Find the Capacity of the Water Tank?
A water tank has three taps attached, $A,B$ and $D$. $A$ and $B$ fill the water tank completely in $\displaystyle\frac{25}{3}$ minutes and $\displaystyle\...
Apr 12, 2026 1 VIEWS
Topic: General
5104 Articles 
How is addition defined?
I've been reading On Numbers and Games and I noticed that Conway defines addition in his number system in terms of addition. Similarly in the analysi...
Apr 12, 2026 1 VIEWS
Identity Element of Subtraction (Solution Verification)
This is about an exercise from Norman L. Biggs Discrete Mathematics. One is asked to check which binary operations are valid when $*$ represents the usual...
Apr 12, 2026 1 VIEWS
When does a finite ring become a finite field?
I'm relatively new to ring theory so this is probably a simple question. Its easy to see that a finite ring that is commutative and has no-zero divis...
Apr 12, 2026 1 VIEWS
Finding the Mid-Point of the side of a square.
Given a square drawn on a piece of paper, is it possible to find the midpoint of one of its sides using the following tools: -A pencil (used ONLY to draw ...
Apr 12, 2026 1 VIEWS
Euler's formula for connected planar graphs
Euler's formula for connected planar graphs (i.e. a single connected component) states that $v-e+f=2$. State the generalization of Euler's formu...
Apr 12, 2026 1 VIEWS
Distance between point and line in the complex plane
Let $a,b$ be fixed complex numbers and let $L$ be the line $$L=\{a+bt:t\in\Bbb R\}.$$ Let $w\in\Bbb C\setminus L$. Let's calculate $$d(w,L)=\inf\{|w-...
Apr 12, 2026 1 VIEWS
How do I find the y intercept for $P(x)= (x-1)^2(x-3)$?
I am sketching a graph of this polynomial $P(x)= (x-1)^2(x-3)$. I have the zeros, and I have made a sign diagram. Thus, I have all my values except for th...
Apr 12, 2026 1 VIEWS
Is The Union of Intervals an Interval or not?
I have a question on union of intervals. My teacher says the union of intervals is not an interval. Is this always true? I mean $[0,2] \cup [4,5]$ is not ...
Apr 12, 2026 1 VIEWS
Solve for $\sin^2(x) = 3\cos^2(x)$
I am trying to solve the following equation for x. The textbook's answer and my answer differ and I keep getting the same answer. Could someone pleas...
Apr 12, 2026 2 VIEWS
maths - find vertices when 1 vertex and center point is given in polygon
I want to know if there is any general formula to find out vertices (co-ordinates) of a polygon (3 or more equal sides) when following is given: Co-ordina...
Apr 12, 2026 3 VIEWS
Volume of an octagonal dome
I need a way to find the volume of an octagonal dome. Can someone help me with the formula for that? Here's an example of the object I am trying to a...
Apr 12, 2026 2 VIEWS