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AllQuestion and Answers: Page 74

Question Number 206060 Answers: 1 Comments: 0

Question Number 206053 Answers: 1 Comments: 1

Question Number 206048 Answers: 1 Comments: 0

Prove that 2^(sin^2 θ) + 2^(cos^2 θ) ≥ 2(√2).

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{2}^{\mathrm{sin}^{\mathrm{2}} \theta} \:+\:\mathrm{2}^{\mathrm{cos}^{\mathrm{2}} \theta} \:\geqslant\:\mathrm{2}\sqrt{\mathrm{2}}. \\ $$

Question Number 206047 Answers: 1 Comments: 0

Question Number 206045 Answers: 2 Comments: 1

Question Number 206037 Answers: 2 Comments: 0

is it a polynomial? x^3 −2x^2 +(√x^2 )+10

$${is}\:{it}\:{a}\:{polynomial}? \\ $$$${x}^{\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} +\sqrt{{x}^{\mathrm{2}} }+\mathrm{10} \\ $$

Question Number 206036 Answers: 1 Comments: 0

is it a polynomial? 2x^2 +3x−(2/x^(−2) )

$${is}\:{it}\:{a}\:{polynomial}? \\ $$$$\mathrm{2}{x}^{\mathrm{2}} +\mathrm{3}{x}−\frac{\mathrm{2}}{{x}^{−\mathrm{2}} } \\ $$

Question Number 206038 Answers: 2 Comments: 0

(√(1 + 2023(√(1 + 2024(√(1+ 2025(√(1 + 2026(√(1 + ..............∞)))))))))) = ?

$$\sqrt{\mathrm{1}\:+\:\mathrm{2023}\sqrt{\mathrm{1}\:+\:\mathrm{2024}\sqrt{\mathrm{1}+\:\mathrm{2025}\sqrt{\mathrm{1}\:+\:\mathrm{2026}\sqrt{\mathrm{1}\:+\:..............\infty}}}}}\:=\:?\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 206025 Answers: 2 Comments: 0

2^(2024) = x (mod 10)

$$\:\:\:\:\:\mathrm{2}^{\mathrm{2024}} \:=\:{x}\:\left({mod}\:\mathrm{10}\right)\: \\ $$

Question Number 206024 Answers: 2 Comments: 0

proove e^(iπ) +1=0

$${proove} \\ $$$${e}^{{i}\pi} +\mathrm{1}=\mathrm{0} \\ $$

Question Number 206020 Answers: 1 Comments: 0

Question Number 206007 Answers: 1 Comments: 1

(E,<,> ): prouve <x,y>=(1/4)Σ_(k=o) ^3 i^k ∣∣x + i^k y∣∣^2

$$\left({E},<,>\:\right):\:\:\:{prouve} \\ $$$$<{x},{y}>=\frac{\mathrm{1}}{\mathrm{4}}\underset{{k}={o}} {\overset{\mathrm{3}} {\sum}}{i}^{{k}} \mid\mid{x}\:+\:{i}^{{k}} {y}\mid\mid^{\mathrm{2}} \\ $$

Question Number 206003 Answers: 2 Comments: 0

Question Number 205993 Answers: 1 Comments: 0

Given that (3−(√n))^2 =m−6(√2) where m,n are positive integers find m−n

$$\:{Given}\:{that}\:\left(\mathrm{3}−\sqrt{{n}}\right)^{\mathrm{2}} ={m}−\mathrm{6}\sqrt{\mathrm{2}}\:{where} \\ $$$${m},{n}\:{are}\:{positive}\:{integers}\:{find}\:{m}−{n} \\ $$

Question Number 205964 Answers: 0 Comments: 1

To Tinkutara Please remove the user “MathedUp”. He had this profile picture and now he uploaded porn pictures. I made screenshots in case he deletes those before you noticed.

