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Question Number 77186 Answers: 1 Comments: 0

given { ((3^y −1= (6/2^x ))),(((3)^(y/x) = 2 )) :} find (1/x)+(1/y).

$$\mathrm{given}\: \\ $$$$\begin{cases}{\mathrm{3}^{\mathrm{y}} −\mathrm{1}=\:\frac{\mathrm{6}}{\mathrm{2}^{\mathrm{x}} }}\\{\left(\mathrm{3}\right)^{\frac{\mathrm{y}}{\mathrm{x}}} \:=\:\mathrm{2}\:}\end{cases}\:\:\mathrm{find}\:\frac{\mathrm{1}}{\mathrm{x}}+\frac{\mathrm{1}}{\mathrm{y}}. \\ $$

Question Number 77183 Answers: 1 Comments: 0

what is x satisfy inequality 3^x^2 × 5^(x−1) ≥ 3

$$\mathrm{what}\:\mathrm{is}\:\mathrm{x}\: \\ $$$$\mathrm{satisfy}\:\mathrm{inequality}\: \\ $$$$\mathrm{3}^{\mathrm{x}^{\mathrm{2}} } ×\:\mathrm{5}^{\mathrm{x}−\mathrm{1}} \:\geqslant\:\mathrm{3} \\ $$

Question Number 77182 Answers: 1 Comments: 1

evaluate lim_(x→0) ((∫_a ^x (((cos t)/t))dt)/x) .

$$ \\ $$$$ \\ $$$$\mathrm{evaluate}\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\underset{\mathrm{a}} {\overset{\mathrm{x}} {\int}}\left(\frac{\mathrm{cos}\:\mathrm{t}}{\mathrm{t}}\right)\mathrm{dt}}{\mathrm{x}}\:. \\ $$

Question Number 77180 Answers: 1 Comments: 0

given a quadratic equation 3x^2 −x+(t^2 −4t+3)=0 has roots sin α and cos α. find the value (√(t^2 −4t+5)) .

$$ \\ $$$$ \\ $$$$\mathrm{given}\:\mathrm{a}\:\mathrm{quadratic}\:\mathrm{equation}\: \\ $$$$\mathrm{3x}^{\mathrm{2}} −\mathrm{x}+\left(\mathrm{t}^{\mathrm{2}} −\mathrm{4t}+\mathrm{3}\right)=\mathrm{0}\:\mathrm{has} \\ $$$$\mathrm{roots}\:\mathrm{sin}\:\alpha\:\mathrm{and}\:\mathrm{cos}\:\alpha.\:\mathrm{find}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\sqrt{\mathrm{t}^{\mathrm{2}} −\mathrm{4t}+\mathrm{5}}\:. \\ $$

Question Number 77178 Answers: 1 Comments: 0

given cos^(−1) (x)+cos^(−1) (y)+cos^(−1) (z)=π and x+y+z=(3/2) prove that x = y = z .

$$ \\ $$$${given}\:\mathrm{cos}^{−\mathrm{1}} \left({x}\right)+\mathrm{cos}^{−\mathrm{1}} \left({y}\right)+\mathrm{cos}^{−\mathrm{1}} \left({z}\right)=\pi \\ $$$${and}\:{x}+{y}+{z}=\frac{\mathrm{3}}{\mathrm{2}} \\ $$$${prove}\:{that}\:{x}\:=\:{y}\:=\:{z}\:. \\ $$

Question Number 77164 Answers: 1 Comments: 2

Question Number 77160 Answers: 1 Comments: 1

Question Number 77158 Answers: 0 Comments: 4

∫_(−2) ^( 2) (x^3 cos(x/2) + (1/2))(√(4 − x^2 )) dx

$$\int_{−\mathrm{2}} ^{\:\mathrm{2}} \:\left(\mathrm{x}^{\mathrm{3}} \:\mathrm{cos}\frac{\mathrm{x}}{\mathrm{2}}\:+\:\frac{\mathrm{1}}{\mathrm{2}}\right)\sqrt{\mathrm{4}\:−\:\mathrm{x}^{\mathrm{2}} }\:\:\mathrm{dx} \\ $$

Question Number 77154 Answers: 0 Comments: 6

Question Number 77149 Answers: 0 Comments: 2

Any reference to a book or video that coould help me solve Differential equations? please help

$$\mathrm{Any}\:\mathrm{reference}\:\mathrm{to}\:\mathrm{a}\:\mathrm{book}\:\mathrm{or}\:\mathrm{video} \\ $$$$\mathrm{that}\:\mathrm{coould}\:\mathrm{help}\:\mathrm{me}\:\mathrm{solve}\:\mathrm{Differential}\:\mathrm{equations}?\: \\ $$$$\mathrm{please}\:\mathrm{help} \\ $$

