Question Number 118874 by bemath last updated on 20/Oct/20 $${In}\:{xy}−{plane}\:,\:{which}\:{of}\:{the}\:{following} \\ $$$${is}\:{the}\:{reflection}\:{of}\:{the}\:{graph} \\ $$$${of}\:{y}\:=\:\frac{\mathrm{1}+{x}}{{x}^{\mathrm{2}} +\mathrm{1}}\:{about}\:{the}\:{line}\:{y}=\mathrm{2}{x}.\: \\ $$ Answered by bramlexs22 last updated on 20/Oct/20 $${by}\:{transformation}\:{matrix}\:\begin{pmatrix}{\mathrm{cos}\:\mathrm{2}\theta\:\:\:\:\mathrm{sin}\:\mathrm{2}\theta}\\{\mathrm{sin}\:\mathrm{2}\theta\:\:−\mathrm{cos}\:\mathrm{2}\theta}\end{pmatrix}…
Question Number 118868 by bemath last updated on 20/Oct/20 $${If}\:{the}\:{graphs}\:{of}\:{y}={x}^{\mathrm{2}} +\mathrm{2}{ax}+\mathrm{6}{b}\: \\ $$$${and}\:{y}={x}^{\mathrm{2}} +\mathrm{2}{bx}+\mathrm{6}{a}\:{intersect}\:{at}? \\ $$$${only}\:{one}\:{point}\:{in}\:{the}\:{xy}−{plane} \\ $$$$,\:{what}\:{is}\:{the}\:{x}−{coordinate}\:{of}\:{the} \\ $$$${point}\:{of}\:{intersection}\:? \\ $$ Answered by bobhans…
Question Number 53323 by ajfour last updated on 20/Jan/19 Answered by mr W last updated on 20/Jan/19 $${y}=\frac{{x}^{\mathrm{2}} }{{a}}\:{with}\:{a}=\mathrm{1} \\ $$$${A}\left(\mathrm{0},{h}\right) \\ $$$${eqn}.\:{of}\:{big}\:{circle}: \\ $$$${ay}+\left({y}−{h}\right)^{\mathrm{2}}…
Question Number 184349 by alcohol last updated on 05/Jan/23 $${I}_{{n}} \:=\:\int_{\mathrm{0}} ^{\:\mathrm{1}} \left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{{n}} {dx} \\ $$$${Relate}\:{I}_{{n}} \:{and}\:{I}_{{n}−\mathrm{1}} \\ $$$${Find}\:{I}_{{n}} \:{in}\:{terms}\:{of}\:{n} \\ $$$${hence}\:{deduce}\:{that}\:\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}\frac{\left(−\mathrm{1}\right)^{{k}}…
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Question Number 183893 by Sulaymon last updated on 31/Dec/22 Commented by pablo1234523 last updated on 31/Dec/22 $${also}\:{from}\:{the}\:{graph}\:{it}\:{seems}\:{like}\:{a}>{b} \\ $$$${but}\:{none}\:{of}\:{the}\:{option}\:{satisfies}\:{it} \\ $$ Commented by mr W…
Question Number 52731 by ajfour last updated on 12/Jan/19 Commented by MJS last updated on 12/Jan/19 $$\mathrm{for}\:{b}={a}\:\left(\mathrm{circle}\right)\:\mathrm{the}\:\mathrm{equilateral}\:\mathrm{triangle}\:\mathrm{is} \\ $$$$\mathrm{the}\:\mathrm{one}\:\mathrm{with}\:\mathrm{minimum}\:\mathrm{perimeter}. \\ $$$$\mathrm{we}\:\mathrm{can}\:\mathrm{draw}\:\mathrm{an}\:\mathrm{equilateral}\:\mathrm{triangle}\:\mathrm{for}\:\mathrm{a} \\ $$$$\mathrm{circle}\:\mathrm{with}\:{r}={a}\:\mathrm{and}\:\mathrm{then}\:\mathrm{compress}\:\mathrm{with} \\ $$$$\mathrm{the}\:\mathrm{factor}\:\frac{{a}}{{b}}\:\left[{P}=\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:\rightarrow\:{P}'=\begin{pmatrix}{{x}}\\{\frac{{b}}{{a}}{y}}\end{pmatrix}\right]…
Question Number 183803 by Ar Brandon last updated on 30/Dec/22 Answered by mr W last updated on 30/Dec/22 Commented by mr W last updated on…
Question Number 52627 by ajfour last updated on 10/Jan/19 Commented by ajfour last updated on 10/Jan/19 $${Find}\:{radius}\:{of}\:{such}\:{a}\:{circle}. \\ $$ Answered by mr W last updated…