Question Number 63682 by Annmuema last updated on 07/Jul/19 $${given}\:{diameter}\:\mathrm{25}{mm} \\ $$$${half}\:{of}\:{the}\:{drill}\:{point}\:{angle}\:=\mathrm{60} \\ $$$${cutting}\:{velocity}=\mathrm{44000}{mm}/{minute} \\ $$$${length}=\mathrm{60}{mm} \\ $$$${feedrate}=\mathrm{0}.\mathrm{25}{mm}/{revolution} \\ $$$${determine}\:{the}\:{time}\:{needed}\:{to}\:{drill}\:{a}\:{through}\:{hole} \\ $$ Terms of Service…
Question Number 129181 by liberty last updated on 13/Jan/21 $$\:\mathrm{Given}\:\mathrm{tan}\:^{\mathrm{2}} \mathrm{x}−\mathrm{5tan}\:\mathrm{x}=\mathrm{3}\:\mathrm{has}\:\mathrm{the}\:\mathrm{roots}\: \\ $$$$\mathrm{are}\:\mathrm{x}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{x}_{\mathrm{2}} .\:\mathrm{Find}\:\mid\:\mathrm{cos}\:\mathrm{x}_{\mathrm{1}} .\mathrm{cos}\:\mathrm{x}_{\mathrm{2}} \:\mid\:. \\ $$ Commented by MJS_new last updated on…
Question Number 63643 by vajpaithegrate@gmail.com last updated on 06/Jul/19 $$\mathrm{P}\left(\alpha,\beta\right)\:\mathrm{Q}\left(\gamma,\delta\right)\:\mathrm{are}\:\mathrm{two}\:\mathrm{points}\:\mathrm{lie}\:\mathrm{on}\:\mathrm{curve} \\ $$$$\mathrm{tan}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{y}\right)+\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}+\mathrm{y}\right)+\mathrm{y}^{\mathrm{2}} +\mathrm{2y}=\mathrm{0}\:\mathrm{on} \\ $$$$\mathrm{XY}\:\mathrm{plane}.\mathrm{If}\:\mathrm{d}=\mathrm{PQ}\:\mathrm{then}\:\mathrm{cos}\:\mathrm{d}= \\ $$$$\mathrm{ans}:\pm\mathrm{2n}\pi,\mathrm{n}\in\mathrm{N} \\ $$ Answered by MJS last…
Question Number 129073 by amns last updated on 12/Jan/21 $$\boldsymbol{{Prove}}\:\boldsymbol{{that}}: \\ $$$${sec}^{\mathrm{4}} \theta\:−\:{sec}^{\mathrm{2}} \theta\:=\:{tan}^{\mathrm{4}} \theta\:+\:{tan}^{\mathrm{2}} \theta \\ $$$${Please}\:{help}\:{me}\:{quickly}! \\ $$ Commented by benjo_mathlover last updated…
Question Number 129070 by benjo_mathlover last updated on 12/Jan/21 $$\:\mathrm{Solve}\:\mathrm{2cos}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{2x}\:=\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{3}}\:−\mathrm{3x}\right) \\ $$ Answered by liberty last updated on 12/Jan/21 $$\:\Leftrightarrow\:\mathrm{2cos}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{2x}\:=\:\mathrm{cos}\:\left(\frac{\pi}{\mathrm{3}}−\mathrm{3x}\right) \\ $$$$\:\Leftrightarrow\:\mathrm{cos}\:\mathrm{3x}+\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{3x}+\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{sin}\:\mathrm{3x} \\ $$$$\:\Leftrightarrow\:\mathrm{cos}\:\mathrm{x}\:=\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{sin}\:\mathrm{3x}−\frac{\mathrm{1}}{\mathrm{2}}\mathrm{cos}\:\mathrm{3x}\: \\…
Question Number 129063 by benjo_mathlover last updated on 12/Jan/21 $$\:\mathrm{If}\:\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{5}} \\ $$$$\:\mathrm{then}\:\begin{cases}{\mathrm{sin}\:\mathrm{x}=?}\\{\mathrm{cos}\:\mathrm{x}=?}\end{cases} \\ $$ Answered by liberty last updated on 12/Jan/21 $$\:\left(\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{25}}\:\Rightarrow\mathrm{1}−\mathrm{2sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{1}}{\mathrm{25}} \\ $$$$\:\mathrm{let}\:\begin{cases}{{p}=\mathrm{5sin}\:{x}}\\{{q}=\mathrm{5cos}\:{x}}\end{cases}\:{then}\:\mathrm{we}\:\mathrm{have}\:\begin{cases}{{p}−{q}=\mathrm{1}}\\{{pq}=\mathrm{12}}\end{cases}…
Question Number 129051 by oustmuchiya@gmail.com last updated on 12/Jan/21 $${prove}\:{that}\:\frac{\mathrm{1}+\boldsymbol{{sinx}}}{\boldsymbol{{sinxcosx}}}= \\ $$$$\boldsymbol{{tanx}}+\boldsymbol{{cotx}}+\boldsymbol{{secx}}\:\boldsymbol{{hence}} \\ $$$$\boldsymbol{{differentiate}}\:\boldsymbol{{the}}\:\boldsymbol{{function}} \\ $$ Answered by mindispower last updated on 12/Jan/21 $$\mathrm{1}={cos}^{\mathrm{2}} \left({x}\right)+{sin}^{\mathrm{2}}…
Question Number 129019 by bramlexs22 last updated on 12/Jan/21 $$\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\mathrm{3}\left(\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{4}} +\mathrm{6}\left(\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\right)^{\mathrm{2}} + \\ $$$$\:\mathrm{4}\left(\mathrm{sin}\:^{\mathrm{6}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{6}} \mathrm{x}\right). \\ $$ Answered by MJS_new last updated…
Question Number 63466 by vajpaithegrate@gmail.com last updated on 04/Jul/19 $$\mathrm{If}\:\mathrm{A}=\mathrm{sin}^{\mathrm{28}} \theta+\mathrm{cos}^{\mathrm{36}} \theta\:\mathrm{then} \\ $$$$\mathrm{Ans}:\:\mathrm{0}<\mathrm{A}\leqslant\mathrm{1} \\ $$ Commented by MJS last updated on 05/Jul/19 $$\mathrm{0}\leqslant\mathrm{cos}^{\mathrm{36}} \:\theta\:\leqslant\mathrm{1}…
Question Number 128998 by bramlexs22 last updated on 12/Jan/21 $$\:\mathrm{Given}\:\mathrm{sin}\:\mathrm{x}\:+\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{5}}{\mathrm{6}}\:.\:\mathrm{Find} \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\frac{\mathrm{1}}{\mathrm{sin}\:\mathrm{x}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\:\mathrm{x}}\:. \\ $$ Answered by liberty last updated on 12/Jan/21 $$\mathrm{From}\:\mathrm{condition}\:\mathrm{sin}\:\mathrm{x}\:+\:\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{5}}{\mathrm{6}} \\ $$$$\:\mathrm{we}\:\mathrm{get}\:\mathrm{1}+\mathrm{2sin}\:\mathrm{x}\:\mathrm{cos}\:\mathrm{x}\:=\:\frac{\mathrm{25}}{\mathrm{36}} \\…