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Question Number 109929 Answers: 0 Comments: 1

△((♭e)/(Math))▽ lim_(x→∞) (√(81x^2 −10x+1))−4x+3−(√(25x^2 −10x+1)) =?

$$\:\:\:\bigtriangleup\frac{\flat{e}}{\mathcal{M}{ath}}\bigtriangledown \\ $$$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\sqrt{\mathrm{81}{x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{1}}−\mathrm{4}{x}+\mathrm{3}−\sqrt{\mathrm{25}{x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{1}}\:=? \\ $$

Question Number 110181 Answers: 0 Comments: 2

Given the equation of two circles C_1 : x^2 + y^2 −6x−4y + 9 = 0 andC_2 : x^2 +y^2 −2x−6y + 9 =0 find the equation of the common tangent to both circles.

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{two}\:\mathrm{circles} \\ $$$${C}_{\mathrm{1}} :\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \:−\mathrm{6}{x}−\mathrm{4}{y}\:+\:\mathrm{9}\:=\:\mathrm{0}\:\mathrm{and}{C}_{\mathrm{2}} \::\:{x}^{\mathrm{2}} \:+{y}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{6}{y}\:+\:\mathrm{9}\:=\mathrm{0} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{common}\:\mathrm{tangent}\:\mathrm{to}\:\mathrm{both}\:\mathrm{circles}. \\ $$

Question Number 109922 Answers: 1 Comments: 0

Question Number 109923 Answers: 1 Comments: 0

find sin3 in surd form

$${find}\: \\ $$$${sin}\mathrm{3}\:\:\: \\ $$$${in}\:{surd}\:{form} \\ $$

Question Number 109914 Answers: 1 Comments: 0

Prove that tan142°30′+(√6)+(√3)−(√2) is an integer.

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{tan142}°\mathrm{30}'+\sqrt{\mathrm{6}}+\sqrt{\mathrm{3}}−\sqrt{\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{an}\:\mathrm{integer}. \\ $$

Question Number 109913 Answers: 1 Comments: 0

((16))^(1/(x−1)) −5 (4)^(1/(x−1)) +2=0 find x?

$$\sqrt[{{x}−\mathrm{1}}]{\mathrm{16}}−\mathrm{5}\:\:\sqrt[{{x}−\mathrm{1}}]{\mathrm{4}}+\mathrm{2}=\mathrm{0}\:{find}\:{x}? \\ $$

Question Number 109912 Answers: 2 Comments: 1

(1)∫∣((x+3)/(x+1))∣dx (2)∫x∣x−1∣dx (3)∫e^((x−1)/x) dx

$$\left(\mathrm{1}\right)\int\mid\frac{{x}+\mathrm{3}}{{x}+\mathrm{1}}\mid{dx} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\int{x}\mid{x}−\mathrm{1}\mid{dx} \\ $$$$ \\ $$$$\left(\mathrm{3}\right)\int{e}^{\frac{{x}−\mathrm{1}}{{x}}} {dx} \\ $$

Question Number 110178 Answers: 1 Comments: 0

Define the laplace transformation equation and use the transformation equation transform (dy/dx) and (d^2 y/dx^2 ) hence solve the equation : (d^2 y/dx^2 ) + 5 (dy/dx) + 4 = e^(−x) sin 2x Using the laplace transformation equations derived above.

$$\mathrm{Define}\:\mathrm{the}\:\mathrm{laplace}\:\mathrm{transformation}\:\mathrm{equation}\:\mathrm{and} \\ $$$$\mathrm{use}\:\mathrm{the}\:\mathrm{transformation}\:\mathrm{equation}\:\mathrm{transform}\:\frac{{dy}}{{dx}}\:\mathrm{and}\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} } \\ $$$$\mathrm{hence}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{equation}\::\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:+\:\mathrm{5}\:\frac{{dy}}{{dx}}\:+\:\mathrm{4}\:=\:{e}^{−{x}} \:\mathrm{sin}\:\mathrm{2}{x} \\ $$$$\mathrm{Using}\:\mathrm{the}\:\mathrm{laplace}\:\mathrm{transformation}\:\mathrm{equations}\:\mathrm{derived}\:\mathrm{above}. \\ $$

Question Number 109910 Answers: 0 Comments: 2