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AllQuestion and Answers: Page 12

Question Number 220628    Answers: 0   Comments: 0

Question Number 220627    Answers: 3   Comments: 0

Question Number 220626    Answers: 2   Comments: 0

Question Number 220625    Answers: 1   Comments: 0

Question Number 220624    Answers: 0   Comments: 0

Question Number 220602    Answers: 2   Comments: 0

Question Number 220607    Answers: 1   Comments: 1

symplify (((√3)+(√(5+))(√9)+(√(15)))/( (√1)+(√5)+(√(12))))

$${symplify} \\ $$$$\frac{\sqrt{\mathrm{3}}+\sqrt{\mathrm{5}+}\sqrt{\mathrm{9}}+\sqrt{\mathrm{15}}}{\:\sqrt{\mathrm{1}}+\sqrt{\mathrm{5}}+\sqrt{\mathrm{12}}} \\ $$

Question Number 220606    Answers: 1   Comments: 1

Question Number 220590    Answers: 1   Comments: 0

∫_0 ^( ∞) wCi(w)e^(−w) dw=?? Ci(w)=−∫_w ^( ∞) ((cos(t))/t) dt

$$\int_{\mathrm{0}} ^{\:\infty} \:\:{w}\mathrm{Ci}\left({w}\right){e}^{−{w}} \:\mathrm{d}{w}=?? \\ $$$$\mathrm{Ci}\left({w}\right)=−\int_{{w}} ^{\:\infty} \:\:\frac{\mathrm{cos}\left({t}\right)}{{t}}\:\mathrm{d}{t} \\ $$

Question Number 220588    Answers: 0   Comments: 1

Eucleadian Space R^2 and Subset A A={(x,y)∈R^2 ∣x^2 +y^2 =1}, B={(((t−1)/t) cos(t),((t−1)/t)sin(t))∈R^2 ∣1≤t∈R} Show that X=A∪B is Connect set

$$\mathrm{Eucleadian}\:\mathrm{Space}\:\mathbb{R}^{\mathrm{2}} \:\mathrm{and}\:\mathrm{Subset}\:{A} \\ $$$${A}=\left\{\left({x},{y}\right)\in\mathbb{R}^{\mathrm{2}} \mid{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =\mathrm{1}\right\},\:{B}=\left\{\left(\frac{{t}−\mathrm{1}}{{t}}\:\mathrm{cos}\left({t}\right),\frac{{t}−\mathrm{1}}{{t}}\mathrm{sin}\left({t}\right)\right)\in\mathbb{R}^{\mathrm{2}} \mid\mathrm{1}\leq{t}\in\mathbb{R}\right\} \\ $$$$\mathrm{Show}\:\mathrm{that}\:{X}={A}\cup{B}\:\mathrm{is}\:\mathrm{Connect}\:\mathrm{set} \\ $$

Question Number 220583    Answers: 0   Comments: 0

Question Number 220581    Answers: 1   Comments: 0

An object is thrown vertically upward from the top of a building 20m high. If the object passes the point it was thrown 4 seconds on it way down, find the. (a) Velocity at which the object was thrown. (b) time taken when the object is 10m above the level it was thrown. (c) time taken when the object is 10m below the level it was thrown. (d) Velocity with which the object hit the ground. [Take g = 10m/s²]

An object is thrown vertically upward from the top of a building 20m high. If the object passes the point it was thrown 4 seconds on it way down, find the. (a) Velocity at which the object was thrown. (b) time taken when the object is 10m above the level it was thrown. (c) time taken when the object is 10m below the level it was thrown. (d) Velocity with which the object hit the ground. [Take g = 10m/s²]

Question Number 220580    Answers: 0   Comments: 0

∫_(−∞i) ^(+∞i) ((atan(w))/w)e^(3iw) dw=??

$$\int_{−\infty\boldsymbol{{i}}} ^{+\infty\boldsymbol{{i}}} \:\frac{\mathrm{atan}\left({w}\right)}{{w}}{e}^{\mathrm{3}\boldsymbol{{i}}{w}} \mathrm{d}{w}=?? \\ $$

