{4+x^2}{x^2}.$$ I believe the original question was $$\frac{f(x)}{3+f(x)}=\frac{4+x^2}{x^2},$$ which has a ...
1
vote
1answer
37 views

Polygon center which always lies inside the polygon (with no hole)

Is there is any type of centre (of polygon) which always lies inside the polygon (with no hole)? Note: Here our polygon may be any type of polygon (convex or concave) but ...
1
vote
1answer
51 views

Can you generate math problems that are solveable?

If you take Linear Programming, it problems are formulated like this: You know that Cabinet X costs 10 cents per unit, requires 6 square feet of floor space, and holds 8 cubic feet of files. ...
-2
votes
0answers
39 views

Solving a math word problem using matrix logic [closed]

There are 4 assembly plants and each one is capable of producing certain type of vehicles Assembly plant A : 4 door compact cars Assembly plant B : 4 door compact cars and light truck Assembly plant C ...
0
votes
1answer
32 views

Odds of Winning Office NCAA Pool

I have 6 coworkers competition in a NCAA bracket. I'm trying to find out how to calculate who has the best chance of winning. For example currently the score card looks like: Player 1. Current Right ...
2
votes
1answer
56 views

Solving an equation for x, characteristics

I am trying to plot characteristics on Matlab for a hyperbolic pde. I need to compute \begin{equation} x=\frac{t}{(1+x^2)}+x_i \end{equation} for every spatial step. Any help with how to do this? ...
2
votes
1answer
26 views

Problem about sum of polynomials

I have this problem I don't know how to solve: Let $f(x)$ be a polynomial of degree $n$ with real coefficients and such that $f(x) \geq 0 \forall x \in \mathbb{R}.$ How do I show that $f(x) + f'(x) + ...
0
votes
1answer
28 views

Some clarifications and a question on basic probability.

I have a few questions and some clarifications. CLARIFICATIONS: 1. Assume we roll 2 four sided dice. What is P({sum of the rolls is even})? I answered the question correctly I: Odd + Odd = Even J: ...
2
votes
2answers
61 views

$\lim_{n\to\infty}a_nb_n=? $ given that $\lim_{n\to\infty}a_n=0$ and $\lim_{n\to\infty}b_n=\infty$

A. $\lim_{n\to\infty}a_nb_n=?$ given that $\lim_{n\to\infty}a_n=0$ and $ \lim_{n\to\infty}b_n=\infty$ B. $\lim_{n\to\infty}{a_n \over b_n}=?$ given that $\lim_{n\to\infty}a_n=0$ and ...
2
votes
2answers
74 views

Minimize : $\sqrt{(1+{1\over a})(1+{1\over b})}$ subject to $a+b=\lambda$.

Given positive real variables $a$ and $b$, find the minimum of $$f(a,b)=\sqrt{\left(1+{1\over a}\right)\left(1+{1\over b}\right)}$$ subject to $a+b=\lambda$ where $\lambda$ is a constant . [ISI ...
0
votes
1answer
15 views

Non-convex quadrilateral and pentagon?

Is it possible to draw a non-convex quadrilateral/pentagon and an additional straight line such that the straight line cuts through the interior of each of the quadrilateral/pentagon's edges?
0
votes
1answer
25 views

A question about subspace and finding basis

guys help me I couldn't solve this question I've been working on subspaces for sometime but still cant do this kind of questions.
0
votes
2answers
22 views

Surface Area and Volume relationship

I know that the $SA = 6s^2$ and that the volume is equal to the base $x$ the $side = s^3$. However, I'm not sure how to approach this though.
0
votes
1answer
22 views

How does one find the change?

I tried using ratios but I failed. I need to subtract one to get the correct answer. I remember finding the change before, but I've forgotten how to. Any hints?
4
votes
1answer
51 views

Prove that following polynomial has no non-zero real solution.

