Question and Answers Forum

AllQuestion and Answers: Page 1970

Question Number 10480 Answers: 2 Comments: 0

d/dx(cos^2 xdy/dx)=0

$${d}/{dx}\left(\mathrm{cos}\:^{\mathrm{2}} {xdy}/{dx}\right)=\mathrm{0} \\ $$$$ \\ $$

Question Number 10477 Answers: 0 Comments: 0

maximum and minimum value of 12x^(5−5x^4_(+40x^3_(+6) ) )

$${maximum}\:{and}\:{minimum}\:{value}\:{of}\: \\ $$$$\mathrm{12}{x}^{\mathrm{5}−\mathrm{5}{x}^{\mathrm{4}_{+\mathrm{40}{x}^{\mathrm{3}_{+\mathrm{6}} } } } } \\ $$

Question Number 10475 Answers: 1 Comments: 0

aman walks 600m at a bearing of 45^(0 ) then 500m at a bearing 90^0 then 300m at bearing of 135^(0 ) then 400m at a bearing of 225^0 .find the resultant displacement which the man has made

$${aman}\:{walks}\:\mathrm{600}{m}\:{at}\:{a}\:{bearing}\:{of}\: \\ $$$$\mathrm{45}^{\mathrm{0}\:} {then}\:\mathrm{500}{m}\:{at}\:{a}\:{bearing}\:\mathrm{90}^{\mathrm{0}} \: \\ $$$${then}\:\mathrm{300}{m}\:{at}\:{bearing}\:{of}\:\mathrm{135}^{\mathrm{0}\:} \: \\ $$$${then}\:\mathrm{400}{m}\:{at}\:{a}\:{bearing}\:{of}\:\mathrm{225}^{\mathrm{0}} \\ $$$$.{find}\:{the}\:{resultant}\:{displacement} \\ $$$${which}\:{the}\:{man}\:{has}\:{made} \\ $$

Question Number 10474 Answers: 0 Comments: 1

Just so you all know, I had to make a new username. I am FilupSmith

$$\mathrm{Just}\:\mathrm{so}\:\mathrm{you}\:\mathrm{all}\:\mathrm{know},\:\mathrm{I}\:\mathrm{had}\:\mathrm{to}\:\mathrm{make} \\ $$$$\mathrm{a}\:\mathrm{new}\:\mathrm{username}.\:\mathrm{I}\:\mathrm{am}\:\mathrm{FilupSmith} \\ $$

Question Number 10472 Answers: 0 Comments: 1

My name is Wilton Stewart i have problem with math i would like some help.

$${My}\:{name}\:{is}\:{Wilton}\:{Stewart}\:{i}\:{have}\:{problem}\:{with}\:{math}\:{i}\:{would}\:{like}\:{some}\:{help}. \\ $$$$ \\ $$

Question Number 10470 Answers: 1 Comments: 0

Question Number 10469 Answers: 0 Comments: 0

One definition of Γ(x+1) is: Γ(x+1)=∫_0 ^( ∞) e^(−t) t^x dx According to WolframAlpha, another definition is: Γ(x+1)=(1/(e^(2iπx) −1))∮_L e^(−t) t^x dx Can someone explian to me where this comes from and what it means. Also, its been a long time since I learnt contour integrals, so what does ∮_L mean?

$$\mathrm{One}\:\mathrm{definition}\:\mathrm{of}\:\:\Gamma\left({x}+\mathrm{1}\right)\:\:\mathrm{is}: \\ $$$$\Gamma\left({x}+\mathrm{1}\right)=\int_{\mathrm{0}} ^{\:\infty} {e}^{−{t}} {t}^{{x}} {dx} \\ $$$$\: \\ $$$$\mathrm{According}\:\mathrm{to}\:\mathrm{WolframAlpha},\:\mathrm{another} \\ $$$$\mathrm{definition}\:\mathrm{is}: \\ $$$$\Gamma\left({x}+\mathrm{1}\right)=\frac{\mathrm{1}}{{e}^{\mathrm{2}{i}\pi{x}} −\mathrm{1}}\oint_{{L}} {e}^{−{t}} {t}^{{x}} {dx} \\ $$$$\mathrm{Can}\:\mathrm{someone}\:\mathrm{explian}\:\mathrm{to}\:\mathrm{me}\:\mathrm{where}\:\mathrm{this} \\ $$$$\mathrm{comes}\:\mathrm{from}\:\mathrm{and}\:\mathrm{what}\:\mathrm{it}\:\mathrm{means}. \\ $$$$\: \\ $$$$\mathrm{Also},\:\mathrm{its}\:\mathrm{been}\:\mathrm{a}\:\mathrm{long}\:\mathrm{time}\:\mathrm{since}\:\mathrm{I}\:\mathrm{learnt} \\ $$$$\mathrm{contour}\:\mathrm{integrals},\:\mathrm{so}\:\mathrm{what}\:\mathrm{does}\:\oint_{{L}} \:\mathrm{mean}? \\ $$

