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.

learn more… | top users | synonyms

0
votes
3answers
43 views

Linear Algebra | Determine the values of a for which the system has no solutions, exactly one solution, or infinitely many solutions

I am a college student, and this summer I am taking a 15 week course on linear algebra. I was doing my homework today, and I am not sure if my solution is correct. The problem is stated as follows: ...
1
vote
1answer
50 views

Can you factorial a power?

I know this may be a straight forward question, but I looked around on google for about 20 minutes to find nothing. I am currently a year 8 student and came across a problem where I have to find the ...
3
votes
1answer
67 views

How can I prove this equation has no real solution?

I have an equation $$x^2-5 x+10+(x-4) \sqrt{1+x}=0. \tag{1}$$ Now I am trying to prove this equation has no real solution. I tried. Put $t = \sqrt{1+x}$, then, I got $$t^4+t^3-7 t^2-5 t+16=0. \tag{2}...
0
votes
3answers
30 views

shortcut technique to solve algebric problem

If we multiply three consecutive numbers, we get 120. what the summation of those numbers? Is there any shortcut way of solving this problem without doing much ...
2
votes
1answer
31 views

Probability of selecting a jury

Does anyone know how to find the probability of selecting a jury of $12$ people ($6$ men and $6$ women) out of an initial group of $18$ people ($6$ men and $12$ women)? With my knowledge of ...
3
votes
0answers
60 views

What are the essential tools and proof techniques for beginning smooth manifolds and differential topology?

I am an undergraduate currently taking a first course in smooth manifolds. I feel that I understand the material intuitively. But, I'm having trouble turning my intuition into proofs. I was hoping ...
1
vote
3answers
39 views

Finding Matrix A from Eigenvalues and Eigenvectors (Diagonalization)

Question: Let $A$ be a $3 \times 3$ Matrix such that $[-3,4,1]$ is the eigenvector corresponding to eigenvalue $3$, and $[6,-3,2]$ is an eigenvector corresponding to the eigenvalue $2$. If $v$ = ...
2
votes
1answer
43 views

$f(x)$ is a quadratic polynomial with leading coefficient $1$, $|f(x)| \leq 8 \: \forall \: x \in [1,9]$ find $f(x)$

$f(x)$ is a polynomial of the form ($b,c$ are real numbers) $$f(x) = x^2+bx+c$$ such that $|f(x)| \leq 8 \: \forall \: x \in [1,9]$. Find all $f(x)$ satisfying the given condition. I found ...
0
votes
0answers
47 views

Minimizing the effort after toilet visit

We live together with 5 people (4 men and 1 woman) and the woman wants everyone to close the toilet after every turn (i.e. bring the seat and cover down, for smell reasons). To me this seems unfair. ...
-3
votes
1answer
36 views

$f(x)=-(x-2k)^2(x-4k)-k\quad$ where $k\gt 0\quad$ [closed]

$f(x)=-(x-2k)^2(x-4k)-k\quad$ where $k\gt 0\quad$ (i) Show that the local max occurs at $\left(\frac{10k}3,\frac{32k^3}{27}-k\right)\quad$. (ii) If the local max point is to occur on the x-axis, ...
0
votes
2answers
50 views

Probability of winning a prize in a raffle (that each person can only win once)

There is a raffle coming up. 4000 tickets have been sold, and there are 10 prizes to win. I have bought 8 tickets. What are the odds I will win a prize? Note: each person can only win once. There ...
1
vote
1answer
17 views

Simultaneous equations change expression variables

I have a deceptively simple-looking problem. $$A + B = A'\\ C + D = B'\\ A + C = C'\\ B + D = D'$$ On LHS $4$ variables $A, B, C, D$ On RHS $4$ variables $A', B', C', D'$ Is it possible to ...
0
votes
2answers
54 views

Solving for an unknown symmetric matrix using an answer found by a commutator.

Suppose I have, for $A,X$ real square symmetric matrices, and $B$ skew-symmetric and real, $AX-XA=B$, with $B$ and $A$ known and $X$ unknown. What properties of $X$ need to be satisfied to find $X$ ...
5
votes
3answers
89 views

What's the best way to compute $\frac{a^4 + b^4 + c^4}{a^2 + b^2 + c^2}$

So, my teacher gave us this to compute yesterday, and I'm completly confused on how should I proceed : $$\frac{1^4 + 2012^4 +2013^4}{1^2 + 2012^2 + 2013^2}$$ I've tried several ways, but most of ...
0
votes
1answer
21 views

Right Triangle Angle problem

I know that this can be easy, but I found it a bit difficult so maybe someone can just explain or give a hint to me. I have a right triangle $ABC$ with points $D$ and $E$ on its hypotenuse so $AB=AE$ ...
0
votes
1answer
86 views

How to do complicated problem without messy mind?