Question Number 77147 Answers: 0 Comments: 1

Σ_(r=1) ^∞ (1/r^k ) is divergent for: A. k ≤ 1 B. k > 2 C. k ≤ 2 D. 0 ≤ k < 2

$$\:\underset{{r}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{{r}^{{k}} }\:{is}\:{divergent}\:{for}: \\ $$$${A}.\:{k}\:\leqslant\:\mathrm{1} \\ $$$${B}.\:{k}\:>\:\mathrm{2} \\ $$$${C}.\:{k}\:\leqslant\:\mathrm{2} \\ $$$${D}.\:\mathrm{0}\:\leqslant\:{k}\:<\:\mathrm{2} \\ $$

Question Number 77144 Answers: 1 Comments: 2

Question Number 77143 Answers: 1 Comments: 2

Question Number 77132 Answers: 0 Comments: 1

Question Number 77129 Answers: 1 Comments: 0

solve in R ∣tan2x∣−(√3)≥0

$$\mathrm{solve}\:\mathrm{in}\:\mathrm{R} \\ $$$$\mid\mathrm{tan2}{x}\mid−\sqrt{\mathrm{3}}\geqslant\mathrm{0} \\ $$

Question Number 77128 Answers: 2 Comments: 0

Find the value of constant “a” such that axe^(−x ) is a solution of Differential equation (d^2 y/dx^2 )+3(dy/dx)+2y=2e^(−x) solve D.E for which y=1 and (dy/dx)=3 when x=0

$${Find}\:{the}\:{value}\:{of}\:{constant} \\ $$$$``{a}''\:{such}\:{that}\:{axe}^{−{x}\:} {is} \\ $$$${a}\:{solution}\:{of}\:{Differential} \\ $$$${equation} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{3}\frac{{dy}}{{dx}}+\mathrm{2}{y}=\mathrm{2}{e}^{−{x}} \\ $$$${solve}\:{D}.{E}\:{for}\:\:{which} \\ $$$${y}=\mathrm{1}\:{and}\:\frac{{dy}}{{dx}}=\mathrm{3}\:{when} \\ $$$${x}=\mathrm{0} \\ $$

Question Number 77127 Answers: 2 Comments: 0

Prove that line lx+my+n=0 is tangent to the ellipse (x^2 /a^2 )+(y^2 /b^(2 ) )=1 if a^2 l^2 +b^2 m^2 =n^2

$${Prove}\:{that}\:{line}\:{lx}+{my}+{n}=\mathrm{0} \\ $$$${is}\:{tangent}\:{to}\:{the}\:{ellipse} \\ $$$$\frac{{x}^{\mathrm{2}} }{{a}^{\mathrm{2}} }+\frac{{y}^{\mathrm{2}} }{{b}^{\mathrm{2}\:} }=\mathrm{1}\:{if}\:{a}^{\mathrm{2}} {l}^{\mathrm{2}} +{b}^{\mathrm{2}} {m}^{\mathrm{2}} ={n}^{\mathrm{2}} \\ $$

Question Number 77126 Answers: 1 Comments: 0

1)Express (x/((1−x)^4 )) in partial fraction 2) Solve xdy+ydy−(((xdx−ydy)/(x^2 +y^2 )))=0

$$\left.\mathrm{1}\right){Express}\:\frac{{x}}{\left(\mathrm{1}−{x}\right)^{\mathrm{4}} }\:\:\:{in} \\ $$$${partial}\:{fraction} \\ $$$$\left.\mathrm{2}\right)\:{Solve} \\ $$$${xdy}+{ydy}−\left(\frac{{xdx}−{ydy}}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} }\right)=\mathrm{0} \\ $$$$ \\ $$

