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AllQuestion and Answers: Page 170

Question Number 206074 Answers: 0 Comments: 1

(x_1 − x_2 + x_3 )^2 = x_2 (x_4 + x_5 − x_2 ) (x_2 − x_3 + x_4 )^2 = x_3 (x_5 + x_1 − x_3 ) (x_3 − x_4 + x_5 )^2 = x_4 (x_1 + x_2 − x_4 ) (x_4 − x_5 + x_1 )^2 = x_5 (x_2 + x_3 − x_5 ) (x_5 − x_1 + x_2 )^2 = x_1 (x_3 + x_4 − x_1 ) Find ((2x_1 + x_2 + x_3 )/(3x_4 − x_5 )) .

$$\left({x}_{\mathrm{1}} \:−\:{x}_{\mathrm{2}} \:+\:{x}_{\mathrm{3}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{2}} \left({x}_{\mathrm{4}} \:+\:{x}_{\mathrm{5}} \:−\:{x}_{\mathrm{2}} \right) \\ $$$$\left({x}_{\mathrm{2}} \:−\:{x}_{\mathrm{3}} \:+\:{x}_{\mathrm{4}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{3}} \left({x}_{\mathrm{5}} \:+\:{x}_{\mathrm{1}} \:−\:{x}_{\mathrm{3}} \right) \\ $$$$\left({x}_{\mathrm{3}} \:−\:{x}_{\mathrm{4}} \:+\:{x}_{\mathrm{5}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{4}} \left({x}_{\mathrm{1}} \:+\:{x}_{\mathrm{2}} \:−\:{x}_{\mathrm{4}} \right) \\ $$$$\left({x}_{\mathrm{4}} \:−\:{x}_{\mathrm{5}} \:+\:{x}_{\mathrm{1}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{5}} \left({x}_{\mathrm{2}} \:+\:{x}_{\mathrm{3}} \:−\:{x}_{\mathrm{5}} \right) \\ $$$$\left({x}_{\mathrm{5}} \:−\:{x}_{\mathrm{1}} \:+\:{x}_{\mathrm{2}} \right)^{\mathrm{2}} \:=\:{x}_{\mathrm{1}} \left({x}_{\mathrm{3}} \:+\:{x}_{\mathrm{4}} \:−\:{x}_{\mathrm{1}} \right) \\ $$$$\mathrm{Find}\:\frac{\mathrm{2}{x}_{\mathrm{1}} \:+\:{x}_{\mathrm{2}} \:+\:{x}_{\mathrm{3}} }{\mathrm{3}{x}_{\mathrm{4}} \:−\:{x}_{\mathrm{5}} }\:. \\ $$

Question Number 206072 Answers: 0 Comments: 0

∫_0 ^π arctan(((ln(sin(x)))/x))dx=...?

$$\int_{\mathrm{0}} ^{\pi} {arctan}\left(\frac{{ln}\left({sin}\left({x}\right)\right)}{{x}}\right){dx}=...? \\ $$

Question Number 206069 Answers: 1 Comments: 0

lim_(x→0) ((−x^3 +x)/(sin x))

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{−{x}^{\mathrm{3}} +{x}}{\mathrm{sin}\:{x}} \\ $$

Question Number 206066 Answers: 2 Comments: 0

Find: (3/4) ∙ (8/9) ∙ ((15)/(16)) ∙ ... ∙ ((120)/(121)) = ?

$$\mathrm{Find}: \\ $$$$\frac{\mathrm{3}}{\mathrm{4}}\:\centerdot\:\frac{\mathrm{8}}{\mathrm{9}}\:\centerdot\:\frac{\mathrm{15}}{\mathrm{16}}\:\centerdot\:...\:\centerdot\:\frac{\mathrm{120}}{\mathrm{121}}\:=\:? \\ $$

Question Number 206064 Answers: 3 Comments: 1

Question Number 206063 Answers: 2 Comments: 0

If (x + (√(1 + x^2 )))(y + (√(1 + y^2 ))) = 1 then find (x + y)^2 .

$$\mathrm{If}\:\left({x}\:+\:\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\right)\left({y}\:+\:\sqrt{\mathrm{1}\:+\:{y}^{\mathrm{2}} }\right)\:=\:\mathrm{1}\:\mathrm{then} \\ $$$$\mathrm{find}\:\left({x}\:+\:{y}\right)^{\mathrm{2}} . \\ $$

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 ))

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

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