Question Number 220577    Answers: 1   Comments: 0

Calculate the perimeter of a rectangle whose area is represented by the polynomial 25x^2 −35x+12(Given that the length and breath are not constant)

$${Calculate}\:{the}\:{perimeter}\:{of}\:{a}\:{rectangle} \\ $$$${whose}\:{area}\:{is}\:{represented}\:{by}\:{the}\:{polynomial} \\ $$$$\mathrm{25}{x}^{\mathrm{2}} −\mathrm{35}{x}+\mathrm{12}\left({Given}\:{that}\:{the}\:{length}\:{and}\:{breath}\:{are}\:{not}\:{constant}\right) \\ $$

Question Number 220579    Answers: 1   Comments: 0

A=7×19×31×43×.....upto 29 terms find the last four digits of A.

$$\:{A}=\mathrm{7}×\mathrm{19}×\mathrm{31}×\mathrm{43}×.....{upto}\:\mathrm{29}\:{terms} \\ $$$$\:{find}\:{the}\:{last}\:{four}\:{digits}\:{of}\:{A}. \\ $$

Question Number 220563    Answers: 1   Comments: 0

Calculate the exact value of : I=∫_0 ^4 e^(−x^2 ) dx

$${Calculate}\:{the}\:{exact}\:{value}\:{of}\:: \\ $$$${I}=\int_{\mathrm{0}} ^{\mathrm{4}} {e}^{−{x}^{\mathrm{2}} } {dx} \\ $$

Question Number 220562    Answers: 1   Comments: 0

∫_0 ^( ∞) ((ln(z^2 +1))/(z^2 +1)) dz=I I(t)=∫_0 ^( ∞) ((ln(z^2 +1))/(z^2 +1))e^(−zt) dz I′(t)=−∫_0 ^( ∞) ((z∙ln(z^2 +1))/(z^2 +1))e^(−zt) dz I′(t)=−∫_0 ^( ∞) ((z^2 ln(z^2 +1)+ln(z^2 +1)−ln(z^2 +1))/(z(z^2 +1)))e^(−zt) dz I′(t)=−∫_0 ^( ∞) ((ln(z^2 +1))/z)e^(−zt ) dz+∫_0 ^( ∞) ((ln(z^2 +1))/(z(z^2 +1)))e^(−zt) dz I′′(t)=∫_0 ^∞ ln(z^2 +1)e^(−zt) dz−∫_0 ^( ∞) ((ln(z^2 +1))/(z^2 +1))e^(−zt) dz I^((2)) (t)+I(t)=∫_0 ^( ∞) ln(z^2 +1)e^(−zt) dz........(A) ∫_0 ^( ∞) ln(z^2 +1)e^(−zt) dz cos^2 (α)+sin^2 (α)=1 → 1+tan^2 (α)=sec^2 (α) z=tan(u) → u=tan^(−1) (z) (dz/du)=sec^2 (u) → dz=sec^2 (u)du ∫_0 ^( ∞) ln(z^2 +1)e^(−st) dz=∫_0 ^( (π/2)) sec^2 (u)∙ln(sec^2 (u))e^(−s∙tan(u)) du i can′t Calculate anymore.... can′t solve ODE....(A) that Equation(A) Seems to Weird cus Feynman trick ...... How can i solve ∫_0 ^( ∞) ((ln(z^2 +1))/(z^2 +1)) dz or....Should i do Complex integral.. ∮_( C) f(z) dz.....??