Prove that following equation has no non-zero real solution. $$ \sum_{ 1 \leq n \leq 120,\, 2|n \;\textrm{or}\; 3|n } x^n = 0$$ Any idea?
1
vote
1answer
59 views

Find the condition for a center of a circle with exactly one lattice point on its circumference

Statement Find the condition for a center of a circle with exactly one lattice point on its circumference (this lattice point must not be the only one lattice point of the disk) What I have ...
0
votes
3answers
61 views

Pennies, Nickels, Dimes, and Quarters Summation of Money

Peter has only pennies, Norma only Nickels, Diane only dimes, and Quincy only quarters. Peter and Norma have the same number of coins, and Diane and Quincy have the same number of coins. What is the ...
1
vote
2answers
102 views

Solve for “x” and “y” [duplicate]

What would be the easiest way to solve the following set of equations:$$ x + y^2 = 7 $$$$ x^2 + y = 11$$ I've been trying substitution method but end up in a $4$th degree bi-quadratic equation. ...
1
vote
0answers
9 views

Determinant of partition matirx

Let $X$ be $n\times p$ matrix as $X=(x_1, x_2, \ldots x_p)$. I partition the matrix as follows $X=(X_1, X_2)$ where $X_1$ is a $n\times p_1$ matrix and $X_2$ is a $n\times (p-p_1)$ matrix. Then how ...
1
vote
1answer
34 views

Finding a uncountable subset of P(N)

How to find an uncountable subset of $P(\mathbb{N})$ such that every two elements of it can be compared. In fact, give an uncountable subset of $P(\mathbb{N})$ such that has totality property. We mean ...
1
vote
0answers
14 views

Green's function inhomogeneous DE

I'm having a little bit of trouble with a question which is: By using the Green's function, solve the differential equation $2y''+y'-y=e^{-x}$ with boundary conditions $y(0)=y(2)=0$ I've worked out ...
5
votes
3answers
371 views

Solving a quintic function for zero

I got this question on my homework and I cannot for the life of me figure out how to solve for $0$. $$x^5+2x-10=0$$ I have tried this every which way and this is my last resort. Thanks in advanced. ...
4
votes
1answer
402 views

Given two potatoes, prove that there is a loop of wire which fits around both

This is a classic problem in geometric continuity and I want to see if there are some solutions other than the one I'm thinking of: Two potatoes are given. Prove that there exists a closed loop of ...
0
votes
1answer
34 views

Getting rid of product of sequence sign

I am having trouble with equation containing product of sequence: $$\frac {1}{2} = 1 - \frac {\prod \limits_{i=1} ^{n} (366 - i)}{365^n} $$ How can I convert the $\prod \limits_{i=1} ^{n} (366 - i)$ ...
-1
votes
0answers
43 views

Finding a solution manual for A course in Probability Theory, Kai Lai Chung. [on hold]

I am learning a book, $A \ Course\ in\ Probability\ Theory$, writen by Kai Lai Chung. I am wondering whether there exists a solution manual for the book because I find parts of exercises in this books ...
3
votes
1answer
58 views

$\prod_{i=1}^{n-1} a_i = 1 \Rightarrow \prod_{i=1}^{n-1} (1+ a_i)^{i+1} > n^n$?

Let $n>3$ be an integer number and $a_1, a_2, \dots, a_{n-1}$ positive real numbers, such that $\prod_{i=1}^{n-1} a_i = 1$. Is the following inequality true? $$ \prod_{i=1}^{n-1} (1+ a_i)^{i+1} ...
0
votes
2answers
39 views

Solve $x^4+3x+20=0$ by Ferrari's method

Comparing the equation $$x^4+3x+20=0$$ With the equation $$(x^2+\lambda)^2-(mx+n)^2=0$$ we get $m^2=2\lambda,$ $-2mn=3,$ $n^2=\lambda^2-20$ Now, $4m^2n^2=9\Rightarrow ...
0
votes
2answers
28 views

What's the probability a die irolled 4 times you will get only two kinds of faces?

Let $A$ be the event "only $2$ different faces in $4$ rolls of a die." At each roll there's $6$ possibilities, so: $$\omega = 6\cdot 6\cdot 6\cdot 6$$ Considering that it can be only two kinds of ...
0
votes
0answers
31 views

What is the probability that the fourth and fifth coins tossed are the same?

A biased coin is tossed infinitely many times and has probability $p$ of being "heads". 1) What is the probability that the fourth and fifth coins are the same? 2) And given that the first 10 tosses ...
0
votes
1answer
43 views

Solving a cubic equation

Solve $y=ax^3+bx^2+cx+d$ I need $x$ in terms of $y$ . I do not need the roots of the cubic equation . I need to express $x$ in terms of $y, x>0$
0
votes
2answers
19 views

What is the probability that exactly 7 of the first 10 coin tosses are heads?