I have trouble when doing complicated problem, when I look at a problem with so much information. (e.g. deal with some concrete example such as proving a 'ugly' space is homeomorphic to another 'ugly' ...
1
vote
2answers
26 views

Solving Trig Equation with Unknown Inside and Outside of Function

In my physics course, we're covering physical pendulums, and we are to essentially analyze the range of angles within the interval $\left[0, \frac{\pi}{6}\right]$ to show that $\sin\theta \approx \...
55
votes
8answers
8k views

How to debug math?

May seem strange as I'm good in programming, but I just started diving into math. ATM I'm learning combinatorics at Khan Academy, and here's an example of a question that I struggled with (that's not ...
-1
votes
1answer
36 views

Three screw problem

There are three identical screws with diffrent amounts of nuts and disks on them. Here is the problem picture: How do you calculate the weight of a screw, the nuts and the disks?
0
votes
0answers
10 views

Minimizing log-likelihood function

Below is a problem I'm currently working on. I am having trouble seeing how I can obtain the wk and wko values for equation (1). I cannot see how one would solve the negative log-likelihood function ...
0
votes
0answers
17 views

How does one get $p=2$ from a condition that there be non-trivial linear transformations of every dimension that to any power are $p$-norm-preserving?

Verifying that (p=2) satisfies $$\forall n\in\mathbb{Z}^+.\exists A\in(\mathbb{R}^{n\times n}\setminus\{I_n\}).\forall k\in\mathbb{R}.\forall v\in\mathbb{R}^{n}.\left\|A^kv\right\|_p\!\!=\left\|v\...
1
vote
1answer
22 views

Solve transport equations by using Laplace transform

I'm trying to solve rather formally one-dimensional transport equation: $$ u_{t}+cu_{x}=0\quad\text{in $(0,\infty)\times(-\infty,\infty)$} $$ with an initial data $u_{0}$, which is bounded and ...
0
votes
1answer
22 views

Find the perimeter of the given trapezoid

Find the perimeter of the given trapezoid (The diagram is not drawn to scale) I thought I could use the pythagorean theorem, but I have two unknow sides. What do I do now?? Thank you
0
votes
1answer
13 views

Calculate the amount of hours in $x$ minutes, and the amount of minutes left over.

I was recently given the following question, and I'm unsure how to go about solving it. Help would be appreciated. Using only addition, subtraction, multiplication, and division; and only the ...
1
vote
1answer
31 views

When will all the flowers blossom?

The title is not actually correct, but I chose appeal over correctness ;) I'd like to model a flower blossoming cycle, and these are the assumptions: 1) The instant $T$ in which each flower starts ...
1
vote
0answers
29 views

Number of ways to get from a point to another one in the plane

I was trying to solve the following problem related to "counting cases": Consider the point $(0,0)$ in the plane and another point $(m,n)$ with $m,n>0$ integers. Suppose you want to get from the ...
0
votes
0answers
76 views

Time and distance problem

A train starts from Jammu for Srinagar at 13:30 and reached at 17:30.Another train starts from Srinagar at 15:30 and reaches Jammu at 19:00.At what time both train will meet??. I have solved this ...
3
votes
2answers
63 views

What's the value of $x$ in the following equation?

So this is how I approached this question, the above equations could be simplified to : $$a = \frac{4(b+c)}{b+c+4}\tag{1!}$$ $$b = \frac{10(a+c)}{a+c+10}\tag{2}$$ $$c=\frac{56(a+b)}{a+b+56}\tag{3}$$...
0
votes
4answers
61 views

right circular cylinder inscribed in a sphere

Find the dimensions of the right-circular cylinder of greatest vloume that can be inscribed in a sphere with a radius of 6 $in$ I think I need help visualizing, and maybe the solution. I've already ...
1
vote
1answer
46 views

What are some ways to check if a the information given is enough to solve a problem related to euclidean geometry? [closed]

To know if a the data given produces a unique answer is something important because if you know the data is insufficient to yield a unique answer you can stop looking for one. Example: $\triangle ...
0
votes
1answer
28 views

Showing that a function is not $(d,d)-$ continuous at a point.

Let $d: \mathbb R \times \mathbb R \rightarrow \mathbb R$ be a metric: $$ d(x,y) = \begin{cases} 0 & x = y \\ |x| + |y| + 3|x-y| & x \neq y \end{cases} $$ Show that the function $f: \mathbb R \...
0
votes
1answer
22 views

Recurrence relations, trouble understanding the statement

I have been struggling with the English in some recurrence relations problems, since I am studying it on my own and I'm not in a combinatorial environment. Here is one in which I can't grasp what it ...
0
votes
2answers
28 views

How do I solve for x? Do I need the Lambert W function?

