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Question Number 167536    Answers: 0   Comments: 4

is cos(t+(π/2)) trigonometric function ?

$${is}\:{cos}\left({t}+\frac{\pi}{\mathrm{2}}\right)\:{trigonometric}\:{function}\:? \\ $$

Question Number 167533    Answers: 0   Comments: 3

Find out a,b,c where { ((a^2 +b^2 =c^2 )),((a+b+c=1000)) :}

$$\:\:\:\:\:\:\mathrm{Find}\:\mathrm{out}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\mathrm{where}\:\begin{cases}{\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} =\mathrm{c}^{\mathrm{2}} }\\{\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{1000}}\end{cases}\:\:\: \\ $$

Question Number 167532    Answers: 0   Comments: 5

Question Number 167496    Answers: 0   Comments: 0

Question Number 167493    Answers: 1   Comments: 0

(√(x+6))+(√(8−x))=A x∈Z and A∈R ^( faid Σx=?)

$$\sqrt{{x}+\mathrm{6}}+\sqrt{\mathrm{8}−{x}}={A} \\ $$$${x}\in{Z}\:\:\:{and}\:{A}\in{R}\:\:\:\:\:\:\:\:\:\overset{\:\:\:\:{faid}\:\:\Sigma{x}=?} {\:} \\ $$

Question Number 167492    Answers: 1   Comments: 0

x^a =(√2)+1 .........(1) x^b =(√2)−1 .........(2) (1/x^(a−b) )+(1/x^(b−a) )=? (1)÷(2)⇒(x^a /x^b )=(((√2)+1)/( (√(2−1))))⇒x^(a−b) =(((√2)+1)/( (√(2−1))))⇒(1/x^(a−b) )=(((√2)−1)/( (√2)+1))....(3) (2)÷(1)⇒(x^b /x^a )=(((√2)−1)/( (√2)+1))⇒x^(b−a) =(((√2)−1)/( (√2)+1))⇒(1/x^(b−a) )=(((√2)+1)/( (√2)−1))....(4) (1/x^(a−b) )+(1/x^(b−a) )=(((√2)−1)/( (√2)+1))+(((√2)+1)/( (√2)−1))=((((√2)−1)((√2)−1)+((√2)+1)((√2)+1))/(((√2)+1)((√2)−1))) =((((√2)−1)^2 +((√2)+1)^2 )/(2−1))=2−2(√2)+1+2+2(√2)+1 (1/x^(a−b) )+(1/x^(b−a) )=6

$${x}^{{a}} =\sqrt{\mathrm{2}}+\mathrm{1}\:\:\:\:\:.........\left(\mathrm{1}\right)\: \\ $$$${x}^{{b}} =\sqrt{\mathrm{2}}−\mathrm{1}\:\:\:\:\:.........\left(\mathrm{2}\right) \\ $$$$\frac{\mathrm{1}}{{x}^{{a}−{b}} }+\frac{\mathrm{1}}{{x}^{{b}−{a}} }=? \\ $$$$\left(\mathrm{1}\right)\boldsymbol{\div}\left(\mathrm{2}\right)\Rightarrow\frac{{x}^{{a}} }{{x}^{{b}} }=\frac{\sqrt{\mathrm{2}}+\mathrm{1}}{\:\sqrt{\mathrm{2}−\mathrm{1}}}\Rightarrow{x}^{{a}−{b}} =\frac{\sqrt{\mathrm{2}}+\mathrm{1}}{\:\sqrt{\mathrm{2}−\mathrm{1}}}\Rightarrow\frac{\mathrm{1}}{{x}^{{a}−{b}} }=\frac{\sqrt{\mathrm{2}}−\mathrm{1}}{\:\sqrt{\mathrm{2}}+\mathrm{1}}....\left(\mathrm{3}\right) \\ $$$$\left(\mathrm{2}\right)\boldsymbol{\div}\left(\mathrm{1}\right)\Rightarrow\frac{{x}^{{b}} }{{x}^{{a}} }=\frac{\sqrt{\mathrm{2}}−\mathrm{1}}{\:\sqrt{\mathrm{2}}+\mathrm{1}}\Rightarrow{x}^{{b}−{a}} =\frac{\sqrt{\mathrm{2}}−\mathrm{1}}{\:\sqrt{\mathrm{2}}+\mathrm{1}}\Rightarrow\frac{\mathrm{1}}{{x}^{{b}−{a}} }=\frac{\sqrt{\mathrm{2}}+\mathrm{1}}{\:\sqrt{\mathrm{2}}−\mathrm{1}}....\left(\mathrm{4}\right) \\ $$$$\frac{\mathrm{1}}{{x}^{{a}−{b}} }+\frac{\mathrm{1}}{{x}^{{b}−{a}} }=\frac{\sqrt{\mathrm{2}}−\mathrm{1}}{\:\sqrt{\mathrm{2}}+\mathrm{1}}+\frac{\sqrt{\mathrm{2}}+\mathrm{1}}{\:\sqrt{\mathrm{2}}−\mathrm{1}}=\frac{\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)+\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)}{\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)} \\ $$$$=\frac{\left(\sqrt{\mathrm{2}}−\mathrm{1}\right)^{\mathrm{2}} +\left(\sqrt{\mathrm{2}}+\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{2}−\mathrm{1}}=\mathrm{2}−\cancel{\mathrm{2}\sqrt{\mathrm{2}}}+\mathrm{1}+\mathrm{2}+\cancel{\mathrm{2}\sqrt{\mathrm{2}}}+\mathrm{1} \\ $$$$\frac{\mathrm{1}}{{x}^{{a}−{b}} }+\frac{\mathrm{1}}{{x}^{{b}−{a}} }=\mathrm{6} \\ $$

