Question Number 48500 by peter frank last updated on 24/Nov/18 Commented by Abdo msup. last updated on 24/Nov/18 $${y}\left({x}\right)={e}^{{arctan}\left({x}\right)} \:\Rightarrow{y}^{'} \left({x}\right)=\frac{\mathrm{1}}{\mathrm{1}+{x}^{\mathrm{2}} }\:{y}\left({x}\right)\:\Rightarrow \\ $$$${y}^{''} \left({x}\right)\:=−\frac{\mathrm{2}{x}}{\left(\mathrm{1}+{x}^{\mathrm{2}}…
Question Number 179571 by Ar Brandon last updated on 30/Oct/22 $$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{positive}\:\mathrm{even} \\ $$$$\:\mathrm{3}-\mathrm{digits}\:\mathrm{numbers}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{17}. \\ $$ Commented by Ar Brandon last updated on 30/Oct/22 #include <stdio.h> int main(void) { short sum = 0; for (short i = 102; i < 1000; i += 17) if (i % 2 == 0) sum += i; printf("%hd", sum); return 0; } Commented…
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Question Number 48361 by peter frank last updated on 22/Nov/18 $$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation} \\ $$$$\mathrm{cos}^{−\mathrm{1}} \mathrm{x}+\mathrm{cos}^{−\mathrm{1}} \left(\frac{\mathrm{x}}{\mathrm{2}}+\frac{\sqrt{\mathrm{3}−\mathrm{3x}^{\mathrm{2}} }}{\mathrm{2}}\right)=\frac{\pi}{\mathrm{3}} \\ $$ Commented by MJS last updated on 22/Nov/18…
Question Number 179301 by cherokeesay last updated on 28/Oct/22 Answered by som(math1967) last updated on 28/Oct/22 $$\:{ar}^{\mathrm{5}} =\mathrm{768} \\ $$$${a}×\mathrm{36}{r}^{\mathrm{2}} =\mathrm{3456} \\ $$$$\:\frac{{ar}^{\mathrm{5}} }{{a}×\mathrm{36}{r}^{\mathrm{2}} }=\frac{\mathrm{768}}{\mathrm{3456}}…
Question Number 179281 by cherokeesay last updated on 27/Oct/22 Commented by a.lgnaoui last updated on 28/Oct/22 $$ \\ $$ Answered by ARUNG_Brandon_MBU last updated on…
Question Number 48193 by peter frank last updated on 20/Nov/18 $${In}\:{the}\:{equation}\:{ax}^{\mathrm{2}} +{bx}+{c}=\mathrm{0} \\ $$$${one}\:{root}\:{is}\:{square}\:{of}\: \\ $$$${orther}.{without}\:{solving} \\ $$$${the}\:{equation}.{prove}\:{that} \\ $$$${c}\left({a}−{b}\right)^{\mathrm{3}} ={a}\left({c}−{b}\right)^{\mathrm{3}} \\ $$ Answered by…
Question Number 113689 by Ar Brandon last updated on 14/Sep/20 $$\mathrm{Find}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{p}^{\mathrm{2}} +\mathrm{q}^{\mathrm{2}} =\mathrm{101}^{\mathrm{2}} .\:\mathrm{Where}\:\mathrm{p},\:\mathrm{q}\in\mathbb{Z}\: \\ $$$$\mathrm{different}\:\mathrm{from}\:\mathrm{zero}. \\ $$ Commented by Rasheed.Sindhi last updated…
Question Number 48091 by peter frank last updated on 19/Nov/18 Commented by maxmathsup by imad last updated on 19/Nov/18 $${we}\:{have}\:{e}^{−{x}} {sinx}\:={Im}\left({e}^{−{x}+{ix}} \right)={Im}\left({e}^{\left(−\mathrm{1}+{i}\right){x}} \right)\:{but} \\ $$$${e}^{\left(−\mathrm{1}+\boldsymbol{{i}}\right)\boldsymbol{{x}}}…
Question Number 48090 by peter frank last updated on 19/Nov/18 Answered by tanmay.chaudhury50@gmail.com last updated on 19/Nov/18 $$\left.\mathrm{1}\right){true}\:{value}\:{of}\:{product}\:{of}\:{length}×{width} \\ $$$$=\mathrm{2}.\mathrm{29}×\mathrm{1}.\mathrm{29}=\left(\mathrm{2}.\mathrm{30}−\mathrm{0}.\mathrm{01}\right)\left(\mathrm{1}.\mathrm{30}−\mathrm{0}.\mathrm{01}\right) \\ $$$$=\mathrm{2}.\mathrm{30}×\mathrm{1}.\mathrm{30}−\mathrm{0}.\mathrm{01}\left(\mathrm{2}.\mathrm{30}+\mathrm{1}.\mathrm{30}\right)+\mathrm{0}.\mathrm{0001} \\ $$$$=\mathrm{2}.\mathrm{30}×\mathrm{1}.\mathrm{30}−\mathrm{3}.\mathrm{60}×\mathrm{0}.\mathrm{01}+\mathrm{0}.\mathrm{0001} \\…