$$\mathrm{To}\:\mathrm{Tinkutara} \\ $$$$\mathrm{Please}\:\mathrm{remove}\:\mathrm{the}\:\mathrm{user}\:``\mathrm{MathedUp}''.\:\mathrm{He} \\ $$$$\mathrm{had}\:\mathrm{this}\:\mathrm{profile}\:\mathrm{picture}\:\mathrm{and}\:\mathrm{now}\:\mathrm{he}\:\mathrm{uploaded} \\ $$$$\mathrm{porn}\:\mathrm{pictures}.\:\mathrm{I}\:\mathrm{made}\:\mathrm{screenshots}\:\mathrm{in}\:\mathrm{case} \\ $$$$\mathrm{he}\:\mathrm{deletes}\:\mathrm{those}\:\mathrm{before}\:\mathrm{you}\:\mathrm{noticed}. \\ $$

Question Number 205990 Answers: 2 Comments: 0

If x = ((√3)/2) then (((√(1 + x)) + (√(1 − x)))/( (√(1 + x)) − (√(1 − x)))) = ?

$$\mathrm{If}\:{x}\:=\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}}\:\mathrm{then}\:\frac{\sqrt{\mathrm{1}\:+\:{x}}\:+\:\sqrt{\mathrm{1}\:−\:{x}}}{\:\sqrt{\mathrm{1}\:+\:{x}}\:−\:\sqrt{\mathrm{1}\:−\:{x}}}\:=\:? \\ $$

Question Number 205988 Answers: 1 Comments: 0

Given f(x+1)=2^(f(x)) .f(1) and f(1)= 16 then f(2016)=?

$$\:\:{Given}\:{f}\left({x}+\mathrm{1}\right)=\mathrm{2}^{{f}\left({x}\right)} .{f}\left(\mathrm{1}\right) \\ $$$$\:\:{and}\:{f}\left(\mathrm{1}\right)=\:\mathrm{16}\: \\ $$$$\:\:{then}\:{f}\left(\mathrm{2016}\right)=? \\ $$

Question Number 205941 Answers: 1 Comments: 0

2+(2/(2−(2/(2+(2/(2−(2/(2+(2/3))))))))) =?

$$\:\:\:\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{2}−\frac{\mathrm{2}}{\mathrm{2}+\frac{\mathrm{2}}{\mathrm{3}}}}}}\:=?\: \\ $$$$\: \\ $$

Question Number 205938 Answers: 0 Comments: 0

(dx/dt)= y+4z ....(1) (dy/dt) = z−x.....(2) (dz/dt) = x − y....(3) solve the sistem by operator ( elemination method )

$$\frac{{dx}}{{dt}}=\:{y}+\mathrm{4}{z}\:....\left(\mathrm{1}\right) \\ $$$$\frac{{dy}}{{dt}}\:=\:{z}−{x}.....\left(\mathrm{2}\right) \\ $$$$\frac{{dz}}{{dt}}\:=\:{x}\:−\:{y}....\left(\mathrm{3}\right) \\ $$$${solve}\:{the}\:{sistem}\:{by}\:{operator}\:\left(\:{elemination}\:{method}\:\right) \\ $$$$ \\ $$$$ \\ $$

Question Number 205928 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/(1+x^4 +x^8 ))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{4}} +{x}^{\mathrm{8}} } \\ $$

Question Number 205975 Answers: 0 Comments: 3

As reported some users uploaded wrong pictures. Priviledge of following users are now elevated so that they can delete any post. mr W Rasheed Sindhi ajfour mnjuly1970 cortano12 Frix The above users can now directly delete any post by any user.

$$\mathrm{As}\:\mathrm{reported}\:\mathrm{some}\:\mathrm{users}\:\mathrm{uploaded} \\ $$$$\mathrm{wrong}\:\mathrm{pictures}. \\ $$$$\mathrm{Priviledge}\:\mathrm{of}\:\mathrm{following}\:\mathrm{users}\:\mathrm{are} \\ $$$$\mathrm{now}\:\mathrm{elevated}\:\mathrm{so}\:\mathrm{that}\:\mathrm{they}\:\mathrm{can}\:\mathrm{delete} \\ $$$$\mathrm{any}\:\mathrm{post}. \\ $$$$ \\ $$$$\mathrm{mr}\:\mathrm{W} \\ $$$$\mathrm{Rasheed}\:\mathrm{Sindhi} \\ $$$$\mathrm{ajfour} \\ $$$$\mathrm{mnjuly1970} \\ $$$$\mathrm{cortano12} \\ $$$$\mathrm{Frix} \\ $$$$ \\ $$$$\mathrm{The}\:\mathrm{above}\:\mathrm{users}\:\mathrm{can}\:\mathrm{now}\:\mathrm{directly}\:\mathrm{delete}\:\mathrm{any} \\ $$$$\mathrm{post}\:\mathrm{by}\:\mathrm{any}\:\mathrm{user}. \\ $$

