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Question Number 204072 Answers: 1 Comments: 0

((sin^2 θ)/2)=sin 2θ? (90°>θ>0°)

$$\frac{\mathrm{sin}^{\mathrm{2}} \:\theta}{\mathrm{2}}=\mathrm{sin}\:\mathrm{2}\theta?\:\left(\mathrm{90}°>\theta>\mathrm{0}°\right) \\ $$

Question Number 204062 Answers: 4 Comments: 0

I. A(−5, −1); B(3, −5); C(5, 2) ar(△ABC) = ? II. A(5, 3); B(2, 5); C(−5, 3); D(−4, −3) ar(□ABCD) = ? shortest solution

$$\mathrm{I}.\:\:\:\:\:\:\:\mathrm{A}\left(−\mathrm{5},\:−\mathrm{1}\right);\:\mathrm{B}\left(\mathrm{3},\:−\mathrm{5}\right);\:\mathrm{C}\left(\mathrm{5},\:\mathrm{2}\right)\:\:\:\:\:\:{ar}\left(\bigtriangleup\mathrm{ABC}\right)\:=\:? \\ $$$$\mathrm{II}.\:\:\:\:\:\mathrm{A}\left(\mathrm{5},\:\mathrm{3}\right);\:\mathrm{B}\left(\mathrm{2},\:\mathrm{5}\right);\:\mathrm{C}\left(−\mathrm{5},\:\mathrm{3}\right);\:\mathrm{D}\left(−\mathrm{4},\:−\mathrm{3}\right)\:\:\:\:\:\:\:{ar}\left(\Box\mathrm{ABCD}\right)\:=\:? \\ $$$$\mathrm{shortest}\:\mathrm{solution}\: \\ $$

Question Number 204056 Answers: 2 Comments: 0

{ ((x + 2y + z = 8)),((3x + 2y + z = 10)),((4x + 3y − 2z = 4)) :} Solve with the help of matrix

$$\begin{cases}{\mathrm{x}\:+\:\mathrm{2y}\:+\:\mathrm{z}\:=\:\mathrm{8}}\\{\mathrm{3x}\:+\:\mathrm{2y}\:+\:\mathrm{z}\:=\:\mathrm{10}}\\{\mathrm{4x}\:+\:\mathrm{3y}\:−\:\mathrm{2z}\:=\:\mathrm{4}}\end{cases} \\ $$$$\mathrm{Solve}\:\mathrm{with}\:\mathrm{the}\:\mathrm{help}\:\mathrm{of}\:\mathrm{matrix} \\ $$

Question Number 204055 Answers: 2 Comments: 0

y = (2/3) arctg (x^4 ) find: y^′ = ?

$$\mathrm{y}\:=\:\frac{\mathrm{2}}{\mathrm{3}}\:\mathrm{arctg}\:\left(\mathrm{x}^{\mathrm{4}} \right) \\ $$$$\mathrm{find}:\:\:\mathrm{y}^{'} \:=\:? \\ $$

Question Number 204054 Answers: 2 Comments: 0

y = (√(sinx)) + cos^3 x find: y^′ = ?

$$\mathrm{y}\:=\:\sqrt{\mathrm{sinx}}\:+\:\mathrm{cos}^{\mathrm{3}} \mathrm{x} \\ $$$$\mathrm{find}:\:\:\mathrm{y}^{'} \:=\:? \\ $$

Question Number 204041 Answers: 2 Comments: 0

Find: determinant ((1,7,(−1)),(9,(−3),5),((−1),5,3))= ?

$$\mathrm{Find}:\:\:\:\begin{vmatrix}{\mathrm{1}}&{\mathrm{7}}&{−\mathrm{1}}\\{\mathrm{9}}&{−\mathrm{3}}&{\mathrm{5}}\\{−\mathrm{1}}&{\mathrm{5}}&{\mathrm{3}}\end{vmatrix}=\:? \\ $$

Question Number 204039 Answers: 2 Comments: 0

determinant ((1,7,(−1)),(9,(−3),x),((−1),5,3))= 0 ⇒ x = ?

