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Question Number 77778 Answers: 0 Comments: 2

∫((cosx)/(2−cosx))dx

$$\int\frac{{cosx}}{\mathrm{2}−{cosx}}{dx} \\ $$$$ \\ $$

Question Number 77777 Answers: 1 Comments: 0

The number of words can be made formed using all letters in the word ′amutasia′ by not containing the three vowels side by side is ?

$${The}\:{number} \\ $$$${of}\:{words}\:{can}\:{be}\:{made}\:{formed} \\ $$$${using}\:{all}\:{letters}\:{in}\:{the}\:{word} \\ $$$$'{amutasia}'\:{by}\:{not}\:{containing} \\ $$$${the}\:{three}\:{vowels}\:{side}\:{by}\:{side}\:{is}\:? \\ $$

Question Number 77765 Answers: 0 Comments: 2

Hello please how can we calculate the yield in % of ohmic conductor in actif circuit with Battery( with his resistance) and a motor( with his resistance) knowing theirs caracteristics and the intensity? I need a formula.

$$\mathrm{Hello}\: \\ $$$$\mathrm{please}\:\mathrm{how}\:\mathrm{can}\:\mathrm{we}\:\mathrm{calculate}\:\mathrm{the}\:\mathrm{yield} \\ $$$$\mathrm{in}\:\%\:\mathrm{of}\:\mathrm{ohmic}\:\mathrm{conductor}\:\mathrm{in}\:\mathrm{actif}\:\mathrm{circuit}\: \\ $$$$\mathrm{with}\:\mathrm{Battery}\left(\:\mathrm{with}\:\mathrm{his}\:\mathrm{resistance}\right) \\ $$$$\mathrm{and}\:\mathrm{a}\:\mathrm{motor}\left(\:\mathrm{with}\:\mathrm{his}\:\mathrm{resistance}\right) \\ $$$$\mathrm{knowing}\:\:\mathrm{theirs}\:\mathrm{caracteristics}\:\mathrm{and} \\ $$$$\mathrm{the}\:\mathrm{intensity}? \\ $$$$\mathrm{I}\:\mathrm{need}\:\mathrm{a}\:\mathrm{formula}. \\ $$

Question Number 77760 Answers: 0 Comments: 0

find the value of Σ_(n=0) ^∞ (1/(n^2 +n+1))

$${find}\:{the}\:{value}\:{of}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+{n}+\mathrm{1}} \\ $$

Question Number 77759 Answers: 0 Comments: 0

calculate Σ_(n=0) ^∞ (1/(n^2 +1))

$${calculate}\:\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{{n}^{\mathrm{2}} \:+\mathrm{1}} \\ $$

Question Number 77758 Answers: 0 Comments: 0

calculate ∫_0 ^∞ ((√(3+x^2 ))/((x^2 +1)(√(x^2 −x+2))))dx

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\sqrt{\mathrm{3}+{x}^{\mathrm{2}} }}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\sqrt{{x}^{\mathrm{2}} −{x}+\mathrm{2}}}{dx} \\ $$

Question Number 77757 Answers: 0 Comments: 0

find ∫_1 ^(+∞) (((x^2 −1)dx)/(x^4 −x^2 +1))

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

Question Number 77755 Answers: 0 Comments: 2

1)calculste f(a)=∫_0 ^∞ (dx/(√(x^2 −x+a))) with a >1 2) calculate f^′ (a) at form of integral then find its value.

$$\left.\mathrm{1}\right){calculste}\:\:{f}\left({a}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\sqrt{{x}^{\mathrm{2}} −{x}+{a}}}\:\:{with}\:\:{a}\:>\mathrm{1} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({a}\right)\:{at}\:{form}\:{of}\:{integral}\:{then}\:\:{find} \\ $$$${its}\:{value}. \\ $$$$ \\ $$$$ \\ $$

Question Number 77754 Answers: 1 Comments: 3

U_n isa sequence woch verify U_n +U_(n+1) =n^2 (−1)^n ∀ n≥0 1) detdrmine U_n interm of n 2) find nsture of the serie Σ (U_n /n^4 ) 3) calculate Σ_(k+j=n) U_k U_j

$${U}_{{n}} {isa}\:{sequence}\:{woch}\:{verify} \\ $$$${U}_{{n}} +{U}_{{n}+\mathrm{1}} ={n}^{\mathrm{2}} \left(−\mathrm{1}\right)^{{n}} \:\:\forall\:{n}\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{detdrmine}\:{U}_{{n}} \:{interm}\:{of}\:{n} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nsture}\:{of}\:{the}\:{serie}\:\Sigma\:\frac{{U}_{{n}} }{{n}^{\mathrm{4}} } \\ $$$$\left.\mathrm{3}\right)\:{calculate}\:\sum_{{k}+{j}={n}} \:\:{U}_{{k}} {U}_{{j}} \\ $$

