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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1answer
33 views

What are some effective ways to go about this type of problem?

I need an efficient way to go about this problem, for practice for my problem solving test. This is not a part of the actual test. This is the type of question that I am struggling with There are two ...
0
votes
1answer
11 views

Is there a analytic algorithm to solve for a partially specified constant present in function & its derivative with the rate of change at an x value?

I have a Calculus problem that I am not entirely happy with how I solved it. Given the following information: $$y = x^{k} + x^{k-2}$$ $$(k \in \mathbb{N}) \wedge (k \mod{2} \neq 0) \wedge (k > ...
59
votes
4answers
2k views

Laplace, Legendre, Fourier, Hankel, Mellin, Hilbert, Borel, Z…: unified treatment of transforms?

I understand "transform methods" as recipes, but beyond this they are a big mystery to me. There are two aspects of them I find bewildering. One is the sheer number of them. Is there a unified ...
1
vote
0answers
36 views

partition of $\mathbb{Z}$ into finitely many translation

Few days ago, a friend of mine gave me this problem : Let $X \subset \mathbb{Z}$ and suppose that $a_1, a_2, \cdots, a_n$ are integers such that $X+a_1, \cdots, X+a_n$ is a partition of ...
0
votes
0answers
40 views

Solving for y in $4+x^3+y^3-3xy = 0$

I was trying to solve for $y$ in this equation: $4+x^3+y^3-3xy = 0$. I put it into WolframAlpha and it gave me an complicated answer. It appears like it used the cubic formula, except when I tried to ...
2
votes
0answers
16 views

How do I describe an XYZ velocity in a written sentence?

I'm creating a voice interface for Amazon Echo, providing status information regarding the International Space Station (ISS). I'm attempting to express the XYZ velocity of ISS. Speed inquiry example ...
0
votes
3answers
38 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 ...
0
votes
1answer
181 views

Finding the Compound Interest on 7500 Dollars at 4% per annum for 2 Years

Find compound interest on $\$7500$ at $4\%$ per annum for $2$ years, compounded annually. The choices are as follow: $\$512$, $\$552$, $\$612$, $\$622$. I tried to solve this problem by: C.I. $= ...
3
votes
1answer
65 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. ...
1
vote
1answer
393 views

Solving system if equations containing trigonometric functions with Ti-Nspire

In trying to solve the following system of equation: $20000\times9.81+a\cos b=0$ $a\sin b=6.17\times20000$ Find $a$ and $b$ . It gives me something containing "n2" in bold and I don't know why? ...
0
votes
2answers
495 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
3answers
28 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 ...
4
votes
3answers
363 views

Strategies to find the set of functions $f:\mathbb{R}\to\mathbb{R}$ which satisfy a given functional equation

My question is as follows: What methods can be used to find the set of functions $f:\mathbb{R}\to\mathbb{R}$ satisfying a certain functional equation. An example of a case where this applies is the ...
2
votes
1answer
30 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 ...
0
votes
0answers
17 views

Sites for collective problem solving [closed]

What are the sites for collective solving of (hard) open mathematical problems?
3
votes
0answers
57 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 ...
3
votes
2answers
182 views

Solve first order nonlinear differential equations

I want to solve this nonlinear 1-st order ODE, $$\frac{1}{1+x}=(\frac{1}{x-y}-\frac{1}{y})\frac{dy}{dx}$$ I find it non-separable, and Wolfram Alpha does not give me a closed form solution, but the ...
0
votes
2answers
52 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 $X$ ...
1
vote
3answers
38 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 $v$ = ...
4
votes
2answers
131 views

Expected number of cards fixed in a deck after a certain operation

Problem: Given a standard deck of $52$ cards, extract 26 of the cards at random in one of the $52 \choose{26}$ possible ways and place them on the top of the deck is the same relative order as they ...
2
votes
1answer
39 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
45 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
1answer
431 views

Finding Y coordinate of third triangle point when X coordinate and two other points are already known

Suppose you know the coordinates for points A and B of a triangle. We can refer to those coordinates as (Ay,Ax) and (By,Bx). Also, suppose you know the X coordinate for point C (Cx) but do not know ...
0
votes
2answers
36 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
1answer
82 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' ...
5
votes
3answers
87 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
16 views

Right Triangle Angle problem

So 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 cant post image due to no reputation (this is my first post) so theres the ...
54
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 ...
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2answers
25 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 ...
-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
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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
16 views
1
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1answer
14 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
21 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
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 ...
0
votes
1answer
12 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 ...
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votes
0answers
21 views

Dynamical Systems problem

I have a problem that have been trying to solve but it's not going so good. I would like some guidelines on how to work myself around this problem: Two neighboring countries spy on each other and ...
1
vote
0answers
25 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
73 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 ...
2
votes
2answers
53 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 : $$a = \frac{4(b+c)}{b+c+4}\tag{1!}$$ $$b = \frac{10(a+c)}{a+c+10}\tag{2}$$ ...
0
votes
1answer
87 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
4answers
55 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 ...
0
votes
1answer
46 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 ...
0
votes
2answers
536 views

Solve $4 A (L^{3/4}) - wL (((24 - L) w)^{-3/4}) = -(((24 - L) w)^{1/4})$ for L? Using Mathematica

I'm trying to solve $$4 A (L^{3/4}) - wL (((24 - L) w)^{-3/4}) = -(((24 - L) w)^{1/4})$$ for $L$ using Mathematica, and it spits the following out: ...
0
votes
2answers
48 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, ...
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 ...