I need to solve the next equation x: $d-x+yln[\frac{d}{x}]=b$ y, d, b, and x are all real, positive numbers. How do I solve for x? Do use the lambert W function and if so how is that done? Thanks!
0
votes
1answer
31 views

Recurrence relation. Application to ternary sequences

The question is: How many ternary sequences have no double zero? For this I understand that our $n$-digit sequence either have $0,1,\dots,n$ zeroes, is this ok? If the answer of above is positive, ...
-5
votes
3answers
27 views

Probability: 52 cards in a deck [closed]

If you are dealt two cards successfully (with replacement of the first) from a standard 52-card deck, find the probability of getting a heart on the first card and a diamond on the second.
4
votes
1answer
147 views

Find the coefficient of $x^{19}$ in the expression $(x+1)(x+2)(x+3)\cdots (x+400)$

Find the coefficient of $x^{19}$ in the expression $(x+1)(x+2)(x+3)\cdots (x+400)$ I have no clue how to start. Any kind of help will be appreciated.
0
votes
0answers
24 views

Travelling salesman - organising a tour of any European destination based on the cheapest flights available.

I apologise if this has only a tenuous link to a mathematics forum I'm sure everyone is familiar with the £10 one-way flights by Ryanair and similar airlines in Europe. I was wondering whether there ...
1
vote
0answers
9 views

Sum two nearest function of two class are the nearest function of the sum class

Suppose $x,\mu:[0,1]\rightarrow \mathbb{R^2}$ two smooth function and $\Gamma = \{\gamma : [0, 1] \rightarrow [0, 1]| \gamma (0) = 0, \gamma (1) = 1, \gamma$ is a diffeomorphism $\}$. Here $\Gamma$ ...
2
votes
2answers
52 views

How to solve this question in more time efficient way?

Q) if$$x\sin a=y\cos a=\frac{2z\tan a}{1-\tan^2 a}$$ then find $4z^2(x^2+y^2)$a)$(x^2+y^2)^{3}$b)$(x^2-y^2)^3$c)$(x^2-y^2)^2$d)$(x^2+y^2)^2$ Ans:c i solved this in a very long way: $$x\sin a=y\cos ...
1
vote
0answers
29 views

Linearity in quotient space

Let $\mathcal{C}$ be the space of all parametric curves $x:[0,1]\rightarrow \mathbb{R}^2$. Also let $\mathcal{C}$ is a linear manifold in the sense that $x_1,x_2\in \mathcal{C}$ implies that $cx_1+...
0
votes
1answer
48 views

How can I prove the equation has unique positive real solution?

Without using derivative, prove that the equation $$x^5-2x^4-3x^3-4x^2-5x-6=0$$ has unique positive real solution. I tried, consider function $f: \mathbb{R} \rightarrow \mathbb{R}$ with $$f(x)=x^5-2x^...
0
votes
0answers
25 views

How to create a custom scale for a range of values

I'm utterly sorry for the very non-specific question, but I'm not even sure what I am looking for. Any pointers and terminology so I can document myself would be helpful. Because I do not know how to ...
0
votes
1answer
50 views

Relationship of radius of sphere to an inscribed right circular cylinder for max and min values

I cannot seem to find the correlation between having an interval of a radius of a sphere with finding the greatest lateral surface area of a right circular cylinder inscribed in it. The question goes ...
7
votes
2answers
65 views

Three dimensional spherical excess formula

We all know the spherical excess formula: in a unit sphere, the area of a geodesic triangle is equal to the exceeding from $\pi$ of the sum of the three angles of the triangle. Is there a similar ...
2
votes
3answers
53 views

Ideas for solving this IVP

I am curious how to approach solving the initial value problem: $\begin{cases} y'(t) = 5t - 3\sqrt{y} \\ y(0) = 2 \end{cases}$. The equation isn't separable, and more generally it is not an exact ...
1
vote
1answer
29 views

Ideas for solving this nonlinear IVP

I am curious how to approach solving the initial value problem: $\begin{cases} y'(t) = 5t - 3\sqrt{y} \\ y(0) = 2 \end{cases}$. The equation isn't separable, and more generally it is not an exact ...
0
votes
2answers
50 views

Lambert W function with natural log

I need to solve the next equation x: $d-x+yln[\frac{d}{x}]=b$ I inserted this into Wolfram Alpha and it returned: $x = y \Bbb{W}[\frac{e^\frac{d-b}{y}d}{y})]$ y, d, b, and x are all real, ...
0
votes
0answers
19 views

Find the basis for the kernel, for a linear mapping

Let $T : R^4 \to R^3$ given by $$T(x, y, z, t) = (x−y+z+t, x+2z−t, x+y+3z−3t)$$ Using Gauss-array and reducing the system of equations to row echelon form I got: $\{(1,1,1),(-1,0,1)\}$ as basis for ...
0
votes
1answer
94 views

Probability Riddle

I was told a puzzle recently, and I can't figure out how to solve it. It went like this: You are a prisoner. You play a game with the guard many times a day. This game has a unique probability $...
1
vote
1answer
42 views

The Number of Two-digit Primes Which the Sum of their Digits is 6

Problem: Find the number of two-digit primes which the sum of their digits is six. We had this problem in a mathematic examination. The problem can be solved by testing all two-digit primes, but I ...