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Question Number 9822 by ridwan balatif last updated on 06/Jan/17 Answered by sandy_suhendra last updated on 06/Jan/17 $$\mathrm{f}\:'\left(\mathrm{x}\right)=\mathrm{k}\left(\mathrm{3x}^{\mathrm{2}} −\mathrm{12x}+\mathrm{9}\right)=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{x}^{\mathrm{2}} −\mathrm{4x}+\mathrm{3}=\mathrm{0} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{x}−\mathrm{3}\right)\left(\mathrm{x}−\mathrm{1}\right)=\mathrm{0} \\…
Question Number 9821 by ridwan balatif last updated on 06/Jan/17 Commented by prakash jain last updated on 08/Jan/17 $$\mathrm{Is}\:\mathrm{the}\:\mathrm{question} \\ $$$$\mathrm{Given}\:{f}\left({x}\right)={f}\left({x}+\mathrm{2}\right) \\ $$$$\mathrm{and}\:\int_{\mathrm{0}} ^{\mathrm{2}} {f}\left({x}\right){dx}={B}…
Question Number 140888 by Ahmed1hamouda last updated on 13/May/21 Answered by physicstutes last updated on 14/May/21 $$\left(\mathrm{i}\right)\:\mathrm{let}\:{M}\:=\:\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}&{−\mathrm{3}}\\{\mathrm{3}}&{−\mathrm{1}}&{\mathrm{5}}\\{\mathrm{4}}&{\mathrm{1}}&{{a}^{\mathrm{2}} −\mathrm{14}}\end{bmatrix} \\ $$$$\mathrm{for}\:\mathrm{no}\:\mathrm{solutions}\:,\:\mid{M}\mid\:=\:\mathrm{0} \\ $$$$\mathrm{thus}\:\:\:\begin{vmatrix}{\mathrm{1}}&{\mathrm{2}}&{−\mathrm{3}}\\{\mathrm{3}}&{−\mathrm{1}}&{\mathrm{5}}\\{\mathrm{4}}&{\mathrm{1}}&{{a}^{\mathrm{2}} −\mathrm{14}}\end{vmatrix}=\:\mathrm{0}\:\:\Rightarrow\:\mathrm{1}\begin{vmatrix}{−\mathrm{1}}&{\mathrm{5}}\\{\mathrm{1}}&{{a}^{\mathrm{2}} −\mathrm{14}}\end{vmatrix}−\mathrm{2}\begin{vmatrix}{\mathrm{3}}&{\mathrm{5}}\\{\mathrm{4}}&{{a}^{\mathrm{2}} −\mathrm{14}}\end{vmatrix}−\mathrm{3}\begin{vmatrix}{\mathrm{3}}&{−\mathrm{1}}\\{\mathrm{4}}&{\mathrm{1}}\end{vmatrix}=\mathrm{0}…
Question Number 9818 by j.masanja06@gmail.com last updated on 05/Jan/17 Commented by sandy_suhendra last updated on 06/Jan/17 $$\mathrm{the}\:\mathrm{intervals}\:\mathrm{is}\:\mathrm{usually}\:\mathrm{not}\:\mathrm{overlapping} \\ $$$$\mathrm{such}\:\mathrm{as}\::\:\mathrm{1}−\mathrm{10},\:\mathrm{11}−\mathrm{20},\:\mathrm{21}−\mathrm{30}\:\mathrm{etc} \\ $$ Terms of Service Privacy…
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Question Number 140890 by mathsuji last updated on 13/May/21 $$\mathrm{1}+\mathrm{2}{x}+\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}^{\mathrm{3}} +…+\left({n}+\mathrm{1}\right){x}^{\boldsymbol{{n}}} =? \\ $$ Answered by ajfour last updated on 14/May/21 $${x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +…+{x}^{{n}+\mathrm{1}}…
Question Number 140885 by mnjuly1970 last updated on 13/May/21 $$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:…….\:{Advanced}\:::::::::::\bigstar\bigstar\bigstar::::::::::\:{Calculus}……. \\ $$$$\:\:\:\:\:\:{find}\:{the}\:{value}\:{of}\:\:{the}\:{infinite}\:{series}:: \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\Theta\::=\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}−\mathrm{1}} \mathrm{H}_{\:\mathrm{2}{n}} }{\mathrm{2}{n}−\mathrm{1}}\:=\:??? \\ $$$$\:\:\:\:\:\:\:\:\:\:…….\mathscr{M}.\mathscr{N}.{july}.\mathrm{1970}…….. \\…
Question Number 75351 by TawaTawa last updated on 10/Dec/19 Answered by MJS last updated on 10/Dec/19 $${v}={v}_{\mathrm{0}} −{at} \\ $$$${s}=\int{vdt}=\int\left({v}_{\mathrm{0}} −{at}\right){dt}={v}_{\mathrm{0}} {t}−\frac{{a}}{\mathrm{2}}{t}^{\mathrm{2}} \\ $$$$\left({a}\right)\:\:\mathrm{maximum}\:\mathrm{height}\:\mathrm{when}\:{v}=\mathrm{0} \\…
Question Number 9813 by tawakalitu last updated on 05/Jan/17 $$\mathrm{From}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tower}\:\mathrm{80m}\:\mathrm{high},\:\mathrm{a}\:\mathrm{student} \\ $$$$\mathrm{observe}\:\mathrm{that}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{depression}\:\mathrm{of}\:\mathrm{the}\:\mathrm{top}\: \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{vertical}\:\mathrm{pole}\:\mathrm{A}\:\mathrm{is}\:\mathrm{45}°\:\mathrm{and}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of}\: \\ $$$$\mathrm{depression}\:\mathrm{of}\:\mathrm{point}\:\mathrm{B}\:\mathrm{on}\:\mathrm{the}\:\mathrm{pole}\:\mathrm{is}\:\mathrm{60}°. \\ $$$$\mathrm{if}\:\mathrm{O}\:\mathrm{is}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pole}\:\mathrm{and}\:\mathrm{OB}\:=\:\mathrm{20m}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{A}\:\mathrm{and}\:\mathrm{B}. \\ $$$$\mathrm{leaving}\:\mathrm{your}\:\mathrm{answer}\:\mathrm{in}\:\mathrm{surd}\:\mathrm{form}. \\ $$ Answered…