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Question Number 116524 Answers: 1 Comments: 1

if α+β+γ=180° prove: sin α+sin β+sin γ+sin (π/3) < 4 sin (π/3)

$$\mathrm{if}\:\alpha+\beta+\gamma=\mathrm{180}° \\ $$$$\mathrm{prove}: \\ $$$$\mathrm{sin}\:\alpha+\mathrm{sin}\:\beta+\mathrm{sin}\:\gamma+\mathrm{sin}\:\frac{\pi}{\mathrm{3}}\:<\:\mathrm{4}\:\mathrm{sin}\:\frac{\pi}{\mathrm{3}} \\ $$

Question Number 116523 Answers: 2 Comments: 0

Question Number 116520 Answers: 1 Comments: 0

find the center of circle with radius R and tangent by sides AB and BC of triangle?

$${find}\:{the}\:{center}\:{of}\:{circle}\:{with}\:{radius}\:{R} \\ $$$${and}\:{tangent}\:{by}\:{sides}\:{AB}\:{and}\:{BC}\:{of}\: \\ $$$${triangle}? \\ $$

Question Number 116516 Answers: 2 Comments: 0

Question Number 116513 Answers: 1 Comments: 0

give a∈Z and prove that if (a−2)∣4 than (a−3)can′t∣6

$${give}\:{a}\in{Z}\:{and}\:{prove}\:{that}\:{if}\:\left({a}−\mathrm{2}\right)\mid\mathrm{4}\:{than}\:\left({a}−\mathrm{3}\right){can}'{t}\mid\mathrm{6} \\ $$

Question Number 116512 Answers: 0 Comments: 1

give x∈R and prove that if x=(√(2x+3)) than x=3

$${give}\:{x}\in{R}\:{and}\:{prove}\:{that}\:{if}\:\:{x}=\sqrt{\mathrm{2}{x}+\mathrm{3}}\:{than}\:{x}=\mathrm{3} \\ $$

Question Number 116509 Answers: 2 Comments: 0

x^4 −48x^2 +x+565=0 x=?

$$\mathrm{x}^{\mathrm{4}} −\mathrm{48x}^{\mathrm{2}} +\mathrm{x}+\mathrm{565}=\mathrm{0}\: \\ $$$$\mathrm{x}=? \\ $$

Question Number 116507 Answers: 1 Comments: 0

Question Number 116503 Answers: 2 Comments: 0

If tan α and tan β are the roots of equation 2x^2 −5x+1=0 find { ((tan ((α/2)+2β))),((tan (2α−(β/2)))) :}

$$\mathrm{If}\:\mathrm{tan}\:\alpha\:\mathrm{and}\:\mathrm{tan}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\mathrm{equation}\:\mathrm{2x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{find}\:\begin{cases}{\mathrm{tan}\:\left(\frac{\alpha}{\mathrm{2}}+\mathrm{2}\beta\right)}\\{\mathrm{tan}\:\left(\mathrm{2}\alpha−\frac{\beta}{\mathrm{2}}\right)}\end{cases} \\ $$

Question Number 116501 Answers: 1 Comments: 0

∫ ((sin x−cos x)/( (√(sin 2x)))) dx ?

$$\int\:\frac{\mathrm{sin}\:\mathrm{x}−\mathrm{cos}\:\mathrm{x}}{\:\sqrt{\mathrm{sin}\:\mathrm{2x}}}\:\mathrm{dx}\:? \\ $$

Question Number 116500 Answers: 2 Comments: 0

∫_0 ^∞ ((sin^3 (x))/x) dx =?

$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\:\frac{\mathrm{sin}\:^{\mathrm{3}} \left(\mathrm{x}\right)}{\mathrm{x}}\:\mathrm{dx}\:=? \\ $$

Question Number 116493 Answers: 3 Comments: 0

Given sin^2 x+sin x = 1 , find the value of cos^8 x+cos^6 x+cos^4 x =?

$$\mathrm{Given}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{1}\:,\:\mathrm{find}\: \\ $$$$\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:^{\mathrm{8}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{6}} \mathrm{x}+\mathrm{cos}\:^{\mathrm{4}} \mathrm{x}\:=? \\ $$

Question Number 116491 Answers: 1 Comments: 0

(0.16)^(log _(2.5) ((1/3)+(1/3^2 )+(1/3^3 )+...)) =?

$$\left(\mathrm{0}.\mathrm{16}\right)^{\mathrm{log}\:_{\mathrm{2}.\mathrm{5}} \left(\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{3}^{\mathrm{3}} }+...\right)} \:=? \\ $$

Question Number 116486 Answers: 2 Comments: 0

Question Number 116483 Answers: 2 Comments: 0

If 8 cos x−8 sin x = 3 , what is the value of 55 tan x + ((55)/(tan x)) ?

