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Question-8387

Question Number 8387 by arinto27 last updated on 09/Oct/16 Answered by ridwan balatif last updated on 10/Oct/16 $$\mathrm{1}.\mathrm{f}\left(\mathrm{x}\right)=\mathrm{5x}+\mathrm{1} \\ $$$$\:\:\:\:\:\:\mathrm{y}\:\:\:=\mathrm{5x}+\mathrm{1} \\ $$$$\:\:\:\:\:\:\mathrm{x}\:\:\:=\frac{\mathrm{y}−\mathrm{1}}{\mathrm{5}} \\ $$$$\mathrm{f}^{−\mathrm{1}} \left(\mathrm{x}\right)=\frac{\mathrm{x}−\mathrm{1}}{\mathrm{5}}\Leftrightarrow\mathrm{f}^{−\mathrm{1}}…

ABCD-is-a-rectangle-such-that-AD-2AB-and-its-center-is-O-H-is-the-top-of-a-pyramid-which-has-ABCD-as-base-All-lateral-faces-are-isosceles-triangles-planes-HAB-and-HCD-are-i-have-joined-a-g

Question Number 139419 by mathocean1 last updated on 26/Apr/21 $${ABCD}\:{is}\:{a}\:{rectangle}\:{such}\:{that}\: \\ $$$${AD}=\mathrm{2}{AB}\:{and}\:{its}\:{center}\:{is}\:{O}.\: \\ $$$${H}\:{is}\:{the}\:{top}\:{of}\:{a}\:{pyramid}\:{which} \\ $$$${has}\:{ABCD}\:{as}\:{base}.\:{All}\:{lateral} \\ $$$${faces}\:{are}\:{isosceles}\:{triangles}.\:{planes} \\ $$$$\left({HAB}\right)\:{and}\:\left({HCD}\right)\:{are}\:\bot. \\ $$$${i}\:{have}\:{joined}\:{a}\:{graphic}. \\ $$$$\mathrm{1}.\:{show}\:{that}\:\left({OH}\right)\bot\left({ABC}\right). \\…

0-pi-2-cos-2-x-cos-x-pi-4-dx-

Question Number 139414 by mathdanisur last updated on 26/Apr/21 $$\underset{\:\mathrm{0}} {\overset{\:\pi/\mathrm{2}} {\int}}\frac{{cos}^{\mathrm{2}} {x}}{{cos}\left({x}−\pi/\mathrm{4}\right)}\:{dx} \\ $$ Commented by mr W last updated on 27/Apr/21 $$\frac{\mathrm{1}}{\mathrm{2}}\left[\mathrm{ln}\:\frac{\mathrm{1}+\mathrm{sin}\:\left({x}−\frac{\pi}{\mathrm{4}}\right)}{\mathrm{1}−\mathrm{sin}\:\left({x}−\frac{\pi}{\mathrm{4}}\right)}\right]_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}}…