A biased coin is tossed infinitely many times and has probability $p$ of being "heads". What is the probability that exactly $7$ of the first $10$ coin tosses are "heads", in terms of $p$? It's a ...
3
votes
4answers
56 views

Find $\min\big\{ \lfloor xy + \frac{1}{xy} \rfloor \,\Big|\, (x+1)(y+1)=2 ,\, 0<x,y \in \mathbb{R} \big\}$

I am invited to calculate the minimum of the following set: $\big\{ \lfloor xy + \frac{1}{xy} \rfloor \,\Big|\, (x+1)(y+1)=2 ,\, 0<x,y \in \mathbb{R} \big\}$. Is there any idea? (The question ...
1
vote
4answers
83 views

Solve $16x^{-3}=-2$

Solve $16x^{-3}=-2$. My working: \begin{align} 16x^{-3}&=-2\\ \frac{1}{16x^{3}}&=-2\\ \frac{16x^3}{16x^3}&=-32x^3\\ 1&=-32x^{3}\\ -32x^{3}&=1\\ -32x&=\sqrt[3]{1}\\ ...
1
vote
2answers
33 views

Simplifying $\frac{1/(\frac{1}{z_1}(1-t)+\frac{1}{z_2}t) - z_1}{(z_2 - z_1)}$

This drives me mad! I am not very good in math but thought I could at least do basic things like this one, but can't figure it out and I spent a day on it. I am trying to simplify: ...
4
votes
2answers
31 views

Frogs and switches - problem solving strategies

The question is pretty simple, consider 1000 switches and 1000 light bulbs, every time we press a switch it's light bulb changes it's state(ON to OFF and vice versa). We start with all the light bulbs ...
0
votes
1answer
66 views

Pigeonhole question about distinct sums

How do I show with the pigeonhole principle that no seven positive integers not exceeding $24$ can have sums of all subsets different. As observed by Ross Millikan, the simplest possible approach ...
0
votes
3answers
31 views

Solving a function for a variable, confusion

I have the function $f(t) = -4.9t^2+25t+3$, where $f(t)$ is a the height of a grapefruit after $t$ number of seconds. I need to find out how long the grapefruit is in the air, so I know i need to ...
0
votes
1answer
26 views

Local extension of smooth funtion to a embedded manifold

I'm trying to proof the following problem from Lee's Book: Suppose $M$ is a smooth manifold and $S\subseteq M$ is a smooth submanifold. Show that $S$ is embedded if and only if every $f\in ...
0
votes
0answers
22 views

Finding zeros of a piecewise function

Is there a general strategy for solving $$0 = \sum_i \left\{ \begin{array}{lr} f_i(x) \text{ if }p_i(x) \\ g_i(x) \text{ otherwise} \end{array} \right.$$ for $x$? To what ...
2
votes
0answers
31 views

Get function definition from an equation

My question: I have to find a function $g$ fulfilling the equation $$2\frac{t_k \cdot t_0 - 1}{t_k-t_{-1}} = g(t_k) + g(t_{k+1}) + t_{k+1}\cdot g(t_k)g(t_{k+1})$$ Whereby $t_{n+1}=t_n + h$ with $t_0, ...
1
vote
2answers
64 views

Partitioning positive divisors of 100!

Is it possible to partition all positive divisors of 100! (including 1 and 100!) into 2 subsets so that each subset has the same number of integers and the product of all the divisors making up the ...
0
votes
0answers
33 views

Is it possible to find out how many results were unexpected?

During a school year Andrew was given 40 mathematical problems as part of his assessment, one problem per week. As a result of marking he could receive 2,3,4 or 5 marks for each problem. Andrew called ...
0
votes
1answer
41 views

Perimeter problem involving different sized sticks?

Could you please help me find the answer to this question. I think it has something to do with grouping or pairing some numbers.I would appreciate easy-to-understand solutions. Thank you. There are ...
0
votes
3answers
52 views

How to solve $h(i) = \frac{i^2}{(n-i)^2+i^2}h(i-1) + \frac{(n-i)^2}{(n-i)^2+i^2}h(i+1)$

$h(i) = $P(reach n eventually| the initial state = i) $h(0) = 0$ $h(n) = 1$ 0 and n are stopping time. For $ 0 < i < n$, $$h(i) = \frac{i^2}{(n-i)^2+i^2}h(i-1) + ...
1
vote
1answer
51 views

Two rows or two columns with the same number of plusses

I have tried drawn numerous tables in attempt to explain this and understand that the number of cells must be even however, I am not sure how to create this proof. I appreciate your support. Each ...