$$\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right)}{{z}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{z}={I} \\ $$$${I}\left({t}\right)=\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right)}{{z}^{\mathrm{2}} +\mathrm{1}}{e}^{−{zt}} \:\mathrm{d}{z} \\ $$$${I}'\left({t}\right)=−\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{{z}\centerdot\mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right)}{{z}^{\mathrm{2}} +\mathrm{1}}{e}^{−{zt}} \:\mathrm{d}{z} \\ $$$${I}'\left({t}\right)=−\int_{\mathrm{0}} ^{\:\infty} \:\:\:\frac{{z}^{\mathrm{2}} \mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right)+\mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right)−\mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right)}{{z}\left({z}^{\mathrm{2}} +\mathrm{1}\right)}{e}^{−{zt}} \:\mathrm{d}{z} \\ $$$${I}'\left({t}\right)=−\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right)}{{z}}{e}^{−{zt}\:} \mathrm{d}{z}+\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right)}{{z}\left({z}^{\mathrm{2}} +\mathrm{1}\right)}{e}^{−{zt}} \:\mathrm{d}{z} \\ $$$${I}''\left({t}\right)=\int_{\mathrm{0}} ^{\infty} \:\mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right){e}^{−{zt}} \mathrm{d}{z}−\int_{\mathrm{0}} ^{\:\infty} \:\frac{\mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right)}{{z}^{\mathrm{2}} +\mathrm{1}}{e}^{−{zt}} \:\mathrm{d}{z} \\ $$$${I}^{\left(\mathrm{2}\right)} \left({t}\right)+{I}\left({t}\right)=\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right){e}^{−{zt}} \mathrm{d}{z}........\left(\mathrm{A}\right) \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \:\mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right){e}^{−{zt}} \mathrm{d}{z} \\ $$$$\mathrm{cos}^{\mathrm{2}} \left(\alpha\right)+\mathrm{sin}^{\mathrm{2}} \left(\alpha\right)=\mathrm{1}\:\rightarrow\:\mathrm{1}+\mathrm{tan}^{\mathrm{2}} \left(\alpha\right)=\mathrm{sec}^{\mathrm{2}} \left(\alpha\right) \\ $$$${z}=\mathrm{tan}\left({u}\right)\:\rightarrow\:{u}=\mathrm{tan}^{−\mathrm{1}} \left({z}\right) \\ $$$$\frac{\mathrm{d}{z}}{\mathrm{d}{u}}=\mathrm{sec}^{\mathrm{2}} \left({u}\right)\:\rightarrow\:\mathrm{d}{z}=\mathrm{sec}^{\mathrm{2}} \left({u}\right)\mathrm{d}{u} \\ $$$$\int_{\mathrm{0}} ^{\:\infty} \mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right){e}^{−{st}} \mathrm{d}{z}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\mathrm{sec}^{\mathrm{2}} \left({u}\right)\centerdot\mathrm{ln}\left(\mathrm{sec}^{\mathrm{2}} \left({u}\right)\right){e}^{−{s}\centerdot\mathrm{tan}\left({u}\right)} \mathrm{d}{u} \\ $$$$\mathrm{i}\:\mathrm{can}'\mathrm{t}\:\mathrm{Calculate}\:\mathrm{anymore}.... \\ $$$$\mathrm{can}'\mathrm{t}\:\mathrm{solve}\:\mathrm{ODE}....\left(\mathrm{A}\right) \\ $$$$\mathrm{that}\:\mathrm{Equation}\left(\mathrm{A}\right)\:\mathrm{Seems}\:\mathrm{to}\:\mathrm{Weird}\:\mathrm{cus}\:\mathrm{Feynman}\:\mathrm{trick}\: \\ $$$$...... \\ $$$$\mathrm{How}\:\mathrm{can}\:\mathrm{i}\:\mathrm{solve}\:\int_{\mathrm{0}} ^{\:\infty} \:\:\frac{\mathrm{ln}\left({z}^{\mathrm{2}} +\mathrm{1}\right)}{{z}^{\mathrm{2}} +\mathrm{1}}\:\mathrm{d}{z} \\ $$$$\mathrm{or}....\mathrm{Should}\:\mathrm{i}\:\mathrm{do}\:\mathrm{Complex}\:\mathrm{integral}.. \\ $$$$\oint_{\:{C}} \:{f}\left({z}\right)\:\mathrm{d}{z}.....?? \\ $$

Question Number 220560    Answers: 3   Comments: 0

sinα=0.8 ⇒ ((BE)/(EF))=?

