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Category: Coordinate Geometry

Question-67983

Question Number 67983 by peter frank last updated on 03/Sep/19 Commented by Abdo msup. last updated on 03/Sep/19 $$\left.{b}\right)\:{let}\:{f}\left({x}\right)=\left(\frac{\mathrm{1}}{{x}}\right)^{{x}\:} \:\Rightarrow{f}\left({x}\right)={x}^{−{x}} \:={e}^{−{xln}\left({x}\right)} \\ $$$$\left.{f}\:{is}?{defined}\:{on}\:\right]\mathrm{0},+\infty\left[\right. \\ $$$${lim}_{{x}\rightarrow\mathrm{0}\:{and}\:{x}>\mathrm{0}}…

Question-133275

Question Number 133275 by mr W last updated on 20/Feb/21 Commented by mr W last updated on 20/Feb/21 $${A}\:{hall}\:{with}\:{horizontal}\:{smooth}\:{floor} \\ $$$${has}\:{a}\:{parabola}\:{shaped}\:{wall}\:{as}\:{shown}. \\ $$$${A}\:{ball}\:{is}\:{projected}\:{along}\:{the}\:{floor} \\ $$$${from}\:{point}\:{A}\:{and}\:{returns}\:{back}\:{to}\:{this}…

The-equation-of-an-ellipse-is-given-as-x-2-y-2xcot2-2-1-0-lt-lt-0-25pi-Show-that-the-minimum-and-maximum-distances-from-the-centre-to-the-circumference-of-this-ellipse-are-tan-and-cot

Question Number 2168 by Yozzi last updated on 06/Nov/15 $${The}\:{equation}\:{of}\:{an}\:{ellipse}\:{is}\:{given} \\ $$$${as}\: \\ $$$$\:\:{x}^{\mathrm{2}} +\left({y}+\mathrm{2}{xcot}\mathrm{2}\theta\right)^{\mathrm{2}} =\mathrm{1}\:\:\:\:\left(\mathrm{0}<\theta<\mathrm{0}.\mathrm{25}\pi\right). \\ $$$${Show}\:{that}\:{the}\:{minimum}\:{and}\:{maximum} \\ $$$${distances}\:{from}\:{the}\:{centre}\:{to}\:{the}\: \\ $$$${circumference}\:{of}\:{this}\:{ellipse}\:{are} \\ $$$${tan}\theta\:{and}\:{cot}\theta\:{respectively}.\: \\…

Find-the-ratio-over-one-revolution-of-the-distance-moved-by-a-wheel-rolling-on-a-flat-surface-to-the-distance-traced-out-by-a-point-on-its-circumference-

Question Number 2158 by Yozzis last updated on 05/Nov/15 $${Find}\:{the}\:{ratio},\:{over}\:{one}\:{revolution},\:{of}\:{the}\:{distance}\:{moved}\:{by} \\ $$$${a}\:{wheel}\:{rolling}\:{on}\:{a}\:{flat}\:{surface}\:{to}\:{the}\:{distance}\:{traced}\:{out}\:{by} \\ $$$${a}\:{point}\:{on}\:{its}\:{circumference}.\: \\ $$ Commented by ssahoo last updated on 06/Nov/15 $$\mathrm{Wheel}\:\mathrm{distance}=\mathrm{2}\pi{r} \\…

Question-132809

Question Number 132809 by mr W last updated on 17/Feb/21 Commented by mr W last updated on 18/Feb/21 $${a}\:{mountain}\:{has}\:{the}\:{shape}\:{of}\:{a}\:{right} \\ $$$${circular}\:{cone}\:{as}\:{shown}\:\left({h}>\sqrt{\mathrm{3}}{r}\right). \\ $$$${from}\:{point}\:{A}\:{to}\:{point}\:{B}\:{two} \\ $$$${sightseeing}\:{roads}\:{one}\:{time}\:{around}…

Question-132433

Question Number 132433 by john_santu last updated on 14/Feb/21 Answered by liberty last updated on 14/Feb/21 $$\mathrm{by}\:\mathrm{using}\:\mathrm{Cosine}\:\mathrm{of}\:\mathrm{law}\: \\ $$$$\:\left(\mathrm{r}−\mathrm{0}.\mathrm{5}\right)^{\mathrm{2}} =\mathrm{0}.\mathrm{5}^{\mathrm{2}} +\left(\sqrt{\mathrm{2}}−\mathrm{r}\right)^{\mathrm{2}} −\mathrm{2}×\mathrm{0}.\mathrm{5}×\left(\sqrt{\mathrm{2}}−\mathrm{r}\right)\mathrm{cos}\:\mathrm{45}° \\ $$$$\cancel{\mathrm{r}^{\mathrm{2}} }−\mathrm{r}+\cancel{\frac{\mathrm{1}}{\mathrm{4}}}=\cancel{\frac{\mathrm{1}}{\mathrm{4}}}+\mathrm{2}−\mathrm{2}\sqrt{\mathrm{2}}\mathrm{r}+\cancel{\mathrm{r}^{\mathrm{2}}…

Find-the-circumference-of-an-ellipse-x-2-2-16-y-2-25-1-

Question Number 132402 by bramlexs22 last updated on 14/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{circumference}\:\mathrm{of}\:\mathrm{an} \\ $$$$\mathrm{ellipse}\:\frac{\left(\mathrm{x}−\mathrm{2}\right)^{\mathrm{2}} }{\mathrm{16}}+\frac{\mathrm{y}^{\mathrm{2}} }{\mathrm{25}}\:=\:\mathrm{1} \\ $$ Commented by mr W last updated on 14/Feb/21 $${the}\:{perimeter}\:{of}\:{an}\:{ellipse}\:{can}\:{not}…

Question-132131

Question Number 132131 by Ar Brandon last updated on 11/Feb/21 Commented by Ar Brandon last updated on 11/Feb/21 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{relation}\:\mathrm{between}\:\mathrm{the}\:\mathrm{areas}\:\mathrm{of}\: \\ $$$$\mathrm{triangle}\:\mathrm{ABC}\:\mathrm{and}\:\mathrm{triangle}\:\mathrm{A}'\mathrm{B}'\mathrm{C}' \\ $$ Commented by…