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AllQuestion and Answers: Page 1507

Question Number 59685 Answers: 0 Comments: 0

Question Number 59683 Answers: 3 Comments: 0

prove (1+tanx)(1+tany)=2 if x+y=45°

$${prove}\:\left(\mathrm{1}+{tanx}\right)\left(\mathrm{1}+\mathrm{tany}\right)=\mathrm{2}\:\:{if}\:\:{x}+{y}=\mathrm{45}° \\ $$$$ \\ $$

Question Number 59682 Answers: 2 Comments: 2

if H=X^2 +Y^2 +Z^2 prove (∂^2 H/∂X^2 )+(∂^2 H/∂Y^2 )+(∂^2 H/∂Z^2 )=(2/H)

$${if} \\ $$$$ \\ $$$${H}={X}^{\mathrm{2}} +{Y}^{\mathrm{2}} +{Z}^{\mathrm{2}} \\ $$$$ \\ $$$${prove} \\ $$$$ \\ $$$$\frac{\partial^{\mathrm{2}} {H}}{\partial{X}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} {H}}{\partial{Y}^{\mathrm{2}} }+\frac{\partial^{\mathrm{2}} {H}}{\partial{Z}^{\mathrm{2}} }=\frac{\mathrm{2}}{{H}} \\ $$

Question Number 59679 Answers: 3 Comments: 0

Evaluate ∫_0 ^3 (((x^2 +3x)/x^3 ))

$${Evaluate} \\ $$$$\:\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\left(\frac{{x}^{\mathrm{2}} +\mathrm{3}{x}}{{x}^{\mathrm{3}} }\right) \\ $$$$ \\ $$

Question Number 59678 Answers: 0 Comments: 0

Determine a,b,c in terms of α,β,γ. (a/b)−c=γ (b/c)−a=α (c/a)−b=β

$$\mathcal{D}{etermine}\:{a},{b},{c}\:{in}\:{terms}\:{of}\:\alpha,\beta,\gamma. \\ $$$$\:\:\:\:\frac{{a}}{{b}}−{c}=\gamma \\ $$$$\:\:\:\:\frac{{b}}{{c}}−{a}=\alpha \\ $$$$\:\:\:\:\frac{{c}}{{a}}−{b}=\beta \\ $$

Question Number 59675 Answers: 0 Comments: 0

you are welcome sir ali.

$${you}\:{are}\:{welcome}\:{sir}\:{ali}. \\ $$

Question Number 59667 Answers: 1 Comments: 0

Question Number 59659 Answers: 1 Comments: 5

Question Number 59655 Answers: 1 Comments: 3

Question Number 59647 Answers: 1 Comments: 1

Question Number 59639 Answers: 0 Comments: 3

Question Number 59637 Answers: 1 Comments: 1

lim_(x→∞) (1/x)∫_0 ^x ∣sin x∣

$$\underset{{x}\rightarrow\infty} {{lim}}\frac{\mathrm{1}}{{x}}\int_{\mathrm{0}} ^{{x}} \mid\mathrm{sin}\:{x}\mid \\ $$

Question Number 59631 Answers: 2 Comments: 3

1) calculate ∫_0 ^(2π) (dx/(acosx +bsinx)) with a , b reals 2)find also ∫_0 ^(2π) ((cosx dx)/((acosx +bsinx)^2 )) and ∫_0 ^(2π) ((sinx dx)/((acosx +bsinx)^2 )) 3) find the value of ∫_0 ^(2π) (dx/(2cosx +(√3)sinx))

$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{{acosx}\:+{bsinx}} \\ $$$${with}\:{a}\:,\:{b}\:{reals} \\ $$$$\left.\mathrm{2}\right){find}\:{also}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{cosx}\:{dx}}{\left({acosx}\:+{bsinx}\right)^{\mathrm{2}} }\:\:{and} \\ $$$$\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\frac{{sinx}\:{dx}}{\left({acosx}\:+{bsinx}\right)^{\mathrm{2}} } \\ $$$$\left.\mathrm{3}\right)\:{find}\:{the}\:{value}\:{of}\:\int_{\mathrm{0}} ^{\mathrm{2}\pi} \:\:\:\frac{{dx}}{\mathrm{2}{cosx}\:+\sqrt{\mathrm{3}}{sinx}} \\ $$

