## A Tough Sequence Question

This Possible Solution is by Arunaa Mohandass This entirely “different” possible solution is by me. 🙂 ...

## A Tough Sequence Question

This Possible Solution is by Arunaa Mohandass This entirely “different” possible solution is by me. 🙂 ...

## Brute Force in solving a Math Olympiad-type problem

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## A Tough Geometry Problem

Question Triangle ABC has AC = BC, angle(ACB) = 96 degrees. D is a point in triangle ABC such that angle(DAB) = 18 degrees and angle(DBA) = 30 degrees. What is the measure (in degrees) of angle(ACD)? Solution The key in such geometry problems is to note the given values. It might...

## A Math Proportion Quiz Question

Question If a hen and a half can lay an egg and a half in a day and a half, how many eggs can six hens lay in seven days? Answer Just write the sentences and you will get the answer!? 1.5 hen lays 1.5 eggs in 1.5 day Now think. Now four...

## Trigonometrical Proof Question

Question You have a triangle RST. Prove SinR^2 + CosR^2 = 1 given ST is perpendicular to RT. Answer Firstly, sin R = opposite/hypotenuse and cos R = adjacent/hypotenuse Square and add, to obtain, sin^2 R + cos^2 R = (ST)^2/(SR)^2 + (RT)^2/(SR)^2 sin^2 R + cos^2 R = [(ST)^2 + (RT)^2 ] /...

## A Number Theory Problem: “How many numbers greater than 3000 can be formed from 1,2,3,4,5 without repeating any of them? How many will be even?”

Comments Off on A Number Theory Problem: “How many numbers greater than 3000 can be formed from 1,2,3,4,5 without repeating any of them? How many will be even?”Answer There are two type of numbers greater than 3000 that can be formed here namely, 4 digit numbers and 5 digit numbers,. Note that no repetition allowed. For the 4 digit numbers, First digit can be filled in ‘3’ ways ( from either 3,4, or 5 ) Second digit can be filled in...

## A Diophantine Equation: “How can I find all natural numbers a &b such that a^2 + a + 1 = b^2?”

Comments Off on A Diophantine Equation: “How can I find all natural numbers a &b such that a^2 + a + 1 = b^2?”Answer We assume “natural numbers here includes the number zero” (an old convention – may not be valid today!) If not, there are no solutions! We proceed as follows: a^2 + a + 1 = b^2 Rewrite as, a^2 + 2 a + 1 = b^2 + a ( a + 1 ) ^2...

## Function: Range Problem

Question What is the range of the function f ( x ) = xsquared + 4 when the domain is (-2, 5, 7 )?? Answer Range is the values that a function can take given a domain for its ‘x’ or object value. In our case, f ( x ) = xsquared...

## In triangle ABC, angle ABC=15 degrees, angle ACB=30 degrees, AD is the median to side BC, A-D-C. angle BAD=?

Comments Off on In triangle ABC, angle ABC=15 degrees, angle ACB=30 degrees, AD is the median to side BC, A-D-C. angle BAD=?Answer We will use the Sine Rule. In triangle ABD, AD / sin(ABD) = BD / sin(BAD) So AD / BD = sin(ABD) / sin(BAD) In triangle ADC, AD / sin(ACD) = CD / sin(CAD) and AD / CD = sin(ACD) / sin(CAD) Since BD = CD, ( because D is median in BC...

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