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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1
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1answer
49 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
67 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. ...
0
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1answer
36 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
74 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
29 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
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1answer
32 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
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2answers
64 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
78 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
19 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
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1answer
28 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.
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2answers
50 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
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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
66 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
69 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 ...
1
vote
3answers
113 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
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2answers
104 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
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0answers
13 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 ...
5
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3answers
401 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
429 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
39 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 $\prod \limits_{i=1} ^{n} (366 - i)$ ...
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
68 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
29 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 ...
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0answers
39 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
57 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
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2answers
30 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
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4answers
57 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
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4answers
86 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}\\ ...
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2answers
51 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
84 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
38 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 ...
1
vote
1answer
51 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
26 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
35 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
84 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
36 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
46 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
53 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
57 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 ...
1
vote
1answer
109 views

Solve All Sequence (Rubik's Cube)

Can you prove/disprove that there is a solve-all sequence of moves to complete the Rubik's Cube from any solvable-position? If so, can you explain how long it is? If not, explain why not. Just to be ...
1
vote
1answer
56 views

Prove that $a_i\leq 0$ for $i=1,2,…,N-1$?

Let $a_0,a_1,...,a_N$ be real number satisfying $a_0=a_N=0$ and $$a_{i+1}-2a_i +a_{i-1}=a_{i}^{2}$$ for all $i=1,2,...,N-1$. Prove that $a_i\leq 0$ for $i=1,2,...,N-1$. I saw the problem in ...
0
votes
2answers
76 views

How should a programmer store and solve simultaneous algebraic equations?

I need to store and solve simultaneous algebraic equations (no trig, no calc, no logs) as part of a larger program. I am not yet committed to a particular language, so long as it's a free one. For ...
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0answers
65 views

A Challenging Problem of Spherical Rectangle

Find out the area (in sq. units) covered by a spherical rectangle, having length & width (each as a great circle arc) of 15 & 4 units respectively, on a spherical surface with a radius ...
1
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1answer
46 views

Can problem solving be axiomatized? [closed]

Is it possible to develop a set of axioms for solving any problem, that are certain to work? Similar to problem solving strategies or proof strategies, though a set of steps that work indefinitely if ...
0
votes
1answer
91 views

How to find the minimum value of this integral?

I am struggling to find the solution to this problem. If anyone could help to explain how to solve this problem to me, it would be really appreciated. Let $$ f(x)=-\sqrt{3}x+(1+\sqrt{3}) $$ $$ ...
0
votes
1answer
16 views

For probabilities in sets, why multiply together for the complement but not for the normal probability?

For the birthday problem, the probability that a set of n birthdays (where n=1) contains your birthday is 1/365. The complement is that there is a 364/365 chance that it does not contain your ...
0
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1answer
13 views

Find caluclation to equal this value?

How can I find the calculation needed to reach the given value? This is related to programming but I don't see how I can do this myself. ...
0
votes
0answers
17 views

Ratio and rate using of SI units

When you have been given the ratio and rate of 4kg:500g do you change the values both to grams making it (8g:1g) or do you keep them in the SI units that they are placed in (1kg:125g) and for what ...
0
votes
1answer
35 views

Problem Analysis - Answer but no procedure - Differential Eq.

I stumbled with this problem in a notebook that has been bothering me...The answer is written but there's no explanation nor a steb-by-step procedure or anything. If you know how to analyse the ...
0
votes
1answer
27 views

What is the name for an ODE with an integral as a side condition?

My question: I have to find a function $y: \mathbb R \rightarrow \mathbb R$ fulfilling $$y^\prime(t) = f(t, y(t)),\ \int_{-\infty}^\infty y(t) dt = c$$ with a given $c \in \mathbb R$. What is the ...