$${sin}\alpha=\mathrm{0}.\mathrm{8}\:\Rightarrow\:\frac{{BE}}{{EF}}=? \\ $$

Question Number 220544    Answers: 1   Comments: 0

Prove that inequality; ∫_( 0) ^( 1) ((ln(1 + x^2 ))/(1 + x^2 )) dx < ∫_( 0) ^( 1) ((x ln(1 + x^2 ))/(1 + x^2 )) dx + (1/3)

$$ \\ $$$$\:\:\:\:\:\:\:\:\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{inequality}}; \\ $$$$\:\:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{\mathrm{ln}\left(\mathrm{1}\:+\:{x}^{\mathrm{2}} \right)}{\mathrm{1}\:+\:{x}^{\mathrm{2}} }\:{dx}\:<\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\frac{{x}\:\mathrm{ln}\left(\mathrm{1}\:+\:{x}^{\mathrm{2}} \right)}{\mathrm{1}\:+\:{x}^{\mathrm{2}} \:}\:{dx}\:+\:\frac{\mathrm{1}}{\mathrm{3}}\:\:\:\:\:\:\:\: \\ $$$$ \\ $$

Question Number 220546    Answers: 0   Comments: 3

Question Number 220540    Answers: 2   Comments: 0

Find: 𝛀 = Σ_(n=1) ^∞ (((−1)^(n+1) )/(n^3 ∙(n + 1)^3 ∙(2n + 1)^2 )) = ?

$$\mathrm{Find}:\:\:\:\boldsymbol{\Omega}\:=\:\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\left(−\mathrm{1}\right)^{\boldsymbol{\mathrm{n}}+\mathrm{1}} }{\mathrm{n}^{\mathrm{3}} \centerdot\left(\mathrm{n}\:+\:\mathrm{1}\right)^{\mathrm{3}} \centerdot\left(\mathrm{2n}\:+\:\mathrm{1}\right)^{\mathrm{2}} }\:=\:? \\ $$

Question Number 220538    Answers: 0   Comments: 0

Question Number 220526    Answers: 2   Comments: 0

Question Number 220519    Answers: 0   Comments: 1

Solve in R ((15)/(x^2 - 3x + 4)) + (7/(x^2 + 7x)) + ((10)/(x^2 + 4x - 21)) + 1 = 0

$$\mathrm{Solve}\:\mathrm{in}\:\:\:\mathbb{R} \\ $$$$\frac{\mathrm{15}}{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{3x}\:+\:\mathrm{4}}\:\:+\:\:\frac{\mathrm{7}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{7x}}\:\:+\:\:\frac{\mathrm{10}}{\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4x}\:-\:\mathrm{21}}\:\:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 220511    Answers: 3   Comments: 0

AB=2CE & DE=2(√3)+4 CE ⊥AB & AD⊥BC & AB=AC & EF ⊥BC BF=?

$${AB}=\mathrm{2}{CE}\:\:\&\:\:{DE}=\mathrm{2}\sqrt{\mathrm{3}}+\mathrm{4}\:\:\: \\ $$$${CE}\:\bot{AB}\:\:\:\&\:\:\:{AD}\bot{BC}\:\:\&\:\:{AB}={AC}\:\:\&\:{EF}\:\bot{BC}\: \\ $$$${BF}=? \\ $$$$ \\ $$

Question Number 220486    Answers: 1   Comments: 2

z ∈ C and λ > 0 Then prove that: ∣z + 2λ∣ + ∣z + λ∣ ≥ ∣z + ((3λ − λ(√3)i)/2)∣

$$\mathrm{z}\:\in\:\mathbb{C}\:\:\:\mathrm{and}\:\:\:\lambda\:>\:\mathrm{0} \\ $$$$\mathrm{Then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\mid\mathrm{z}\:+\:\mathrm{2}\lambda\mid\:+\:\mid\mathrm{z}\:+\:\lambda\mid\:\geqslant\:\mid\mathrm{z}\:+\:\frac{\mathrm{3}\lambda\:−\:\lambda\sqrt{\mathrm{3}}\mathrm{i}}{\mathrm{2}}\mid \\ $$

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