Question Number 167490    Answers: 1   Comments: 0

∫sin^3 xcos^2 xdx=?

$$\int{sin}^{\mathrm{3}} {xcos}^{\mathrm{2}} {xdx}=? \\ $$

Question Number 167489    Answers: 1   Comments: 0

a+(√x)=2 b+(x)^(1/4) =9 ^( (4a−b^2 )=?)

$${a}+\sqrt{{x}}=\mathrm{2} \\ $$$${b}+\sqrt[{\mathrm{4}}]{{x}}=\mathrm{9}\:\:\:\:\:\:\:\:\:\overset{\:\:\:\:\:\:\left(\mathrm{4}{a}−{b}^{\mathrm{2}} \right)=?} {\:} \\ $$

Question Number 167488    Answers: 1   Comments: 1

a^2 −4a+2=0 a≻2 (√((a^4 +4)/(12a^2 )))=?

$${a}^{\mathrm{2}} −\mathrm{4}{a}+\mathrm{2}=\mathrm{0}\:\:\:\:\:\:\:\:\:{a}\succ\mathrm{2} \\ $$$$\sqrt{\frac{{a}^{\mathrm{4}} +\mathrm{4}}{\mathrm{12}{a}^{\mathrm{2}} }}=? \\ $$

Question Number 167486    Answers: 1   Comments: 0

cos^2 x = cos (((4x)/3)) ; 0≤x≤2π

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{cos}\:^{\mathrm{2}} {x}\:=\:\mathrm{cos}\:\left(\frac{\mathrm{4}{x}}{\mathrm{3}}\right)\:;\:\mathrm{0}\leqslant{x}\leqslant\mathrm{2}\pi \\ $$

Question Number 167485    Answers: 1   Comments: 0

∫∫∫x^n dx

$$\int\int\int\boldsymbol{\mathrm{x}}^{\boldsymbol{\mathrm{n}}} \boldsymbol{\mathrm{dx}} \\ $$

Question Number 167484    Answers: 0   Comments: 0

∫_0 ^1 ln(x)cos^(−1) (x)dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \boldsymbol{\mathrm{ln}}\left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{cos}}^{−\mathrm{1}} \left(\boldsymbol{\mathrm{x}}\right)\boldsymbol{\mathrm{dx}} \\ $$

Question Number 167482    Answers: 0   Comments: 0

montrer que ∀x∈R−{0; 1} on a ((ln(x))/(x−1)) < (1/( (√x))) ?

$$\mathrm{montrer}\:\mathrm{que}\:\forall\mathrm{x}\in\mathbb{R}−\left\{\mathrm{0};\:\mathrm{1}\right\}\:\mathrm{on}\:\mathrm{a} \\ $$$$\frac{\mathrm{ln}\left(\mathrm{x}\right)}{\mathrm{x}−\mathrm{1}}\:<\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}}}\:? \\ $$

Question Number 167644    Answers: 1   Comments: 2

find the exact value of ∫_0 ^(2π) (dx/( (√(1+sin x))+(√(1+cos x))))

$$\mathrm{find}\:\mathrm{the}\:\mathrm{exact}\:\mathrm{value}\:\mathrm{of} \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}\frac{{dx}}{\:\sqrt{\mathrm{1}+\mathrm{sin}\:{x}}+\sqrt{\mathrm{1}+\mathrm{cos}\:{x}}} \\ $$

Question Number 167477    Answers: 0   Comments: 0

Question Number 167473    Answers: 2   Comments: 0

solve ∫_2 ^( 3) ⌊ x^( 2) − 2x +5 ⌋dx=?

$$\:\: \\ $$$$\:\:\:\:\:\:{solve} \\ $$$$ \\ $$$$\:\:\:\:\:\int_{\mathrm{2}} ^{\:\mathrm{3}} \lfloor\:{x}^{\:\mathrm{2}} −\:\mathrm{2}{x}\:+\mathrm{5}\:\rfloor{dx}=? \\ $$$$ \\ $$

Question Number 167471    Answers: 0   Comments: 0

Montrer que (R^n ,d_1 ),(R^n ,d_2 ) et(R^n ,d_(oo) ) sont des espaces metrique

$${Montrer}\:{que} \\ $$$$\left({R}^{{n}} ,{d}_{\mathrm{1}} \right),\left({R}^{{n}} ,{d}_{\mathrm{2}} \right)\:{et}\left({R}^{{n}} ,{d}_{{oo}} \right) \\ $$$${sont}\:{des}\:{espaces}\:{metrique} \\ $$

Question Number 167468    Answers: 1   Comments: 0

Question Number 167462    Answers: 2   Comments: 0

4^x +6^x =9^x How much the x is?

$$\mathrm{4}^{{x}} +\mathrm{6}^{{x}} =\mathrm{9}^{{x}} \\ $$$${How}\:{much}\:{the}\:{x}\:{is}? \\ $$

Question Number 167456    Answers: 1   Comments: 0

Question Number 167454    Answers: 0   Comments: 0

Question Number 168097    Answers: 0   Comments: 0

Question Number 167449    Answers: 0   Comments: 1

Question Number 167448    Answers: 0   Comments: 2

Question Number 167441    Answers: 0   Comments: 0

Question Number 167438    Answers: 2   Comments: 0

∫ ((sin 4x)/(4sin^4 x−4sin^2 x+1)) dx=?

$$\:\:\int\:\frac{\mathrm{sin}\:\mathrm{4x}}{\mathrm{4sin}\:^{\mathrm{4}} \mathrm{x}−\mathrm{4sin}\:^{\mathrm{2}} \mathrm{x}+\mathrm{1}}\:\mathrm{dx}=? \\ $$

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