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Question Number 141469 Answers: 3 Comments: 0

simplify (log_3 11)(log_(11) 13)(log_(13) 15)(log_(15) 27)(log_(27) 81) please i need help

$$\mathrm{simplify} \\ $$$$\left(\mathrm{log}_{\mathrm{3}} \mathrm{11}\right)\left(\mathrm{log}_{\mathrm{11}} \mathrm{13}\right)\left(\mathrm{log}_{\mathrm{13}} \mathrm{15}\right)\left(\mathrm{log}_{\mathrm{15}} \mathrm{27}\right)\left(\mathrm{log}_{\mathrm{27}} \mathrm{81}\right) \\ $$$$\mathrm{please}\:\mathrm{i}\:\mathrm{need}\:\mathrm{help} \\ $$

Question Number 141489 Answers: 2 Comments: 0

Question Number 141463 Answers: 1 Comments: 2

lim_(x→∞) x^2 ( (((x^3 +x)/(x^3 +1)))^(1/(7 )) −cos (1/x))?

$$\:\:\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:{x}^{\mathrm{2}} \left(\:\sqrt[{\mathrm{7}\:\:}]{\frac{{x}^{\mathrm{3}} +{x}}{{x}^{\mathrm{3}} +\mathrm{1}}}\:−\mathrm{cos}\:\frac{\mathrm{1}}{{x}}\right)? \\ $$

Question Number 141457 Answers: 6 Comments: 0

Question Number 141454 Answers: 0 Comments: 0

Let a,b,c ≥ 0 and a+b+c = 4. Prove that ((a^2 +ab+b^2 )/((a+b+4)^2 ))+((b^2 +bc+c^2 )/((b+c+4)^2 ))+((c^2 +ca+a^2 )/((c+a+4)^2 )) ≤ (1/2)

$$\mathrm{Let}\:{a},{b},{c}\:\geqslant\:\mathrm{0}\:\mathrm{and}\:{a}+{b}+{c}\:=\:\mathrm{4}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{2}} +{ab}+{b}^{\mathrm{2}} }{\left({a}+{b}+\mathrm{4}\right)^{\mathrm{2}} }+\frac{{b}^{\mathrm{2}} +{bc}+{c}^{\mathrm{2}} }{\left({b}+{c}+\mathrm{4}\right)^{\mathrm{2}} }+\frac{{c}^{\mathrm{2}} +{ca}+{a}^{\mathrm{2}} }{\left({c}+{a}+\mathrm{4}\right)^{\mathrm{2}} }\:\leqslant\:\frac{\mathrm{1}}{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 141453 Answers: 3 Comments: 1

Question Number 141452 Answers: 1 Comments: 1

Evaluate the integral ∫sin(dx)

$${Evaluate}\:{the}\:{integral}\:\:\:\int{sin}\left({dx}\right) \\ $$

Question Number 141446 Answers: 1 Comments: 0

Let P be the point ((a/2)(t^2 +(1/t^2 )),a(t−(1/t))) Find the locus of P, as t varies.

$$\mathrm{Let}\:\mathrm{P}\:\mathrm{be}\:\mathrm{the}\:\mathrm{point}\:\left(\frac{{a}}{\mathrm{2}}\left({t}^{\mathrm{2}} +\frac{\mathrm{1}}{{t}^{\mathrm{2}} }\right),{a}\left({t}−\frac{\mathrm{1}}{{t}}\right)\right) \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{locus}\:\mathrm{of}\:\mathrm{P},\:\mathrm{as}\:{t}\:\mathrm{varies}. \\ $$

Question Number 141444 Answers: 0 Comments: 0

Question Number 141492 Answers: 0 Comments: 1

Question Number 141437 Answers: 0 Comments: 0

Question Number 141435 Answers: 1 Comments: 0

Find all the arraangment of all the letters of the word SYLLABUSES such that each word contains the word BUS.

$$\mathrm{Find}\:\mathrm{all}\:\mathrm{the}\:\mathrm{arraangment}\:\mathrm{of}\:\mathrm{all}\:\mathrm{the}\:\mathrm{letters} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\mathrm{SYLLABUSES}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{each}\:\mathrm{word}\:\mathrm{contains}\:\mathrm{the}\:\mathrm{word}\:\mathrm{BUS}. \\ $$

Question Number 141431 Answers: 2 Comments: 0

2∫_0 ^( 1) ∫_0 ^( 2) (x+2y)^8 dxdy

$$\mathrm{2}\int_{\mathrm{0}} ^{\:\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{2}} \left({x}+\mathrm{2}{y}\right)^{\mathrm{8}} \:{dxdy} \\ $$

Question Number 141419 Answers: 2 Comments: 0

𝛗:=∫_0 ^( ∞) ((ln(cosh(x)))/(cosh(x)))dx=^? ∫_0 ^( (π/2)) log((1/(sin(x))))dx

$$ \\ $$$$\:\:\:\:\boldsymbol{\phi}:=\int_{\mathrm{0}} ^{\:\infty} \frac{{ln}\left({cosh}\left({x}\right)\right)}{{cosh}\left({x}\right)}{dx}\overset{?} {=}\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} {log}\left(\frac{\mathrm{1}}{{sin}\left({x}\right)}\right){dx} \\ $$