$$\begin{vmatrix}{\mathrm{1}}&{\mathrm{7}}&{−\mathrm{1}}\\{\mathrm{9}}&{−\mathrm{3}}&{\boldsymbol{\mathrm{x}}}\\{−\mathrm{1}}&{\mathrm{5}}&{\mathrm{3}}\end{vmatrix}=\:\mathrm{0}\:\:\:\Rightarrow\:\boldsymbol{\mathrm{x}}\:=\:? \\ $$

Question Number 204038 Answers: 1 Comments: 0

y = (x^3 + 1) ∙ 3^x ⇒ y^′ = ?

$$\mathrm{y}\:=\:\left(\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{1}\right)\:\centerdot\:\mathrm{3}^{\boldsymbol{\mathrm{x}}} \\ $$$$\Rightarrow\:\mathrm{y}^{'} \:=\:? \\ $$

Question Number 204024 Answers: 1 Comments: 0

Find the Cartesian equation of x(t) = 2 cos t And y(t) = 3 cos t

Question Number 204019 Answers: 1 Comments: 2

G is a group : prove that : (G/(Z (G ))) ≅ Inn(G ) Where , Inn(G)= {f ∣ f: G →^(f is an Automorphism) G}

$$ \\ $$$$\:\:\:\:\:{G}\:{is}\:{a}\:{group}\:: \\ $$$$\:\:\:\:\:{prove}\:{that}\::\:\:\frac{{G}}{{Z}\:\left({G}\:\right)}\:\cong\:{Inn}\left({G}\:\right) \\ $$$$\:\:\:\:{Where}\:,\:{Inn}\left({G}\right)=\:\left\{{f}\:\mid\:{f}:\:{G}\:\overset{{f}\:{is}\:{an}\:{Automorphism}} {\rightarrow}\:{G}\right\} \\ $$$$ \\ $$

Question Number 204018 Answers: 1 Comments: 0

Aut (Z )= ? where , Aut (G )= { f ∣ f :G →_(G is a group) ^(f is a isomorphism) G}

$$ \\ $$$$\:\:\:\:\:\:\:\:\:{Aut}\:\left(\mathbb{Z}\:\right)=\:? \\ $$$$\:\:\:\:\:\:\:{where}\:,\:{Aut}\:\left({G}\:\right)=\:\left\{\:{f}\:\mid\:{f}\::{G}\:\underset{{G}\:{is}\:{a}\:{group}} {\overset{{f}\:{is}\:{a}\:{isomorphism}} {\rightarrow}}\:{G}\right\} \\ $$

Question Number 204005 Answers: 2 Comments: 1

Find: cos44° − cos84° + ctg45° = ?

$$\mathrm{Find}: \\ $$$$\mathrm{cos44}°\:−\:\mathrm{cos84}°\:+\:\mathrm{ctg45}°\:=\:? \\ $$

Question Number 203995 Answers: 3 Comments: 0

3x+4x=5

$$\mathrm{3}{x}+\mathrm{4}{x}=\mathrm{5} \\ $$

Question Number 203994 Answers: 2 Comments: 0

d(((x!)/dx))=?

$${d}\left(\frac{{x}!}{{dx}}\right)=? \\ $$

Question Number 203988 Answers: 0 Comments: 0

Question Number 203985 Answers: 0 Comments: 8

Question Number 203980 Answers: 3 Comments: 0

lim_(x→2) ((ax^2 +bx+6)/(x^2 −x−2))=10 ; find a=? ∧ b=?

$$\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\frac{{ax}^{\mathrm{2}} +{bx}+\mathrm{6}}{{x}^{\mathrm{2}} −{x}−\mathrm{2}}=\mathrm{10}\:\:;\:\:\:{find}\:\:{a}=?\:\wedge\:{b}=? \\ $$

Question Number 203975 Answers: 0 Comments: 0

Let P∈C[X] p(x^2 +1)=p^2 (x)+1 p(0)=0 determin all polynom

$$\mathrm{Let}\:\mathrm{P}\in\mathbb{C}\left[\mathrm{X}\right] \\ $$$$\mathrm{p}\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)=\mathrm{p}^{\mathrm{2}} \left(\mathrm{x}\right)+\mathrm{1} \\ $$$$\mathrm{p}\left(\mathrm{0}\right)=\mathrm{0} \\ $$$$\mathrm{determin}\:\mathrm{all}\:\mathrm{polynom}\: \\ $$