Question Number 77123 Answers: 1 Comments: 0

ABC is a non−right triangle. 1) Demonstrate that tan(A^ +B^ )=−tanC^ . 1) By using tan(A^ +B^ )=((tanA^ +tanB^ )/(1−tanA^ tanB^ )) prove that tanA^ +tanB^ +tanC^ =tanAtanBtanC please i need your help

$$\mathrm{ABC}\:\mathrm{is}\:\mathrm{a}\:\mathrm{non}−\mathrm{right}\:\mathrm{triangle}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{Demonstrate}\:\mathrm{that} \\ $$$$\mathrm{tan}\left(\hat {\mathrm{A}}+\hat {\mathrm{B}}\right)=−\mathrm{tan}\hat {\mathrm{C}}. \\ $$$$\left.\mathrm{1}\right)\:\mathrm{By}\:\mathrm{using}\:\mathrm{tan}\left(\hat {\mathrm{A}}+\hat {\mathrm{B}}\right)=\frac{\mathrm{tan}\hat {\mathrm{A}}+\mathrm{tan}\hat {\mathrm{B}}}{\mathrm{1}−\mathrm{tan}\hat {\mathrm{A}tan}\hat {\mathrm{B}}} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{tan}\hat {\mathrm{A}}+\mathrm{tan}\hat {\mathrm{B}}+\mathrm{tan}\hat {\mathrm{C}}=\mathrm{tanAtanBtanC} \\ $$$$\mathrm{please}\:\mathrm{i}\:\mathrm{need}\:\mathrm{your}\:\mathrm{help} \\ $$

Question Number 77119 Answers: 2 Comments: 0

suppose the equations x^2 +px+4=0 and x^2 +qx+3=0 have a common root, write this root in terms of the other root.

$${suppose}\:{the}\:{equations}\:{x}^{\mathrm{2}} +{px}+\mathrm{4}=\mathrm{0} \\ $$$${and}\:{x}^{\mathrm{2}} +{qx}+\mathrm{3}=\mathrm{0}\:\:{have}\:{a}\:{common}\:{root}, \\ $$$${write}\:{this}\:{root}\:{in}\:{terms}\:{of}\:{the}\:{other}\:{root}. \\ $$

Question Number 77117 Answers: 0 Comments: 0

Interview indicates that all the 4 maths students,5 physics and 7 chemistry students who applied for a scholarship in their respective disciplines qualified for an award. In how many ways the aeard can be made if; (i)only one scholarship is available in each of the disciplines (ii)only two scholarships are availablr in each of the disciplines.

$${Interview}\:{indicates}\:{that}\:{all}\:{the}\:\mathrm{4}\:{maths} \\ $$$${students},\mathrm{5}\:{physics}\:{and}\:\mathrm{7}\:{chemistry} \\ $$$${students}\:{who}\:{applied}\:{for}\:{a}\:{scholarship} \\ $$$${in}\:{their}\:{respective}\:{disciplines}\:{qualified} \\ $$$${for}\:{an}\:{award}.\:{In}\:{how}\:{many}\:{ways}\:{the}\:{aeard} \\ $$$${can}\:{be}\:{made}\:{if}; \\ $$$$\left({i}\right){only}\:{one}\:{scholarship}\:{is}\:{available}\:{in} \\ $$$${each}\:{of}\:{the}\:{disciplines} \\ $$$$\left({ii}\right){only}\:{two}\:{scholarships}\:{are}\:{availablr} \\ $$$${in}\:{each}\:{of}\:{the}\:{disciplines}. \\ $$

Question Number 77103 Answers: 1 Comments: 1

Question Number 77091 Answers: 0 Comments: 3

Question Number 77089 Answers: 0 Comments: 2

Cheap ⇊ ∫(√(x/(√(x/(√(x/(...)))))))dx

$$\boldsymbol{{Cheap}}\:\downdownarrows \\ $$$$\int\sqrt{\frac{\boldsymbol{{x}}}{\sqrt{\frac{\boldsymbol{{x}}}{\sqrt{\frac{\boldsymbol{{x}}}{...}}}}}}\boldsymbol{{dx}} \\ $$$$ \\ $$$$ \\ $$

Question Number 77087 Answers: 1 Comments: 1

∫_0 ^(a/2) x^2 (a^2 −x^2 )^((−3)/2) dx Help!!!

$$\int_{\mathrm{0}} ^{\frac{\boldsymbol{{a}}}{\mathrm{2}}} \boldsymbol{{x}}^{\mathrm{2}} \left(\boldsymbol{{a}}^{\mathrm{2}} −\boldsymbol{{x}}^{\mathrm{2}} \right)^{\frac{−\mathrm{3}}{\mathrm{2}}} \boldsymbol{{dx}} \\ $$$$\boldsymbol{{Help}}!!! \\ $$$$ \\ $$

Question Number 77086 Answers: 1 Comments: 2

∫_0 ^1 xtan^(−1) xdx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {xtan}^{−\mathrm{1}} {xdx} \\ $$$$ \\ $$

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