Question Number 141409 Answers: 1 Comments: 0

Prove that ∀n∈N ∫^( n+1) _n lnt dt ≤ ln(n+(1/2))

$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\forall\mathrm{n}\in\mathbb{N}\:\:\:\:\underset{\mathrm{n}} {\int}^{\:\mathrm{n}+\mathrm{1}} \mathrm{lnt}\:\mathrm{dt}\:\leqslant\:\mathrm{ln}\left(\mathrm{n}+\frac{\mathrm{1}}{\mathrm{2}}\right) \\ $$

Question Number 141407 Answers: 2 Comments: 0

Ω:=∫_0 ^( ∞) (dx/((x^4 −x^2 +1)^3 ))=?

$$ \\ $$$$\:\:\:\:\:\:\Omega:=\int_{\mathrm{0}} ^{\:\infty} \frac{{dx}}{\left({x}^{\mathrm{4}} −{x}^{\mathrm{2}} +\mathrm{1}\right)^{\mathrm{3}} }=? \\ $$

Question Number 141405 Answers: 1 Comments: 0

Find the minimum value of k such that for arbitrary a,b >0 we have (a)^(1/(3 )) + (b)^(1/(3 )) ≤ k ((a+b))^(1/(3 ))

$$\:\:\:\:\:{Find}\:{the}\:{minimum}\:{value}\:{of}\:{k} \\ $$$$\:\:\:\:\:{such}\:{that}\:{for}\:{arbitrary}\:{a},{b}\:>\mathrm{0} \\ $$$$\:\:\:\:\:{we}\:{have}\:\:\sqrt[{\mathrm{3}\:}]{{a}}\:+\:\sqrt[{\mathrm{3}\:}]{{b}}\:\leqslant\:{k}\:\sqrt[{\mathrm{3}\:}]{{a}+{b}}\: \\ $$

Question Number 141423 Answers: 1 Comments: 0

tan (x+y)= ((12)/5) sin (x−y) = (3/5) x+y , x−y are acute angles . tan x tan y = ?

$$\mathrm{tan}\:\left({x}+{y}\right)=\:\frac{\mathrm{12}}{\mathrm{5}} \\ $$$$\mathrm{sin}\:\left({x}−{y}\right)\:=\:\frac{\mathrm{3}}{\mathrm{5}} \\ $$$${x}+{y}\:,\:{x}−{y}\:\:{are}\:\:{acute}\:\:{angles}\:. \\ $$$$\mathrm{tan}\:{x}\:\mathrm{tan}\:{y}\:=\:\:? \\ $$

Question Number 141400 Answers: 3 Comments: 0

fjnd inverse of matrix [(2,(−5)),(1,3) ]

$${fjnd}\:{inverse}\:{of}\:{matrix}\begin{bmatrix}{\mathrm{2}}&{−\mathrm{5}}\\{\mathrm{1}}&{\mathrm{3}}\end{bmatrix} \\ $$

Question Number 141398 Answers: 0 Comments: 0

Question Number 141395 Answers: 1 Comments: 0

A 64.00 cm3 piece of wood is in the shape of a cube. A lazy ant wants to walk from one corner to the very opposite corner of the cube. What is its minimum path length?

$$ \\ $$A 64.00 cm3 piece of wood is in the shape of a cube. A lazy ant wants to walk from one corner to the very opposite corner of the cube. What is its minimum path length?

Question Number 141365 Answers: 1 Comments: 0

log _(9/4) ((1/(2(√3)))(√(6−(1/(2(√3)))(√(6−(1/(2(√3)))(√(6−(1/(2(√3)))(√(...))))))))) =?

$$\:\mathrm{log}\:_{\frac{\mathrm{9}}{\mathrm{4}}} \left(\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{\mathrm{6}−\frac{\mathrm{1}}{\mathrm{2}\sqrt{\mathrm{3}}}\sqrt{...}}}}\right)\:=? \\ $$

Question Number 141360 Answers: 0 Comments: 1

∫_0 ^(π/2) (√(cosxsenx))dx

$$\int_{\mathrm{0}} ^{\pi/\mathrm{2}} \sqrt{{cosxsenx}}{dx} \\ $$

Question Number 141359 Answers: 0 Comments: 2

Question Number 141356 Answers: 2 Comments: 0

lim_(x→+∞) (((x+1)/( (√(x^2 +1)))) −1)

$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}\left(\frac{{x}+\mathrm{1}}{\:\sqrt{{x}^{\mathrm{2}} +\mathrm{1}}}\:−\mathrm{1}\right) \\ $$

Question Number 141362 Answers: 1 Comments: 0

∫sen(2θ)cos^4 (2θ)dθ

$$\int{sen}\left(\mathrm{2}\theta\right){cos}^{\mathrm{4}} \left(\mathrm{2}\theta\right){d}\theta \\ $$

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