Question Number 203970 Answers: 0 Comments: 0

In a convex quadrilateral ABCD , if sinA = cosB, then find the range of S = 3sinA + 4sinB + 5(√2)sinC + 5(√2)sinD.

$$\mathrm{In}\:\mathrm{a}\:\mathrm{convex}\:\mathrm{quadrilateral}\:{ABCD}\:,\: \\ $$$$\mathrm{if}\:\mathrm{sin}{A}\:=\:\mathrm{cos}{B},\:\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{range}\:\mathrm{of} \\ $$$${S}\:=\:\mathrm{3sin}{A}\:+\:\mathrm{4sin}{B}\:+\:\mathrm{5}\sqrt{\mathrm{2}}\mathrm{sin}{C}\:+\:\mathrm{5}\sqrt{\mathrm{2}}\mathrm{sin}{D}. \\ $$

Question Number 203969 Answers: 1 Comments: 0

Question Number 203964 Answers: 2 Comments: 0

Advanced calculus ... Q: If , ∫_0 ^1 ∫_0 ^( 1) (( xln(x)ln^2 (y ))/(1−xy)) dxdy = λ Σ_(n=1) ^∞ (( 1)/(n^( 3) ( n+1 )^2 )) ⇒ Find , λ =?

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:{Advanced}\:\:{calculus}\:... \\ $$$$\:\:{Q}:\:\:\:{If}\:,\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{\:{x}\mathrm{ln}\left({x}\right)\mathrm{ln}^{\mathrm{2}} \left({y}\:\right)}{\mathrm{1}−{xy}}\:{dxdy}\:=\:\lambda\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\mathrm{1}}{{n}^{\:\mathrm{3}} \left(\:{n}+\mathrm{1}\:\right)^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\Rightarrow\:\:{Find}\:,\:\:\:\:\:\lambda\:=? \\ $$$$ \\ $$

Question Number 203955 Answers: 0 Comments: 10

50%+50%=75%?

$$\mathrm{50\%}+\mathrm{50\%}=\mathrm{75\%}? \\ $$

Question Number 203941 Answers: 5 Comments: 0

If a^(2 ) −a+2=0 and x^2 =a^6 +2a^4 +a^2 then find x? IIT−JEE based question. Find sol^n .

$$\boldsymbol{{If}}\:\boldsymbol{{a}}^{\mathrm{2}\:} −\boldsymbol{{a}}+\mathrm{2}=\mathrm{0}\:\boldsymbol{{and}}\:\boldsymbol{{x}}^{\mathrm{2}} =\boldsymbol{{a}}^{\mathrm{6}} +\mathrm{2}\boldsymbol{{a}}^{\mathrm{4}} +\boldsymbol{{a}}^{\mathrm{2}} \:\boldsymbol{{then}}\:\boldsymbol{{find}}\:\boldsymbol{{x}}? \\ $$$$\boldsymbol{{IIT}}−\boldsymbol{{JEE}}\:\boldsymbol{{based}}\:\boldsymbol{{question}}.\:\boldsymbol{{Find}}\:\boldsymbol{{sol}}^{\boldsymbol{{n}}} . \\ $$

Question Number 203935 Answers: 2 Comments: 0

((cos(x/3)+sin (x/3))/(cos (x/3)−sin (x/3)))=?

$$\frac{{cos}\frac{{x}}{\mathrm{3}}+{sin}\:\frac{{x}}{\mathrm{3}}}{{cos}\:\frac{{x}}{\mathrm{3}}−{sin}\:\frac{{x}}{\mathrm{3}}}=? \\ $$

Question Number 203933 Answers: 2 Comments: 0

a^2 +b^2 +2c^2 =22 prove a+2b+c≤11

$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +\mathrm{2}{c}^{\mathrm{2}} =\mathrm{22} \\ $$$${prove}\:{a}+\mathrm{2}{b}+{c}\leqslant\mathrm{11} \\ $$

Question Number 203919 Answers: 1 Comments: 0

. Z^5 = 1 ??

$$ . \\ $$$$\:\:\:\:\:\:\:\mathrm{Z}^{\mathrm{5}} \:=\:\mathrm{1}\:\:\:?? \\ $$

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