Question Number 44805 by jasno91 last updated on 05/Oct/18 Answered by Kunal12588 last updated on 05/Oct/18 $${let}\:{the}\:{numbers}\:{be}\:{a},{b},{c} \\ $$$${a}:{b}:{c}=\mathrm{4}:\mathrm{5}:\mathrm{6} \\ $$$${let}\:{a}=\mathrm{4}{x},\:{b}=\mathrm{5}{x},\:{c}=\mathrm{6}{x} \\ $$$${here}\:\mathrm{6}{x}>\mathrm{5}{x}>\mathrm{4}{x} \\ $$$$\therefore\:\mathrm{6}{x}+\mathrm{4}{x}=\mathrm{5}{x}+\mathrm{55}…
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Question Number 175821 by daus last updated on 07/Sep/22 Commented by daus last updated on 07/Sep/22 $${help}\:{me}\:{for}\:{a} \\ $$ Answered by Rasheed.Sindhi last updated on…
Question Number 110288 by mathdave last updated on 28/Aug/20 Answered by bemath last updated on 28/Aug/20 $$\:\:\:\:\:\Delta\frac{{be}}{{math}}\bigtriangledown \\ $$$${let}\:{y}\:=\:{vx}\:\Rightarrow{dy}={v}\:{dx}+\:{x}\:{dv} \\ $$$$\Leftrightarrow\left(\mathrm{4}{vx}−\mathrm{2}{x}\right){dx}=\left({x}+{vx}\right)\left({v}\:{dx}+{x}\:{dv}\right) \\ $$$$\left(\mathrm{4}{v}−\mathrm{2}\right){dx}=\left(\mathrm{1}+{v}\right)\left({v}\:{dx}\:+\:{x}\:{dv}\:\right) \\ $$$$\left(\mathrm{4}{v}−\mathrm{2}\right){dx}=\left({v}+{v}^{\mathrm{2}}…
Question Number 110287 by mathdave last updated on 28/Aug/20 Commented by bemath last updated on 28/Aug/20 $$\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{5}\right)=\frac{\pi}{\mathrm{2}}−\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{5}\right) \\ $$$$\mathrm{sin}\:\left(\mathrm{sin}^{−\mathrm{1}} \left(\mathrm{5}\right)\right)=\mathrm{sin}\:\left(\frac{\pi}{\mathrm{2}}−\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{5}\right)\right) \\ $$$$\Rightarrow\:\mathrm{5}\:=\:\mathrm{cos}\:\left(\mathrm{cos}^{−\mathrm{1}}…
Question Number 110286 by mathdave last updated on 28/Aug/20 Answered by mathmax by abdo last updated on 28/Aug/20 $$\mathrm{f}\left(\mathrm{a}\right)\:=\mathrm{ln}\left(\mathrm{a}\right)\int\:\frac{\mathrm{a}^{\mathrm{3x}} −\mathrm{1}}{\mathrm{a}^{\mathrm{2x}} +\mathrm{1}}\mathrm{dx}\:\:\mathrm{changement}\:\mathrm{a}^{\mathrm{x}} \:=\mathrm{t}\:\mathrm{give}\:\mathrm{e}^{\mathrm{xln}\left(\mathrm{a}\right)} \:=\mathrm{t}\:\Rightarrow \\ $$$$\mathrm{xln}\left(\mathrm{a}\right)\:=\mathrm{ln}\left(\mathrm{t}\right)\:\Rightarrow\mathrm{x}\:=\frac{\mathrm{ln}\left(\mathrm{t}\right)}{\mathrm{lna}}\:\Rightarrow\mathrm{f}\left(\mathrm{a}\right)\:=\mathrm{ln}\left(\mathrm{a}\right)\int\:\frac{\mathrm{t}^{\mathrm{3}}…
Question Number 110285 by mathdave last updated on 28/Aug/20 Answered by 1549442205PVT last updated on 29/Aug/20 $$\mathrm{we}\:\mathrm{have}\:\mathrm{x}^{\mathrm{8}} +\mathrm{4}=\left(\mathrm{x}^{\mathrm{4}} +\mathrm{2}\right)^{\mathrm{2}} −\mathrm{2x}^{\mathrm{4}} = \\ $$$$\left(\mathrm{x}^{\mathrm{4}} +\sqrt{\mathrm{2}}\:\mathrm{x}^{\mathrm{2}} +\mathrm{2}\right)\left(\mathrm{x}^{\mathrm{4}}…
Question Number 175806 by Ml last updated on 07/Sep/22 Answered by cortano1 last updated on 07/Sep/22 $$\:\frac{\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{x}+\mathrm{1}}−\mathrm{1}}\:=\:\frac{\sqrt{\mathrm{x}}\:\left(\sqrt{\mathrm{x}+\mathrm{1}}\:+\mathrm{1}\right)}{\mathrm{x}} \\ $$$$\:=\:\frac{\sqrt{\mathrm{x}+\mathrm{1}}\:+\mathrm{1}}{\:\sqrt{\mathrm{x}}}\: \\ $$$$\:\mathrm{let}\:\sqrt{\mathrm{x}}\:=\mathrm{tan}\:\mathrm{u}\Rightarrow\mathrm{x}=\mathrm{tan}\:^{\mathrm{2}} \left(\mathrm{u}\right) \\ $$$$\:\begin{cases}{\mathrm{x}=\mathrm{1}\Rightarrow\mathrm{u}=\frac{\pi}{\mathrm{4}}}\\{\mathrm{x}=\mathrm{3}\Rightarrow\mathrm{u}=\frac{\pi}{\mathrm{3}}}\end{cases} \\…
Question Number 110254 by ZiYangLee last updated on 28/Aug/20 $$\mathrm{Given}\:\mathrm{tan}\:\alpha\:\mathrm{and}\:\mathrm{tan}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{two}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\mathrm{2}{x}^{\mathrm{2}} −{x}−\mathrm{2}=\mathrm{0},\:\mathrm{then} \\ $$$$\mathrm{sin}\left(\mathrm{2}\alpha+\mathrm{2}\beta\right)+\mathrm{cos}\left(\mathrm{2}\alpha+\mathrm{2}\beta\right)+\mathrm{tan}\left(\mathrm{2}\alpha+\mathrm{2}\beta\right)=? \\ $$ Answered by som(math1967) last updated on 28/Aug/20 $$\mathrm{tan}\alpha+\mathrm{tan}\beta=\frac{\mathrm{1}}{\mathrm{2}}…
Question Number 175785 by otchereabdullai@gmail.com last updated on 06/Sep/22 Commented by Ar Brandon last updated on 07/Sep/22 #include <stdio.h> #include <math.h> int main(void) { double fx, gx, xn, x_m; printf("Enter initial value:"); scanf("%lf", &xn); for(int i=0; i<100; i++) { fx = pow(xn, log(2)/log(3))-sqrt(xn)-1; gx = log(2)/log(3)*pow(xn,log(2)/log(3)-1) -0.5/sqrt(xn); x_m = xn - fx / gx; xn = x_m; } printf("x ≈ %.2f\n", xn); return 0; } Commented by Ar Brandon last updated on…