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with-f-x-x-2-12x-30-and-x-R-solve-f-f-f-f-f-x-0-

Question Number 202184 by mr W last updated on 22/Dec/23 $${with}\:{f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{12}{x}+\mathrm{30}\:{and}\:{x}\in{R} \\ $$$${solve}\:{f}\left({f}\left({f}\left({f}\left({f}\left({x}\right)\right)\right)\right)\right)=\mathrm{0} \\ $$ Answered by cortano12 last updated on 22/Dec/23 $$\mathrm{f}\left(\mathrm{x}\right)=\left(\mathrm{x}+\mathrm{6}\right)^{\mathrm{2}} −\mathrm{6}\:\Rightarrow\mathrm{x}=\sqrt{\mathrm{f}\left(\mathrm{x}\right)+\mathrm{6}}−\mathrm{6}…

Question-202153

Question Number 202153 by sonukgindia last updated on 22/Dec/23 Answered by witcher3 last updated on 22/Dec/23 $$\mathrm{ln}\left(\mathrm{x}\right)\mathrm{y}'+\frac{\mathrm{y}}{\mathrm{x}}=\left(\mathrm{ln}\left(\mathrm{x}\right)\right)\mathrm{y}'+\left(\mathrm{ln}\left(\mathrm{x}\right)\right)'\mathrm{y} \\ $$$$=\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{ln}\left(\mathrm{x}\right)\mathrm{y}\right) \\ $$$$\Leftrightarrow\begin{cases}{\frac{\mathrm{d}}{\mathrm{dx}}\left(\mathrm{y}.\left(\mathrm{ln}\left(\mathrm{x}\right)\right)=\mathrm{x}^{\mathrm{2}} \mathrm{sin}\left(\mathrm{x}\right)\right.}\\{\mathrm{y}\left(\pi\right)=\frac{\pi^{\mathrm{2}} }{\mathrm{ln}\left(\pi\right)}}\end{cases} \\ $$$$\Rightarrow\int_{\pi}…

Question-202208

Question Number 202208 by hardmath last updated on 22/Dec/23 Commented by mr W last updated on 22/Dec/23 $${which}\:{country}\:{are}\:{you}\:{from}? \\ $$$${internationally}\:{the}\:{ABO}\:{blood} \\ $$$${group}\:{system}\:{is}\:{common},\:{see}\:{below}. \\ $$$${but}\:{you}\:{are}\:{talking}\:{about}\:{blood}\: \\…

find-x-in-the-interval-0-lt-x-lt-360-if-f-x-6sinx-is-12-

Question Number 202143 by otchereabdullai@gmail.com last updated on 21/Dec/23 $$\:{find}\:{x}\:{in}\:{the}\:{interval}\:\:\mathrm{0}°<{x}<\mathrm{360}°\:{if} \\ $$$$\:\:{f}\left({x}\right)=\:\mathrm{6}{sinx}\:{is}\:−\mathrm{12} \\ $$ Commented by otchereabdullai@gmail.com last updated on 22/Dec/23 $${answer}\:{in}\:{the}\:{book}\:{is}\:\mathrm{210}°\:{and}\:\mathrm{330}°\: \\ $$$${but}\:{i}\:{dont}\:{know}\:{how}\:\:{he}\:{come}\:{about}\: \\…

If-p-9999-then-4p-3-p-2p-1-6p-3-

Question Number 202129 by MATHEMATICSAM last updated on 21/Dec/23 $$\mathrm{If}\:{p}\:=\:\mathrm{9999}\:\mathrm{then}\:\frac{\mathrm{4}{p}^{\mathrm{3}} \:−\:{p}}{\left(\mathrm{2}{p}\:+\:\mathrm{1}\right)\left(\mathrm{6}{p}\:−\:\mathrm{3}\right)}\:=\:? \\ $$ Answered by AST last updated on 21/Dec/23 $$\frac{{p}\left(\mathrm{2}{p}−\mathrm{1}\right)\left(\mathrm{2}{p}+\mathrm{1}\right)}{\mathrm{3}\left(\mathrm{2}{p}+\mathrm{1}\right)\left(\mathrm{2}{p}−\mathrm{1}\right)}=\frac{{p}=\mathrm{9999}}{\mathrm{3}}=\mathrm{3333} \\ $$ Terms of…