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Author: Tinku Tara

If-n-p-q-Z-and-p-and-q-are-coprimes-then-prove-that-HCF-of-n-p-1-and-n-q-1-is-n-1-Assume-n-gt-1-

Question Number 3296 by prakash jain last updated on 09/Dec/15 $$\mathrm{If}\:{n},{p},{q}\in\mathbb{Z}^{+} \:\mathrm{and}\:{p}\:\mathrm{and}\:{q}\:\mathrm{are}\:\mathrm{coprimes}, \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{HCF}\:\mathrm{of}\:\left({n}^{{p}} −\mathrm{1}\right)\:\mathrm{and}\:\left({n}^{{q}} −\mathrm{1}\right)\:\mathrm{is}\:\left({n}−\mathrm{1}\right). \\ $$$$\mathrm{Assume}\:{n}>\mathrm{1}. \\ $$ Commented by Rasheed Soomro last…

The-square-ABCD-has-side-equal-to-1-and-the-distance-AP-is-1-8-Calculate-the-side-of-the-equilateral-triangle-PMN-inscribed-in-the-square-

Question Number 68831 by Maclaurin Stickker last updated on 15/Sep/19 $$\mathrm{The}\:\mathrm{square}\:{ABCD}\:\mathrm{has}\:\mathrm{side}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{1} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{distance}\:{AP}\:\:\mathrm{is}\:\:\frac{\mathrm{1}}{\mathrm{8}}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{side}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equilateral} \\ $$$$\mathrm{triangle}\:{PMN}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{the}\:\mathrm{square}. \\ $$ Commented by Maclaurin Stickker last updated…

A-curve-is-defined-by-f-x-What-is-the-length-of-curve-from-x-a-to-x-b-

Question Number 3291 by Rasheed Soomro last updated on 09/Dec/15 $$\mathcal{A}\:{curve}\:{is}\:{defined}\:\:{by}\:{f}\left({x}\right).\mathcal{W}{hat}\:{is}\:{the}\:{length} \\ $$$${of}\:{curve}\:{from}\:{x}={a}\:\:{to}\:\:{x}={b}\:? \\ $$ Answered by 123456 last updated on 09/Dec/15 $$\mathrm{if}\:{f}\:\mathrm{is}\:\mathrm{differentiable} \\ $$$$\underset{{a}}…

For-a-triangle-with-perpandicular-height-h-and-base-length-b-the-area-of-the-triangle-is-given-by-A-1-2-hb-Why-is-this-the-case-I-understand-that-two-identicle-triangles-can-construct-a-rectangl

Question Number 3280 by Filup last updated on 09/Dec/15 $$\mathrm{For}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{with}\:\mathrm{perpandicular} \\ $$$$\mathrm{height}\:{h}\:\mathrm{and}\:\mathrm{base}\:\mathrm{length}\:{b},\:\mathrm{the}\: \\ $$$$\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by}: \\ $$$${A}=\frac{\mathrm{1}}{\mathrm{2}}{hb} \\ $$$$ \\ $$$$\mathrm{Why}\:\mathrm{is}\:\mathrm{this}\:\mathrm{the}\:\mathrm{case}? \\ $$$$\mathrm{I}\:\mathrm{understand}\:\mathrm{that}\:\mathrm{two}\:\mathrm{identicle}\:\mathrm{triangles} \\ $$$$\mathrm{can}\:\mathrm{construct}\:\mathrm{a}\:{rectangle},\:\mathrm{so}\:\mathrm{the}\:\mathrm{area} \\…