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Question Number 52814 Answers: 0 Comments: 6

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Question Number 52806 Answers: 1 Comments: 2

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Question Number 52795 Answers: 2 Comments: 0

Question Number 52790 Answers: 1 Comments: 0

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Question Number 52741 Answers: 1 Comments: 0

please help me solve this question sir. In a survey of 100 out-patients who reported at the hospital one day, It was found out that 70 coplained of fever, 50 complained of stomach ache and 30 were injured. All patients had at least one of the complaints and 44 had exactly two of the complaints. How many had all complaints?

$$\: \\ $$$${please}\:{help}\:{me}\:{solve}\:{this}\:{question}\:{sir}. \\ $$$$\mathrm{I}{n}\:{a}\:{survey}\:{of}\:\:\mathrm{100}\:{out}-{patients}\:{who}\: \\ $$$${reported}\:{at}\:{the}\:{hospital}\:{one}\:{day},\:{It}\: \\ $$$${was}\:{found}\:{out}\:{that}\:\mathrm{70}\:{coplained}\:{of}\: \\ $$$${fever},\:\mathrm{50}\:{complained}\:{of}\:{stomach}\: \\ $$$${ache}\:{and}\:\mathrm{30}\:{were}\:\:{injured}.\:{All}\:\: \\ $$$${patients}\:{had}\:{at}\:{least}\:{one}\:{of}\:{the}\: \\ $$$${complaints}\:{and}\:\mathrm{44}\:{had}\:{exactly}\:{two}\: \\ $$$${of}\:{the}\:{complaints}.\:{How}\:{many}\:{had}\:{all}\: \\ $$$${complaints}? \\ $$

Question Number 52730 Answers: 0 Comments: 0

The area of a re

$${The}\:{area}\:{of}\:\:{a}\:{re} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 52731 Answers: 1 Comments: 11

Question Number 52728 Answers: 0 Comments: 0

How can you proove what follows ? If (4n+1) is prime, then : 4n + 1 = a^2 + b^2 with a, b ∈ N Thank you

$${How}\:{can}\:{you}\:{proove}\:{what}\:{follows}\:? \\ $$$$ \\ $$$$\mathrm{If}\:\left(\mathrm{4}{n}+\mathrm{1}\right)\:\mathrm{is}\:\mathrm{prime},\:\mathrm{then}\:: \\ $$$$\:\:\:\mathrm{4}{n}\:+\:\mathrm{1}\:=\:{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:\:\:\:\mathrm{with}\:{a},\:{b}\:\in\:\mathbb{N} \\ $$$$ \\ $$$${Thank}\:{you} \\ $$

Question Number 52713 Answers: 2 Comments: 1

if ∣x∣=∣y∣ is (x/y)=−1?

$${if}\:\mid{x}\mid=\mid{y}\mid\:{is}\:\frac{{x}}{{y}}=−\mathrm{1}? \\ $$

Question Number 52708 Answers: 0 Comments: 0

Question Number 52703 Answers: 0 Comments: 1

let f(t) =∫_0 ^∞ ((cos^2 (tx))/((x^2 +3)^2 )) dx with t ≥0 1) give a explicit form of f(t) 2) find the value of ∫_0 ^∞ ((xsin(2tx))/((x^2 +3)^2 )) dx 3) give the values of integrals ∫_0 ^∞ (dx/((x^2 +3)^2 )) and ∫_0 ^∞ ((cos^2 (πx))/((x^2 +3)^2 ))dx 4) give the values of integrals ∫_0 ^∞ ((xsin(πx))/((x^2 +3)^2 )) and ∫_0 ^∞ ((xsin(((πx)/2)))/((x^2 +3)^2 )) dx .

