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
24 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
30 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
81 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
68 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
48 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
23 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
32 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, ...
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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
158 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
25 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
53 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
49 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
26 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
56 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
54 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
53 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
96 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
46 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 ...
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
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1answer
13 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
121 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
22 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
71 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: $$\frac{2^{...
1
vote
2answers
35 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
46 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
136 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 ...
3
votes
2answers
57 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
32 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
2answers
76 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 $f\left(x\right):\mathbb{R}_{+}\rightarrow\mathbb{R}...
0
votes
7answers
63 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 - ...
2
votes
4answers
87 views

Coin flipping problem

Suppose that you are flipping a coin endless times. what's the expected round where you would get the same side $3$ consecutive times? I'm guessing it would take $7$ flips to see either ...
2
votes
1answer
75 views

Let $1 + 2^m = 3^n$. What the max value of $(m+n)$?

How do I determine the maximum value of $(m+n)$ if $m$ and $n$ are natural numbers if $1 + 2^m = 3^n$ holds? I have got $\text {max} (m+n)$ to be $5$ so far, but I do not know how to determine whether ...
0
votes
2answers
43 views

Work and time problem

I came up with this problem: $150$ workers were employed to do a particular work. On first day, $150$ workers worked. On second day, $146$.. and each subsequent day, workers kept on decreasing by 4. ...
1
vote
1answer
22 views

Smallest number of groups to sniff

The question given: The sniffer dog at the airport stops beside a trolley piled high with 60 suitcases. One of the suitcases contains contraband peanuts. The dog can tell whether peanuts are hidden in ...
0
votes
0answers
35 views

$n$-couples of people in a row.

For the following problem, I feel my reasoning is something wrong, so I would like if it is in the right direction or if it needs to be rephrased/corrected. The problem reads: How many ways are ...
-1
votes
3answers
44 views

Solving two variables with one equation

I have been trying to solve the following equation, but I am still stuck after trying many different methods. I have been given this equation to solve: $$(1 + z^{-1})^4 (a + bz^{-1} + az^{-2}) - (1 -...
0
votes
1answer
32 views

How does one establish a path of least resistance when solving equations?

For certain systems of equations, it is obvious what the easiest way to organize and manipulate the equations should be. For instance, $$y = 10x + 5$$ $$2x + y = 125$$ So you take the first ...
0
votes
1answer
38 views

solving an equation $x^x= c$ [duplicate]

I would like to find a solution $x$ for $x^x = c$ where $c$ is a positive constant. Firstly I'm looking for an approximative solution when $c$ tends to infinity. Thank you in advance
8
votes
2answers
92 views

Find a succinct problem whose solution requires methods from many sub-branches of mathematics

Some mathematical problems require solution techniques from a single branch (sub-discipline) of mathematics. For instance, most problems in formal logic can be addressed by the methods of formal ...
1
vote
1answer
92 views

What is the optimal strategy when playing `head or tail` per team

Introduction Once a week, we are playing head or tail in my favorite bar. There are $N$ people in the room and each person is guessing whether ...