Question Number 149031 by puissant last updated on 02/Aug/21 Answered by EDWIN88 last updated on 02/Aug/21 $$\Rightarrow\frac{\mathrm{1}+\mathrm{cos}\:\mathrm{2}{x}+\mathrm{1}+\mathrm{cos}\:\mathrm{4}{x}+\mathrm{1}+\mathrm{cos}\:\mathrm{6}{x}}{\mathrm{2}}=\mathrm{1} \\ $$$$\Rightarrow\mathrm{cos}\:\mathrm{6}{x}+\mathrm{cos}\:\mathrm{4}{x}+\mathrm{cos}\:\mathrm{2}{x}=−\mathrm{1} \\ $$$$\Rightarrow\mathrm{2cos}\:\mathrm{4}{x}\:\mathrm{cos}\:\mathrm{2}{x}+\mathrm{cos}\:\mathrm{4}{x}=−\mathrm{1} \\ $$$$\Rightarrow\mathrm{cos}\:\mathrm{4}{x}\left(\mathrm{2cos}\:\mathrm{2}{x}+\mathrm{1}\right)=−\mathrm{1} \\ $$$$\Rightarrow\left(\mathrm{2cos}\:^{\mathrm{2}}…
Question Number 17948 by b.e.h.i.8.3.417@gmail.com last updated on 12/Jul/17 Commented by mrW1 last updated on 12/Jul/17 $$\mathrm{area}\:\mathrm{of}\:\Delta\mathrm{ABC}=\mathrm{S}=\frac{\mathrm{1}}{\mathrm{2}}\mathrm{ah}_{\mathrm{a}} \\ $$$$\Rightarrow\frac{\mathrm{1}}{\mathrm{h}_{\mathrm{a}} }=\frac{\mathrm{1}}{\mathrm{2S}}\:\mathrm{a}=\mathrm{ka} \\ $$$$\mathrm{similarly} \\ $$$$\Rightarrow\frac{\mathrm{1}}{\mathrm{h}_{\mathrm{b}} }=\mathrm{kb}\:…
Question Number 17939 by ibraheem160 last updated on 12/Jul/17 $$\int{secxdx}\: \\ $$ Commented by prakash jain last updated on 12/Jul/17 $$\mathrm{sec}\:{x}=\frac{\mathrm{sec}\:{x}\left(\mathrm{sec}\:{x}+\mathrm{tan}\:{x}\right)}{\mathrm{sec}\:{x}+\mathrm{tan}\:{x}} \\ $$$$\int\mathrm{sec}\:{x}\:\mathrm{d}{x}=\int\frac{{d}\left(\mathrm{sec}\:{x}+\mathrm{tan}\:{x}\right)}{\mathrm{sec}\:{x}+\mathrm{tan}\:{x}} \\ $$…
Question Number 17935 by Rishabh#1 last updated on 12/Jul/17 $$\mathrm{Ball}\:{A}\:\mathrm{is}\:\mathrm{dropped}\:\mathrm{from}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{building}. \\ $$$$\mathrm{At}\:\mathrm{the}\:\mathrm{same}\:\mathrm{instant}\:\mathrm{ball}\:{B}\:\mathrm{is}\:\mathrm{thrown} \\ $$$$\mathrm{vertically}\:\mathrm{upwards}\:\mathrm{from}\:\mathrm{the}\:\mathrm{ground}. \\ $$$$\mathrm{When}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{collide},\:\mathrm{they}\:\mathrm{are}\:\mathrm{moving}\:\:\mathrm{in} \\ $$$$\mathrm{opposite}\:\mathrm{directions}\:\mathrm{and}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:{A}\left({u}\right) \\ $$$$\mathrm{is}\:\mathrm{twice}\:\mathrm{the}\:\mathrm{speed}\:\mathrm{of}\:{B}.\:\mathrm{The}\:\mathrm{relative}\: \\ $$$$\mathrm{velocity}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ball}\:\mathrm{just}\:\mathrm{before}\:\mathrm{collision} \\ $$$$\mathrm{and}\:\mathrm{relative}\:\mathrm{acceleration}\:\mathrm{between}\:\mathrm{them} \\…
Question Number 148993 by gsk2684 last updated on 02/Aug/21 $${if}\:{M}\:{is}\:{a}\:{point}\:{on}\:{the}\:{line}\:{y}={x}\:{and} \\ $$$${points}\:{P}\left(\mathrm{0},\mathrm{1}\right),{Q}\left(\mathrm{2},\mathrm{0}\right)\:{are}\:{such}\:{that} \\ $$$${PM}+{PQ}\:{is}\:{minimum}\:{then}\:{find}\:{P} \\ $$ Commented by mr W last updated on 02/Aug/21 $${i}\:{think}\:{the}\:{question}\:{should}\:{be}…
Question Number 83471 by mr W last updated on 02/Mar/20 Commented by mr W last updated on 02/Mar/20 $${The}\:{distances}\:{from}\:{a}\:{point}\:{M}\:{to}\:{the} \\ $$$${vertices}\:{of}\:{a}\:{given}\:{triangle}\:{with} \\ $$$${side}\:{lengthes}\:\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}}\:{are}\:\boldsymbol{{p}},\:\boldsymbol{{q}},\:\boldsymbol{{r}} \\ $$$${respectively}.…
Question Number 148991 by gsk2684 last updated on 02/Aug/21 $${The}\:{largest}\:{value}\:{of}\:{k}\:{for}\:{which}\: \\ $$$${the}\:{circle}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={k}^{\mathrm{2}} \:{lies}\:{completely} \\ $$$${in}\:{the}\:{interior}\:{of}\:{the}\:{parabola} \\ $$$${y}^{\mathrm{2}} =\mathrm{4}{x}+\mathrm{16}\:? \\ $$ Answered by mr…
Question Number 17901 by chux last updated on 12/Jul/17 Commented by chux last updated on 12/Jul/17 $$\mathrm{find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{big}\:\mathrm{and} \\ $$$$\mathrm{small}\:\mathrm{circle} \\ $$ Commented by chux last…
Question Number 17886 by b.e.h.i.8.3.417@gmail.com last updated on 11/Jul/17 Commented by b.e.h.i.8.3.417@gmail.com last updated on 12/Jul/17 $$\left.\mathrm{1}\right){circle}\:{radius}={R} \\ $$$$\left.\mathrm{2}\right){acute}\:{angle}\:{between}\:{chords}:{AB}\:,\:{CD}=\varphi \\ $$$${find}:\:{AP}^{\mathrm{2}} +{BP}^{\mathrm{2}} +{CP}^{\mathrm{2}} +{DP}^{\mathrm{2}} .…
Question Number 17884 by b.e.h.i.8.3.417@gmail.com last updated on 11/Jul/17 Commented by b.e.h.i.8.3.417@gmail.com last updated on 11/Jul/17 $${diagonals}\:{of}\:{trapezoid}:\:{ABCD},{create} \\ $$$$\mathrm{4}\:{triangles}.{area}\:{of}\:{two}\:{this}\:{triangles} \\ $$$${are}\:{equail}\:{to}:\:{a}^{\mathrm{2}} \:,{and}\:,\:{b}^{\mathrm{2}} . \\ $$$${find}\:{area}\:{of}\:{trapezoid}\:{in}\:{terms}\:{of}:\:{a},{b}.…