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Category: Arithmetic

A-plant-group-of-company-is-to-convey-a-machinery-from-city-X-with-co-ordinate-300-200-to-city-Z-with-co-ordinate-700-900-The-machinery-can-be-air-lifted-at-a-cost-of-9-per-kilometer-or-through

Question Number 9776 by tawakalitu last updated on 01/Jan/17 $$\mathrm{A}\:\mathrm{plant}\:\mathrm{group}\:\mathrm{of}\:\mathrm{company}\:\mathrm{is}\:\mathrm{to}\:\mathrm{convey}\:\mathrm{a}\: \\ $$$$\mathrm{machinery}\:\mathrm{from}\:\mathrm{city}\:\mathrm{X}\:\mathrm{with}\:\mathrm{co}\:\mathrm{ordinate} \\ $$$$\left(\mathrm{300},\mathrm{200}\right)\:\mathrm{to}\:\mathrm{city}\:\mathrm{Z}\:\mathrm{with}\:\mathrm{co}\:\mathrm{ordinate}\:\left(\mathrm{700},\mathrm{900}\right). \\ $$$$\mathrm{The}\:\mathrm{machinery}\:\mathrm{can}\:\mathrm{be}\:\mathrm{air}\:\mathrm{lifted}\:\mathrm{at}\:\mathrm{a}\:\mathrm{cost}\:\mathrm{of} \\ $$$$#\mathrm{9}\:\mathrm{per}\:\mathrm{kilometer}\:\mathrm{or}\:\mathrm{through}\:\mathrm{city}\:\mathrm{Y}\:\mathrm{with} \\ $$$$\mathrm{co}\:\mathrm{ordinate}\:\left(\mathrm{700},\mathrm{200}\right)\:\mathrm{by}\:\mathrm{an}\:\mathrm{articulated}\:\mathrm{truck} \\ $$$$\mathrm{at}\:\mathrm{a}\:\mathrm{cost}\:\mathrm{of}\:#\mathrm{7}\:\mathrm{per}\:\mathrm{kilometer}.\: \\ $$$$\mathrm{Determine}\:\mathrm{the}\:\mathrm{route}\:\mathrm{that}\:\mathrm{is}\:\mathrm{least}\:\mathrm{expensive}. \\…

Question-9752

Question Number 9752 by tawakalitu last updated on 30/Dec/16 Answered by mrW last updated on 31/Dec/16 $$\mathrm{let}\:\mathrm{a}_{\mathrm{1}} \:\mathrm{be}\:\mathrm{the}\:\mathrm{first}\:\mathrm{term}\:\mathrm{and} \\ $$$$\mathrm{d}\:\mathrm{the}\:\mathrm{common}\:\mathrm{difference}\:\mathrm{of}\:\mathrm{the}\:\mathrm{A}.\mathrm{P}. \\ $$$$ \\ $$$$\mathrm{N}=\frac{\left[\mathrm{2a}_{\mathrm{1}} +\left(\mathrm{n}−\mathrm{1}\right)\mathrm{d}\right]×\mathrm{n}}{\mathrm{2}}…

Prove-that-1-2-5-3-6-1-3-1-2-5-3-6-1-3-2-

Question Number 140774 by ajfour last updated on 12/May/21 $${Prove}\:{that} \\ $$$$\:\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}+\frac{\mathrm{5}}{\mathrm{3}\sqrt{\mathrm{6}}}\right)^{\mathrm{1}/\mathrm{3}} +\left(\frac{\mathrm{1}}{\:\sqrt{\mathrm{2}}}−\frac{\mathrm{5}}{\mathrm{3}\sqrt{\mathrm{6}}}\right)^{\mathrm{1}/\mathrm{3}} =\:\sqrt{\mathrm{2}} \\ $$ Commented by ajfour last updated on 12/May/21 $${All}\:{are}\:{Excellent}\:{solutions}\:: \\…