Question Number 77772 Answers: 0 Comments: 3

Question Number 77752 Answers: 0 Comments: 1

let f(λ) =∫_(−∞) ^(+∞) ((sin( λe^x +e^(−x) ))/(x^2 +λ^2 ))dx with λ≥0 1) detdrmine a explicit form of f(λ) 2) calculate f^′ (λ) at form ofintergral and find its value.

$${let}\:{f}\left(\lambda\right)\:=\int_{−\infty} ^{+\infty} \:\frac{{sin}\left(\:\lambda{e}^{{x}} \:+{e}^{−{x}} \right)}{{x}^{\mathrm{2}} \:+\lambda^{\mathrm{2}} }{dx}\:{with}\:\lambda\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{detdrmine}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left(\lambda\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left(\lambda\right)\:{at}\:{form}\:{ofintergral}\:{and}\:{find} \\ $$$${its}\:{value}. \\ $$

Question Number 77751 Answers: 0 Comments: 2

calculate ∫_(−∞) ^(+∞) ((cos(e^x +e^(−x) ))/((x^2 +x+1)^2 ))dx

$${calculate}\:\int_{−\infty} ^{+\infty} \:\frac{{cos}\left({e}^{{x}} +{e}^{−{x}} \right)}{\left({x}^{\mathrm{2}} +{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

Question Number 77746 Answers: 0 Comments: 4

Master comes after Chess disappeared. Boyka comes after Master disappeared. BK comes after Boyka disappeared. What comes after BK disappeared? 1. A−Team 2. Girlka 3. Bezirksschornsteinfegermeister 4. none from above [A question from NMO 2019 in Madagascar]

$${Master}\:{comes}\:{after}\:{Chess}\:{disappeared}. \\ $$$${Boyka}\:{comes}\:{after}\:{Master}\:{disappeared}. \\ $$$${BK}\:{comes}\:{after}\:{Boyka}\:{disappeared}. \\ $$$${What}\:{comes}\:{after}\:{BK}\:{disappeared}? \\ $$$$\mathrm{1}.\:\:{A}−{Team} \\ $$$$\mathrm{2}.\:\:{Girlka} \\ $$$$\mathrm{3}.\:\:{Bezirksschornsteinfegermeister} \\ $$$$\mathrm{4}.\:\:{none}\:{from}\:{above} \\ $$$$ \\ $$$$\left[{A}\:{question}\:{from}\:{NMO}\:\mathrm{2019}\:{in}\:{Madagascar}\right] \\ $$

Question Number 77745 Answers: 0 Comments: 1

ABC is any triangle. C′ . B′ .A′ are respectively middles of [AB] . [AC] and [BC]. we suppose that AB=c AC=b BC=a. 1) u^(→ ) =a^2 BC^→ +b^(2 ) C^→ A+c^2 AB^→ is a vector Demonstrate that u^→ =(a^2 −b^2 )AC^→ +(c^2 −a^2 )AB^→ . i have done it. 2)Deduct that u^→ is not a null vector.

$$\mathrm{ABC}\:\mathrm{is}\:\mathrm{any}\:\mathrm{triangle}. \\ $$$$\mathrm{C}'\:.\:\mathrm{B}'\:\:.\mathrm{A}'\:\:\mathrm{are}\:\mathrm{respectively}\:\mathrm{middles} \\ $$$$\mathrm{of}\:\left[\mathrm{AB}\right]\:.\:\left[\mathrm{AC}\right]\:\:\mathrm{and}\:\:\left[\mathrm{BC}\right]. \\ $$$$\mathrm{we}\:\mathrm{suppose}\:\mathrm{that}\: \\ $$$$\mathrm{AB}=\mathrm{c}\:\:\:\mathrm{AC}=\mathrm{b}\:\:\:\:\mathrm{BC}=\mathrm{a}. \\ $$$$\left.\mathrm{1}\right)\:\overset{\rightarrow\:} {\mathrm{u}}=\mathrm{a}^{\mathrm{2}} \mathrm{B}\overset{\rightarrow} {\mathrm{C}}+\mathrm{b}^{\mathrm{2}\:} \overset{\rightarrow} {\mathrm{C}A}+\mathrm{c}^{\mathrm{2}} \mathrm{A}\overset{\rightarrow} {\mathrm{B}}\:\:\mathrm{is}\:\mathrm{a}\:\mathrm{vector} \\ $$$$\mathrm{Demonstrate}\:\mathrm{that}\:\overset{\rightarrow} {\mathrm{u}}=\left(\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} \right)\mathrm{A}\overset{\rightarrow} {\mathrm{C}}+\left(\mathrm{c}^{\mathrm{2}} −\mathrm{a}^{\mathrm{2}} \right)\mathrm{A}\overset{\rightarrow} {\mathrm{B}}. \\ $$$${i}\:{have}\:{done}\:{it}. \\ $$$$\left.\mathrm{2}\right){D}\mathrm{educt}\:\mathrm{that}\:\overset{\rightarrow} {\mathrm{u}}\:\mathrm{is}\:\mathrm{not}\:\mathrm{a}\:\mathrm{null}\:\mathrm{vector}. \\ $$

Question Number 77741 Answers: 1 Comments: 1