Question Number 10468 Answers: 0 Comments: 0

Show why: Γ(x+1)≈(√(2π))e^(−x) x^(x+(1/2))

$$\mathrm{Show}\:\mathrm{why}: \\ $$$$\Gamma\left({x}+\mathrm{1}\right)\approx\sqrt{\mathrm{2}\pi}{e}^{−{x}} {x}^{{x}+\frac{\mathrm{1}}{\mathrm{2}}} \\ $$

Question Number 10464 Answers: 1 Comments: 0

Question Number 10463 Answers: 1 Comments: 0

x∈Z −1≤∣x−3∣<5 ⇒Σ=?

$${x}\in{Z} \\ $$$$−\mathrm{1}\leqslant\mid{x}−\mathrm{3}\mid<\mathrm{5}\:\Rightarrow\Sigma=? \\ $$

Question Number 10458 Answers: 1 Comments: 0

what is the maximum and minimum value of sinx + cosx + sinxcosx

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{sin}{x}\:+\:\mathrm{cos}{x}\:+\:\mathrm{sin}{x}\mathrm{cos}{x} \\ $$

Question Number 10455 Answers: 5 Comments: 4

Question Number 10451 Answers: 2 Comments: 0

Question Number 10435 Answers: 1 Comments: 1

Question Number 10429 Answers: 3 Comments: 0

2^(cos2x) +2^(cos^2 x) =3×2^(−cos2x) x=...? i′m so sorry, it′s my mistake, the true question is 2^(cos2x) +2^(cos^2 x) =3×2^(−cos2π)

$$\mathrm{2}^{\mathrm{cos2x}} +\mathrm{2}^{\mathrm{cos}^{\mathrm{2}} \mathrm{x}} =\mathrm{3}×\mathrm{2}^{−\mathrm{cos2x}} \: \\ $$$$\mathrm{x}=...? \\ $$$$\mathrm{i}'\mathrm{m}\:\mathrm{so}\:\mathrm{sorry},\:\mathrm{it}'\mathrm{s}\:\mathrm{my}\:\mathrm{mistake},\:\mathrm{the}\:\mathrm{true}\:\mathrm{question}\:\mathrm{is} \\ $$$$\mathrm{2}^{\mathrm{cos2x}} +\mathrm{2}^{\mathrm{cos}^{\mathrm{2}} \mathrm{x}} =\mathrm{3}×\mathrm{2}^{−\mathrm{cos2}\pi} \: \\ $$

Question Number 10426 Answers: 0 Comments: 0

good morning!!!! we have f(x)=x^2 +2x g(x)=−2x^2 −3x+2 and d(m)=mx+2m 1)determine the coordonate of M_1 and M_2 intersection points respectively of (Cf) and d(m) or(Cg) and d(m)

$${good}\:{morning}!!!! \\ $$$${we}\:{have}\:\:{f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{2}{x}\:\:\:{g}\left({x}\right)=−\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2} \\ $$$${and}\:{d}\left({m}\right)={mx}+\mathrm{2}{m} \\ $$$$\left.\mathrm{1}\right){determine}\:{the}\:{coordonate}\:{of}\:{M}_{\mathrm{1}} \:{and}\:{M}_{\mathrm{2}} \: \\ $$$${intersection}\:{points}\:{respectively}\:{of}\:\left({Cf}\right)\:{and}\:{d}\left({m}\right) \\ $$$${or}\left({Cg}\right)\:{and}\:{d}\left({m}\right) \\ $$$$ \\ $$$$ \\ $$

Question Number 10417 Answers: 2 Comments: 0

hence or otherwise solve sin 6θ−sin 2θ=0 for 0≤θ≤(π/2).

$${hence}\:{or}\:{other}\mathrm{wise}\:\mathrm{solve}\:\mathrm{sin}\:\mathrm{6}\theta−\mathrm{sin}\:\mathrm{2}\theta=\mathrm{0}\:{for}\:\mathrm{0}\leqslant\theta\leqslant\frac{\pi}{\mathrm{2}}. \\ $$$$ \\ $$

Question Number 10415 Answers: 1 Comments: 0

find all the possible values of cos θ such that 2cot^2 θ + cos θ=0

$${find}\:{all}\:{the}\:{possible}\:{values}\:{of}\:\mathrm{cos}\:\theta\:{such}\:{that}\:\mathrm{2cot}\:^{\mathrm{2}} \theta\:+\:\mathrm{cos}\:\theta=\mathrm{0} \\ $$$$ \\ $$

Question Number 10414 Answers: 2 Comments: 2