$${let}\:{f}\left({t}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}^{\mathrm{2}} \left({tx}\right)}{\left({x}^{\mathrm{2}} +\mathrm{3}\right)^{\mathrm{2}} }\:{dx}\:\:{with}\:{t}\:\geqslant\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{give}\:{a}\:{explicit}\:{form}\:{of}\:{f}\left({t}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{xsin}\left(\mathrm{2}{tx}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }\:{dx} \\ $$$$\left.\mathrm{3}\right)\:{give}\:{the}\:{values}\:{of}\:{integrals}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }\:{and}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{cos}^{\mathrm{2}} \left(\pi{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{4}\right)\:{give}\:{the}\:{values}\:{of}\:{integrals}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{xsin}\left(\pi{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }\:{and}\:\:\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{xsin}\left(\frac{\pi{x}}{\mathrm{2}}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{3}\right)^{\mathrm{2}} }\:{dx}\:. \\ $$

Question Number 52683 Answers: 0 Comments: 3

let f(λ) =∫_(−∞) ^(+∞) ((sin(λx))/((x^2 +2λx +1)^2 ))dx with ∣λ∣<1 1) find the value of f(λ) 2) calculate ∫_(−∞) ^(+∞) ((sin((x/(2 ))))/((x^2 +x+1)^2 ))dx 3) find A(θ) =∫_(−∞) ^(+∞) ((sin((cosθ)x))/((x^2 +2cosθ x +1)^2 )) that we suppose 0<θ<(π/2)

$${let}\:{f}\left(\lambda\right)\:=\int_{−\infty} ^{+\infty} \:\:\frac{{sin}\left(\lambda{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{2}\lambda{x}\:+\mathrm{1}\right)^{\mathrm{2}} }{dx}\:\:\:\:{with}\:\mid\lambda\mid<\mathrm{1} \\ $$$$\left.\mathrm{1}\right)\:{find}\:{the}\:{value}\:{of}\:{f}\left(\lambda\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{sin}\left(\frac{{x}}{\mathrm{2}\:}\right)}{\left({x}^{\mathrm{2}} \:\:+{x}+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$$$\left.\mathrm{3}\right)\:{find}\:\:{A}\left(\theta\right)\:=\int_{−\infty} ^{+\infty} \:\:\:\:\frac{{sin}\left(\left({cos}\theta\right){x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{2}{cos}\theta\:{x}\:+\mathrm{1}\right)^{\mathrm{2}} }\:\:{that}\:{we}\:{suppose}\:\mathrm{0}<\theta<\frac{\pi}{\mathrm{2}} \\ $$

Question Number 52682 Answers: 1 Comments: 1

find nature of the serie Σ_(n=1) ^∞ (((√(n+1))−(√n))/(nln(n+1)))

$${find}\:{nature}\:{of}\:{the}\:{serie}\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\:\frac{\sqrt{{n}+\mathrm{1}}−\sqrt{{n}}}{{nln}\left({n}+\mathrm{1}\right)} \\ $$

Question Number 52680 Answers: 0 Comments: 1

let f_n (x)=((sin(nx))/n^3 ) and f(x)=Σ_(n=1) ^∞ f_n (x) calculate ∫_0 ^π f(x)dx .

$${let}\:{f}_{{n}} \left({x}\right)=\frac{{sin}\left({nx}\right)}{{n}^{\mathrm{3}} }\:\:\:{and}\:{f}\left({x}\right)=\sum_{{n}=\mathrm{1}} ^{\infty} \:{f}_{{n}} \left({x}\right) \\ $$$${calculate}\:\int_{\mathrm{0}} ^{\pi} \:{f}\left({x}\right){dx}\:. \\ $$

Question Number 52679 Answers: 0 Comments: 1

let f_n (x)=(((−1)^n )/(n+x)) with x>0 1) study the simple convergence of Σ f_n (x) 2) calculate f^′ (x)

$${let}\:{f}_{{n}} \left({x}\right)=\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}+{x}}\:\:{with}\:{x}>\mathrm{0} \\ $$$$\left.\mathrm{1}\right)\:{study}\:{the}\:{simple}\:{convergence}\:{of}\:\Sigma\:{f}_{{n}} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:{f}^{'} \left({x}\right) \\ $$

Question Number 52678 Answers: 1 Comments: 1

let u_n =ln{cos(2^(−n) )} calculate Σ_(n=0) ^∞ u_n