$$\mathrm{If}\:\mathrm{8}\:\mathrm{cos}\:\mathrm{x}−\mathrm{8}\:\mathrm{sin}\:\mathrm{x}\:=\:\mathrm{3}\:,\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{value}\:\mathrm{of}\:\mathrm{55}\:\mathrm{tan}\:\mathrm{x}\:+\:\frac{\mathrm{55}}{\mathrm{tan}\:\mathrm{x}}\:? \\ $$

Question Number 116480 Answers: 1 Comments: 0

(1/8)+(1/(18))+(1/(30))+(1/(44))+(1/(60))+(1/(78))+(1/(98))+(1/(120))+........

$$\frac{\mathrm{1}}{\mathrm{8}}+\frac{\mathrm{1}}{\mathrm{18}}+\frac{\mathrm{1}}{\mathrm{30}}+\frac{\mathrm{1}}{\mathrm{44}}+\frac{\mathrm{1}}{\mathrm{60}}+\frac{\mathrm{1}}{\mathrm{78}}+\frac{\mathrm{1}}{\mathrm{98}}+\frac{\mathrm{1}}{\mathrm{120}}+........ \\ $$

Question Number 116466 Answers: 0 Comments: 5

Question Number 116459 Answers: 2 Comments: 0

Question Number 116457 Answers: 1 Comments: 0

Use Laplace transform to solve the initial value problem ty′′+(4t−2)y′+(13t−4)y=0 where y(0)=0 and y′(0)=0

$$\mathrm{Use}\:\mathrm{Laplace}\:\mathrm{transform}\:\mathrm{to}\:\mathrm{solve}\:\mathrm{the}\: \\ $$$$\mathrm{initial}\:\mathrm{value}\:\mathrm{problem}\:\mathrm{ty}''+\left(\mathrm{4t}−\mathrm{2}\right)\mathrm{y}'+\left(\mathrm{13t}−\mathrm{4}\right)\mathrm{y}=\mathrm{0} \\ $$$$\mathrm{where}\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{0}\:\mathrm{and}\:\mathrm{y}'\left(\mathrm{0}\right)=\mathrm{0} \\ $$

Question Number 116455 Answers: 0 Comments: 0

Question Number 116452 Answers: 2 Comments: 0

Question Number 116451 Answers: 3 Comments: 1

lim_(n→∞) ((((n+1)(n+2)(n+3)...(n+n)))^(1/n) /n) =?

$$\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\frac{\sqrt[{\mathrm{n}}]{\left(\mathrm{n}+\mathrm{1}\right)\left(\mathrm{n}+\mathrm{2}\right)\left(\mathrm{n}+\mathrm{3}\right)...\left(\mathrm{n}+\mathrm{n}\right)}}{\mathrm{n}}\:=? \\ $$

Question Number 116448 Answers: 2 Comments: 0

If sin (P) = −(8/(17)) ,where ((3π)/2)<P<2π and cos (Q)=−((24)/(25)), where π<Q<((3π)/2) what is the value of cos (2P+Q) =?

$$\mathrm{If}\:\mathrm{sin}\:\left(\mathrm{P}\right)\:=\:−\frac{\mathrm{8}}{\mathrm{17}}\:,\mathrm{where}\:\frac{\mathrm{3}\pi}{\mathrm{2}}<\mathrm{P}<\mathrm{2}\pi \\ $$$$\mathrm{and}\:\mathrm{cos}\:\left(\mathrm{Q}\right)=−\frac{\mathrm{24}}{\mathrm{25}},\:\mathrm{where}\:\pi<\mathrm{Q}<\frac{\mathrm{3}\pi}{\mathrm{2}} \\ $$$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{cos}\:\left(\mathrm{2P}+\mathrm{Q}\right)\:=? \\ $$

Question Number 116443 Answers: 0 Comments: 0

Question Number 116441 Answers: 2 Comments: 0

If sin (45°−x) = −(1/3) , where 45°<x<90° .What is the value of (6sin x−(√2))^2

$$\mathrm{If}\:\mathrm{sin}\:\left(\mathrm{45}°−\mathrm{x}\right)\:=\:−\frac{\mathrm{1}}{\mathrm{3}}\:,\:\mathrm{where}\:\mathrm{45}°<\mathrm{x}<\mathrm{90}° \\ $$$$.\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{6sin}\:\mathrm{x}−\sqrt{\mathrm{2}}\right)^{\mathrm{2}} \\ $$

Question Number 116437 Answers: 2 Comments: 0

Prove that π<((22)/7)

$$\mathrm{Prove}\:\mathrm{that}\:\pi<\frac{\mathrm{22}}{\mathrm{7}} \\ $$

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