Question Number 59627 Answers: 1 Comments: 0

Question Number 59626 Answers: 1 Comments: 0

Rationalize the denominator of (2/(1 − (√(2 + (4)^(1/3) ))))

$${Rationalize}\:\:{the}\:\:{denominator}\:\:{of} \\ $$$$\:\:\:\:\:\:\:\:\frac{\mathrm{2}}{\mathrm{1}\:−\:\sqrt{\mathrm{2}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{4}}}} \\ $$

Question Number 59625 Answers: 0 Comments: 0

Sum the series: ((( ^n C_1 )/( ^n C_0 )))^2 + (2 × (( ^n C_2 )/( ^n C_1 ))) + (3 × (( ^n C_3 )/( ^n C_2 )))^2 + .... n terms

$$\mathrm{Sum}\:\mathrm{the}\:\mathrm{series}:\:\:\:\:\:\:\:\left(\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{1}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{0}} }\right)^{\mathrm{2}} \:+\:\left(\mathrm{2}\:×\:\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{2}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{1}} }\right)\:+\:\left(\mathrm{3}\:×\:\frac{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{3}} }{\overset{\boldsymbol{\mathrm{n}}} {\:}\boldsymbol{\mathrm{C}}_{\mathrm{2}} }\right)^{\mathrm{2}} \:+\:....\:\:\boldsymbol{\mathrm{n}}\:\mathrm{terms} \\ $$

Question Number 59624 Answers: 1 Comments: 0

Rationalize the denominator of (2/((√(x+2)) + (√(x+1)) + (√x)))

$${Rationalize}\:\:\:{the}\:\:{denominator}\:\:{of} \\ $$$$\:\:\:\:\:\:\frac{\mathrm{2}}{\sqrt{{x}+\mathrm{2}}\:\:+\:\:\sqrt{{x}+\mathrm{1}}\:\:+\:\:\sqrt{{x}}} \\ $$

Question Number 59620 Answers: 1 Comments: 2

Question Number 59615 Answers: 1 Comments: 0

6+((1/5)×7)

$$\mathrm{6}+\left(\frac{\mathrm{1}}{\mathrm{5}}×\mathrm{7}\right) \\ $$

Question Number 59614 Answers: 1 Comments: 0

1(1/7)+1(1/(14))

$$\mathrm{1}\frac{\mathrm{1}}{\mathrm{7}}+\mathrm{1}\frac{\mathrm{1}}{\mathrm{14}} \\ $$

Question Number 59608 Answers: 0 Comments: 0

For your development solve this (d^2 r/dt^2 )=(A/(r^2 (t))) where r(t)=αt^β

$${For}\:{your}\:{development}\:{solve}\:{this} \\ $$$$\frac{{d}^{\mathrm{2}} {r}}{{dt}^{\mathrm{2}} }=\frac{{A}}{{r}^{\mathrm{2}} \left({t}\right)}\:\:{where}\:{r}\left({t}\right)=\alpha{t}^{\beta} \\ $$

Question Number 59600 Answers: 1 Comments: 0

Question Number 59599 Answers: 1 Comments: 0

Question Number 59595 Answers: 1 Comments: 1

Question Number 59588 Answers: 1 Comments: 1

find x,y in R (x+yi)^3 =((1+(√(15)) i)/((√5) − (√3) i))

$${find}\:{x},{y}\:{in}\:{R} \\ $$$$\left({x}+{yi}\right)^{\mathrm{3}} =\frac{\mathrm{1}+\sqrt{\mathrm{15}}\:{i}}{\sqrt{\mathrm{5}}\:−\:\sqrt{\mathrm{3}}\:{i}} \\ $$

Question Number 59581 Answers: 2 Comments: 0

Determine a , b , c in terms of α , β , γ. ab+c=γ bc+a=α ca+b=β

$$\mathcal{D}{etermine}\:{a}\:,\:{b}\:,\:{c}\:{in}\:{terms}\:{of}\:\alpha\:,\:\beta\:,\:\gamma. \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ab}+{c}=\gamma\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{bc}+{a}=\alpha \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{ca}+{b}=\beta \\ $$

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