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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0
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3answers
44 views

how to solve a equation of degree 4?

Suppose i have a equation of a degree of 4 and i don't know a proper method of solving this type of equation (like completing the square is a proper method to solve the quadratic equation) so how or ...
1
vote
2answers
13 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 ...
32
votes
7answers
4k 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
34 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?
-1
votes
2answers
54 views

Solve defined integral exp(x^2+x) from -inf to inf [on hold]

Solve $$\int_{-\infty}^{\infty} e^{x^2+x} \,dx$$
0
votes
0answers
9 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
15 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 ...
1
vote
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
20 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
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 ...
-1
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
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
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
24 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
4answers
52 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
0answers
89 views

Bernoulli Probability Question [closed]

Customers depart from a bookstore according to a Bernoulli process with parameter p = 0.15 (per minute). Each customer buys a book with probability 2/3, independent of everything else. What is the ...
1
vote
1answer
45 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
26 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
26 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
25 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
23 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
114 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
20 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
48 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 ...
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 ...
0
votes
1answer
42 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 ...
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
40 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
61 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
48 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
44 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
86 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
36 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 ...
0
votes
0answers
28 views

calculus book recommendations [duplicate]

i want to learn single variable calculus i completed schooling and i love calculus for now i am focusing on single variable calculus i tried many books like Calculus - "A Complete Course 7th ed - R. ...
0
votes
1answer
12 views

Question about invariants.

There is a list of $n$ numbers. We pick any two numbers, $u$ and $v$ and replace them by $uv + u + v$. Does the final answer after $n-1$ operations, depend on the initial choice. I noticed that if ...
3
votes
6answers
97 views

Why isn't $-2$ solution for $x$?

I came across an logarithm problem recently. I don't know why solution to this problem cannot be $-2$. Now, don't downvote now because you don't know why I'm asking this. I know that logarithms' ...
0
votes
1answer
21 views

Generating functions, problem solving. Distribute distinguishable balls to people

The problem reads: How many ways are there to distribute $26$ of $34$ distinguishable balls to $5$ people if Lucy gets at most $4$ balls? The generating function to distribute distinguishable balls ...
2
votes
1answer
66 views

How can you solve for s in this very complex problem?

I recently stumped across a problem, which I need to solve. Of course, I used an calculator and I got $s=3$, but I want to know how to do it step by step. The problem is kind of complex: ...
1
vote
2answers
31 views

Pink Kangaroo Maths Challenge: Ria Bakes Six Raspberry Pies

I have been doing some practice papers for an upcoming UKMT Maths Challenge. There's one question I can't seem to grasp. I'm not sure entirely sure where to start. I'm open to any ideas. Thank you ...
2
votes
1answer
42 views

Find the basis for the kernel and the image, for a linear mapping

Let $T : \Bbb{R}^3 → \Bbb{R}^3$ given by $$T(x, y, z) = (x + 2y − z, y + z, x + y − 2z).$$ Using Gauss-array and reducing the system of equations to row echelon form I got: $\{(3,-1,1)\}$ is a basis ...
2
votes
2answers
129 views

A unit square contains 1 million rectangles without any common points. Show that the total area of rectangles is less than 1.

"A unit square contains 1,000,000 rectangles without common points. Show that the total area of rectangles is less than 1." This statement is somewhat imprecise. Let's say that these are closed ...
2
votes
2answers
55 views

The Diophantine Equation: $x^3-3=k(x-3)$

I wish to know how to resolve the diophantine equation: $x^3-3=k(x-3)$ ? The problem is: Find all integers $x\ne3$ such that $x-3\mid x^3-3$. - From 250 Problem's in Elementary Number Theory, by ...
0
votes
1answer
27 views

One tap fills a pool. The other one empties it. It's a word problem.

In a pool there are two taps, one for filling and one for emptying. Once, when the pool was empty they opened the filling tap for $4$ hours. Afterwards, they opened by mistake the emptying tap and ...
3
votes
1answer
65 views

What type of functional equation is this?

I'm trying to solve the following functional equation $f\left(x\right)=A\mbox{ exp}\left\{ \int\frac{1}{f\left(x\right)x^{2}+Bx}dx\right\}$ where ...
0
votes
7answers
61 views

How do you work out the angle in this square?

I have labelled all the angles that I can work out. But I can't think of any other way to find the other angles without being 100% sure. Thank you! P.S. I have attached the official question - ...