Question Number 175766 by BaliramKumar last updated on 06/Sep/22 $${Number}\:{of}\:\:{even}\:{composite}\:{factors}\:{of}\:\mathrm{2520}? \\ $$ Commented by mr W last updated on 06/Sep/22 $$\mathrm{2520}=\mathrm{2}^{\mathrm{3}} ×\mathrm{3}^{\mathrm{2}} ×\mathrm{5}×\mathrm{7} \\ $$$${for}\:{even}\:{factors}\:\mathrm{2}\:{must}\:{be}\:{contained}…
Question Number 175758 by Stephan last updated on 06/Sep/22 Answered by Jamshidbek last updated on 06/Sep/22 $$\mathrm{Solution}. \\ $$$$\mathrm{we}\:\mathrm{know}\:\mathrm{tr}\left(\mathrm{XY}\right)=\mathrm{tr}\left(\mathrm{YX}\right)\:\Rightarrow\:\mathrm{tr}\left(\mathrm{XY}\right)=\mathrm{1} \\ $$$$\mathrm{U}+\mathrm{V}=\mathrm{1}\:\left[\mathrm{1}\right] \\ $$$$\mathrm{det}\left(\mathrm{XY}\right)=\mathrm{det}\left(\mathrm{X}\right)\mathrm{det}\left(\mathrm{Y}\right) \\ $$$$\mathrm{det}\left(\mathrm{YX}\right)=\mathrm{det}\left(\mathrm{X}\right)\mathrm{det}\left(\mathrm{Y}\right)…
Question Number 110181 by Rio Michael last updated on 27/Aug/20 $$\mathrm{Given}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{two}\:\mathrm{circles} \\ $$$${C}_{\mathrm{1}} :\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:−\mathrm{6}{x}−\mathrm{4}{y}\:+\:\mathrm{9}\:=\:\mathrm{0}\:\mathrm{and}{C}_{\mathrm{2}} \::\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{6}{y}\:+\:\mathrm{9}\:=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{common}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{both}\:\mathrm{circles}. \\ $$ Commented by…
Question Number 109950 by 675480065 last updated on 26/Aug/20 Answered by Aziztisffola last updated on 26/Aug/20 $$\:\left(\mathrm{i}\right)\:\left(\mathrm{x}−\mathrm{1}\right)^{\mathrm{2}} >\mathrm{0}\:\Rightarrow\:\mathrm{x}^{\mathrm{2}} −\mathrm{2x}+\mathrm{1}>\mathrm{0} \\ $$$$\:\Rightarrow\mathrm{x}^{\mathrm{2}} >\mathrm{2x}−\mathrm{1}\:\underset{\mathrm{2x}−\mathrm{1}>\mathrm{1}} {\overset{\mathrm{x}>\mathrm{1}} {\Rightarrow}}\:\:\:\:\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{2x}−\mathrm{1}}>\mathrm{1}…
Question Number 44325 by Rio Michael last updated on 26/Sep/18 Commented by Rio Michael last updated on 26/Sep/18 $${The}\:{farm}\:{land}\:{above}\:{has}\:{lenght}\:\mathrm{80}{m}\:{and}\:{width}\:\mathrm{25}{m},{it}\: \\ $$$${seperated}\:{by}\:{paths}\:{of}\:{width}\:\mathrm{1}{m}\:{to}\:{two}\:{farm}\:{lands}\:{as}\:{shown} \\ $$$${above}.{find}\:{the}\:{total}\:{area}\:{of}\:{the}\:{paths}. \\ $$…
Question Number 44324 by Rio Michael last updated on 26/Sep/18 $$\:\:\:\:\:\:\:\:\:\mathrm{5}\:\mathrm{2}\:{a} \\ $$$$\:\:\:\:+\:\:\:\:\mathrm{3}\:\:\mathrm{5} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\_\_\_\:\:\:\:\:{the}\:{addition}\:{on}\:{the}\:{left}\:{is}\:{in}\:{base}\:\mathrm{6}.{find}\:{a}. \\ $$$$\:\:\:\:\:\:\:\:\mathrm{1001} \\ $$ Answered by MJS last updated on…
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Question Number 44222 by Necxx last updated on 23/Sep/18 $${A}\:{man}\:{borrowed}\:{x}\:{at}\:\mathrm{5\%}\:{per}\:{annum} \\ $$$${simple}\:{interest}.{He}\:{paid}\:\mathrm{198000}\: \\ $$$${after}\:\mathrm{2}{years}.{Calculate}\:_{} \\ $$$$\left.{a}\right){the}\:{value}\:{of}\:{x} \\ $$$$\left.{b}\right){simple}\:{interest} \\ $$ Answered by olj55336@awsoo.com last updated…
Question Number 109746 by Joel574 last updated on 25/Aug/20 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{{n}\:=\:\mathrm{0}} {\overset{\mathrm{2020}} {\sum}}\:\left[\frac{\mathrm{2}^{{n}} }{\mathrm{1}\:+\:\mathrm{3}^{\left(\mathrm{2}^{{n}} \right)} }\right] \\ $$ Commented by Her_Majesty last updated on…
Question Number 44094 by peter frank last updated on 21/Sep/18 Commented by tanmay.chaudhury50@gmail.com last updated on 22/Sep/18 $${is}\:{it}\:{z}^{\mathrm{5}} \:\:\:{or}\:{z}^{\mathrm{3}} \:\:\:{pls}\:{clarify} \\ $$ Commented by peter…