Author Archives: Sumant Sumant

About Sumant Sumant

I love Math and I am always looking forward to collaborate with fellow learners. If you need help learning math then please do contact me.

Find the radius of the Circle given these adjacent squares

Posted on June 26, 2024 by Sumant Sumant
Posted in Geometry | Tagged | Leave a comment

Perimeter of a triangle when Median is Perpendicular to the Angle Bisector

Posted on June 26, 2024 by Sumant Sumant

The side lengths of a triangle are consecutive integers, find the perimeter of the triangle if its known that a median of this triangle is perpendicular to the angle bisector

Posted in Geometry | Tagged , | Leave a comment

Total number of integer ordered pairs that satisfy the difference between Arithmetic mean and Geometric mean is 1

Posted on June 25, 2024 by Sumant Sumant

Suppose (a,b) are non negative integers such that and . Find the number of ordered pairs that satisfy the above condition. (Australian Mathematical Olympiad, 2020)

Posted in Algebra, Inequalities | Tagged , , | Leave a comment

Nested dodecagon problem

Posted on June 24, 2024 by Sumant Sumant

Two regular dodecagon.What fraction is not colored ?

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How to think about the proof (anbn)->(a,b) when

Posted on June 24, 2024 by Sumant Sumant

This is one of the standard proof in introductory analysis course about why the product of a converging sequence is a converging sequence. Here I am distilling how to think about the proof when you see the first time.

Posted in Proof, Real Analysis | Tagged | Leave a comment

Find the radius of the inscribed circle between a parabola and x axis

Posted on June 23, 2024 by Sumant Sumant
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Maximizing with ratio of slant height to radius

Posted on June 23, 2024 by Sumant Sumant

A cone has radius r and fixed slant height of s cm. Find the ratio s:r which maximizes the volume of the cone.

Posted in Calculus | Tagged , , , | Leave a comment

Max profit when total cost and selling cost are given

Posted on June 23, 2024 by Sumant Sumant

The total cost of producing a blanket per day is pounds and for this production level each blanket may be sold for pounds. How many blankets should be produced per day to maximize the total profit?

Posted in Calculus | Tagged , , , | Leave a comment

Related rate problem of a conical heap

Posted on June 23, 2024 by Sumant Sumant

Wheat runs from a hole in a silo at a constant rate and forms a conical heap whose base radius is treble it’s height After 1 minute the height of the heap is 20 cm. Find the rate at which … Continue reading →

Posted in Calculus | Tagged , , | Leave a comment

Coloring a 3 by 3 grid using two colors ( blue and orange) so that no row or column contains more than one orange color

Posted on June 23, 2024 by Sumant Sumant

Sumant colors each square in an empty 3 by 3 grid either blue or orange. Find the total number of ways to color the grid so that no toes or columns contain more than one orange.

Posted in Combinatorics | Tagged , , | Leave a comment