Question Number 205971 Answers: 2 Comments: 1

9 Mathematical Analysis ( I ) (X , d ) is a metric space and { p_n }_(n=1) ^∞ is a sequence in X such that , p_n →^(convergent) p . If , K= {p_n }_(n=1) ^∞ ∪ { p } then prove K , is compact in X .

$$\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\mathrm{9}\:\:\mathscr{M}{athematical}\:\:\:\:\mathscr{A}{nalysis}\:\left(\:{I}\:\right) \\ $$$$\:\:\left({X}\:,\:{d}\:\right)\:{is}\:{a}\:{metric}\:{space}\:{and}\:\:\:\:\:\:\: \\ $$$$\:\:\:\left\{\:{p}_{{n}} \right\}_{{n}=\mathrm{1}} ^{\infty} {is}\:{a}\:{sequence}\:{in}\:{X}\: \\ $$$$\:\:\:\:\:{such}\:{that}\:,\:{p}_{{n}} \overset{{convergent}} {\rightarrow}\:{p}\:.\:{If}\:,\:{K}=\:\left\{{p}_{{n}} \right\}_{{n}=\mathrm{1}} ^{\infty} \cup\:\left\{\:{p}\:\right\}\:{then} \\ $$$$\:\:\:\:\:{prove}\:\:{K}\:,\:{is}\:{compact}\:{in}\:{X}\:.\: \\ $$$$\:\:\:\: \\ $$

Question Number 205935 Answers: 1 Comments: 0

∫∫_D (4y^2 sin(xy))dxdy = ??? D: x=y x=0 y=(√(π/2)) 0≤x≤y 0≤y≤(√(π/2))

$$\int\underset{{D}} {\int}\left(\mathrm{4}{y}^{\mathrm{2}} {sin}\left({xy}\right)\right){dxdy}\:\:=\:??? \\ $$$${D}:\:\:\:\:\:\:\:{x}={y}\:\:\:\:\:\:{x}=\mathrm{0}\:\:\:\:\:\:\:{y}=\sqrt{\frac{\pi}{\mathrm{2}}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{0}\leqslant{x}\leqslant{y}\:\:\:\:\:\:\:\mathrm{0}\leqslant{y}\leqslant\sqrt{\frac{\pi}{\mathrm{2}}} \\ $$

Question Number 205922 Answers: 2 Comments: 0

x = 2 (mod 7) x=3 (mod 4) x=?

$$\:\:\:{x}\:=\:\mathrm{2}\:\left({mod}\:\mathrm{7}\right) \\ $$$$\:\:\:{x}=\mathrm{3}\:\left({mod}\:\mathrm{4}\right) \\ $$$$\:\:\:{x}=? \\ $$

Question Number 205919 Answers: 1 Comments: 0

write the following recursive function in explicit form f(1)=1 f(n+1)=(n+1)f(n)+n!

$$\mathrm{write}\:\mathrm{the}\:\mathrm{following}\:\mathrm{recursive}\:\mathrm{function}\:\mathrm{in}\:\mathrm{explicit}\:\mathrm{form} \\ $$$${f}\left(\mathrm{1}\right)=\mathrm{1} \\ $$$${f}\left({n}+\mathrm{1}\right)=\left({n}+\mathrm{1}\right){f}\left({n}\right)+{n}! \\ $$

Question Number 205916 Answers: 1 Comments: 0

lim_(x→0^+ ) xln(e^x −1)

$${lim}_{{x}\rightarrow\mathrm{0}^{+} } \:\:{xln}\left({e}^{{x}} −\mathrm{1}\right) \\ $$

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