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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}}}…

Question-73872

Question Number 73872 by azizullah last updated on 16/Nov/19 Answered by $@ty@m123 last updated on 16/Nov/19 $${Rebate}\:{means}\:{part}\:{of}\:{income}\:{on} \\ $$$${which}\:{Income}\:{Tax}\:{is}\:{exempted}. \\ $$$${ATQ}, \\ $$$${Annual}\:{Income}={Rs}.\:\mathrm{8000}×\mathrm{12} \\ $$$$\:\:=\mathrm{96000}…

by-use-Gamma-function-prove-1-0-pi-8-cos-3-4xdx-1-6-2-0-pi-sin-6-x-2-cos-8-x-2-dx-5pi-2-11-

Question Number 139371 by mohammad17 last updated on 26/Apr/21 $${by}\:{use}\:{Gamma}\:{function}\:{prove}\: \\ $$$$ \\ $$$$\left(\mathrm{1}\right)\:\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{8}}} {cos}^{\mathrm{3}} \mathrm{4}{xdx}=\frac{\mathrm{1}}{\mathrm{6}} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\:\int_{\mathrm{0}} ^{\:\pi} {sin}^{\mathrm{6}} \left(\frac{{x}}{\mathrm{2}}\right){cos}^{\mathrm{8}} \left(\frac{{x}}{\mathrm{2}}\right){dx}=\frac{\mathrm{5}\pi}{\mathrm{2}^{\mathrm{11}}…