f-1-f-2-f-3-f-n-n-2-f-n-n-gt-1-f-1-2016-So-f-2016-

Question Number 9517 by Joel575 last updated on 12/Dec/16 $${f}\left(\mathrm{1}\right)\:+\:{f}\left(\mathrm{2}\right)\:+\:{f}\left(\mathrm{3}\right)\:+\:…\:+\:{f}\left({n}\right)\:=\:{n}^{\mathrm{2}} .\:{f}\left({n}\right) \\ $$$${n}\:>\:\mathrm{1};\:{f}\left(\mathrm{1}\right)\:=\:\mathrm{2016} \\ $$$$\mathrm{So},\:{f}\left(\mathrm{2016}\right)\:=\:? \\ $$ Commented by sou1618 last updated on 12/Dec/16 $$…

S-r-12-12r-1-12r-2-12r-3-12r-4-with-1-lt-r-lt-1-If-S-a-S-a-2016-with-1-lt-a-lt-1-What-is-the-value-of-S-a-S-a-

Question Number 9484 by Joel575 last updated on 10/Dec/16 $$\mathrm{S}\left({r}\right)\:=\:\mathrm{12}\:+\:\mathrm{12}{r}^{\mathrm{1}} \:+\:\mathrm{12}{r}^{\mathrm{2}} \:+\:\mathrm{12}{r}^{\mathrm{3}} \:+\:\mathrm{12}{r}^{\mathrm{4}} \:+\:… \\ $$$$\mathrm{with}\:−\mathrm{1}\:<\:{r}\:<\:\mathrm{1} \\ $$$$ \\ $$$$\mathrm{If}\:\:\mathrm{S}\left({a}\right)\:.\:\mathrm{S}\left(−{a}\right)\:=\:\mathrm{2016},\:\mathrm{with}\:−\mathrm{1}\:<\:{a}\:<\:\mathrm{1} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{S}\left({a}\right)\:+\:\mathrm{S}\left(−{a}\right)\:? \\ $$ Answered…

Question-9460

Question Number 9460 by tawakalitu last updated on 09/Dec/16 Answered by sou1618 last updated on 09/Dec/16 $$\sqrt{\mathrm{11}−\mathrm{2}}=\sqrt{\mathrm{10}+\mathrm{1}−\mathrm{2}}=\sqrt{\mathrm{9}}=\mathrm{3} \\ $$$$\sqrt{\mathrm{1111}−\mathrm{22}}=\sqrt{\mathrm{1000}+\mathrm{100}+\mathrm{10}+\mathrm{1}−\mathrm{20}−\mathrm{2}}=\sqrt{\mathrm{1089}}=\mathrm{33} \\ $$$$…… \\ $$$${X}=\sqrt{\mathrm{1111}……\mathrm{11}_{\mathrm{2000}{digits}} −\mathrm{22}…\mathrm{2}_{\mathrm{1000}{digits}} }…

The-hhpotenuse-of-a-right-angled-triangle-has-its-ends-at-the-points-1-3-and-4-1-Find-an-equation-of-the-legs-perpendicar-sides-of-the-triangle-

Question Number 74948 by vishalbhardwaj last updated on 04/Dec/19 $$\mathrm{The}\:\mathrm{hhpotenuse}\:\mathrm{of}\:\mathrm{a}\:\mathrm{right}\:\mathrm{angled}\:\mathrm{triangle} \\ $$$$\mathrm{has}\:\mathrm{its}\:\mathrm{ends}\:\mathrm{at}\:\mathrm{the}\:\mathrm{points}\:\left(\mathrm{1},\mathrm{3}\right)\:\mathrm{and}\:\left(−\mathrm{4},\mathrm{1}\right) \\ $$$$.\:\mathrm{Find}\:\mathrm{an}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{legs}\:\left(\mathrm{perpendicar}\right. \\ $$$$\left.\:\mathrm{sides}\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}. \\ $$ Answered by MJS last updated on 04/Dec/19…