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When-a-kichen-is-removed-from-an-oven-its-temperature-is-measured-at-300-0-F-Three-minutes-later-its-temperature-is-200-0-F-How-longwill-it-take-the-kitchen-to-cool-of-to-a-room-temperature-o

Question Number 194606 by pete last updated on 10/Jul/23 $$\mathrm{When}\:\mathrm{a}\:\mathrm{kichen}\:\mathrm{is}\:\mathrm{removed}\:\mathrm{from}\:\mathrm{an} \\ $$$$\:\mathrm{oven},\:\mathrm{its}\:\mathrm{temperature}\:\mathrm{is}\:\mathrm{measured}\:\mathrm{at} \\ $$$$\:\mathrm{300}^{\mathrm{0}} \mathrm{F}.\:\mathrm{Three}\:\mathrm{minutes}\:\mathrm{later},\:\mathrm{its} \\ $$$$\:\mathrm{temperature}\:\mathrm{is}\:\mathrm{200}^{\mathrm{0}} \mathrm{F}.\:\mathrm{How}\:\mathrm{longwill} \\ $$$$\:\mathrm{it}\:\mathrm{take}\:\mathrm{the}\:\mathrm{kitchen}\:\mathrm{to}\:\mathrm{cool}\:\mathrm{of}\:\mathrm{to}\:\mathrm{a}\: \\ $$$$\mathrm{room}\:\mathrm{temperature}\:\mathrm{of}\:\mathrm{70}^{\mathrm{0}} \mathrm{F}? \\ $$…

A-mass-of-12kg-rests-on-a-smooth-inclined-plane-which-is-6m-long-and-1m-high-The-mass-is-connected-by-a-light-inextensible-string-which-passes-over-a-smooth-pulley-fixed-at-the-top-of-the-plane-to-a-

Question Number 194563 by pete last updated on 10/Jul/23 $$\mathrm{A}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{12kg}\:\mathrm{rests}\:\mathrm{on}\:\mathrm{a}\:\mathrm{smooth}\:\mathrm{inclined} \\ $$$$\mathrm{plane}\:\mathrm{which}\:\mathrm{is}\:\mathrm{6m}\:\mathrm{long}\:\mathrm{and}\:\mathrm{1m}\:\mathrm{high}. \\ $$$$\mathrm{The}\:\mathrm{mass}\:\mathrm{is}\:\mathrm{connected}\:\mathrm{by}\:\mathrm{a}\:\mathrm{light}\:\mathrm{inextensible} \\ $$$$\mathrm{string}\:\mathrm{which}\:\mathrm{passes}\:\mathrm{over}\:\mathrm{a}\:\mathrm{smooth}\:\mathrm{pulley} \\ $$$$\mathrm{fixed}\:\mathrm{at}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{the}\:\mathrm{plane}\:\mathrm{to}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of} \\ $$$$\mathrm{4kg}\:\mathrm{which}\:\mathrm{is}\:\mathrm{hanging}\:\mathrm{freely}.\:\mathrm{With}\:\mathrm{the} \\ $$$$\mathrm{string}\:\mathrm{taut},\:\mathrm{the}\:\mathrm{system}\:\mathrm{is}\:\mathrm{released}\:\mathrm{from}\:\mathrm{rest}. \\ $$$$\mathrm{Using}\:\mathrm{Polya}\:\mathrm{problem}\:\mathrm{solving}\:\mathrm{approach} \\…

3-x-4-x-5-x-find-x-

Question Number 194499 by Mastermind last updated on 08/Jul/23 $$\mathrm{3}^{\mathrm{x}} \:+\:\mathrm{4}^{\mathrm{x}} \:=\:\mathrm{5}^{\mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{x}\:? \\ $$ Commented by Frix last updated on 08/Jul/23 $$\mathrm{I}\:\mathrm{am}\:\mathrm{a}\:\mathrm{bit}\:\mathrm{blind}\:\mathrm{today}…\:\mathrm{just}\:\mathrm{guessing}: \\…

Ques-1-Let-G-C-5-C-25-C-625-Determine-the-number-of-elements-of-each-order-in-G-Ques-2-List-the-abelian-groups-of-order-16-and-of-order-27-up-to-Isomorphism-Ques

Question Number 194058 by Mastermind last updated on 27/Jun/23 $$\mathrm{Ques}.\:\mathrm{1} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{Let}\:\mathrm{G}\:=\:\mathrm{C}_{\mathrm{5}} \:×\:\mathrm{C}_{\mathrm{25}} \:×\:\mathrm{C}_{\mathrm{625}} .\:\mathrm{Determine} \\ $$$$\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{elements}\:\mathrm{of}\:\mathrm{each}\:\mathrm{order}\:\mathrm{in}\:\mathrm{G} \\ $$$$ \\ $$$$\mathrm{Ques}.\:\mathrm{2} \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{List}\:\mathrm{the}\:\mathrm{abelian}\:\mathrm{groups}\:\mathrm{of}\:\mathrm{order}\:\mathrm{16} \\ $$$$\mathrm{and}\:\mathrm{of}\:\mathrm{order}\:\mathrm{27}\:\mathrm{up}\:\mathrm{to}\:\mathrm{Isomorphism}.…

Prove-that-sin-7-1-64-35sin-21sin3-7sin5-sin7-using-1-sin-e-i-e-i-2i-and-2-cos-isin-n-cos-n-sin-n-

Question Number 193960 by pete last updated on 25/Jun/23 $$\mathrm{Prove}\:\mathrm{that}\:\mathrm{sin}^{\mathrm{7}} \theta\:=\frac{\mathrm{1}}{\mathrm{64}}\left(\mathrm{35sin}\theta\:−\mathrm{21sin3}\theta\right. \\ $$$$+\mathrm{7sin5}\theta−\mathrm{sin7}\theta\:\:\mathrm{using} \\ $$$$\:\mathrm{1}.\:\mathrm{sin}\theta\:=\frac{\mathrm{e}^{\mathrm{i}\theta} −\mathrm{e}^{−\mathrm{i}\theta} }{\mathrm{2i}}\:\mathrm{and}\: \\ $$$$\mathrm{2}.\:\left(\mathrm{cos}\theta+\mathrm{isin}\theta\right)^{\mathrm{n}} \:=\:\mathrm{cos}\:\mathrm{n}\theta+\mathrm{sin}\:\mathrm{n}\theta \\ $$$$ \\ $$ Terms…