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Question Number 204129 Answers: 2 Comments: 0

a , b , x , y ∈ R a + b = 23 ax + by = 79 ax^2 + by^2 = 217 ax^3 + by^3 = 661 Find: ax^4 + by^4 = ?

$$\mathrm{a}\:,\:\mathrm{b}\:,\:\mathrm{x}\:,\:\mathrm{y}\:\in\:\mathbb{R} \\ $$$$\mathrm{a}\:+\:\mathrm{b}\:=\:\mathrm{23} \\ $$$$\mathrm{ax}\:+\:\mathrm{by}\:=\:\mathrm{79} \\ $$$$\mathrm{ax}^{\mathrm{2}} \:+\:\mathrm{by}^{\mathrm{2}} \:=\:\mathrm{217} \\ $$$$\mathrm{ax}^{\mathrm{3}} \:+\:\mathrm{by}^{\mathrm{3}} \:=\:\mathrm{661} \\ $$$$\mathrm{Find}:\:\:\:\mathrm{ax}^{\mathrm{4}} \:+\:\mathrm{by}^{\mathrm{4}} \:=\:? \\ $$

Question Number 204123 Answers: 2 Comments: 1

Question Number 204117 Answers: 0 Comments: 4

solve for θ in terms of y when y = e^θ (cosθ+sinθ)

$${solve}\:{for}\:\theta\:{in}\:{terms}\:{of}\:{y}\:{when}\:{y}\:=\:{e}^{\theta} \left({cos}\theta+{sin}\theta\right)\:\:\: \\ $$

Question Number 204174 Answers: 1 Comments: 0

Question Number 204105 Answers: 3 Comments: 0

find the maximum of (1 + cosx) sinx without derivative.

$$\mathrm{find}\:\mathrm{the}\:\mathrm{maximum}\:\mathrm{of}\:\left(\mathrm{1}\:+\:\mathrm{cos}{x}\right)\:\mathrm{sin}{x} \\ $$$$\mathrm{without}\:\mathrm{derivative}. \\ $$

Question Number 204104 Answers: 0 Comments: 0

Question Number 204102 Answers: 0 Comments: 0

Question Number 204101 Answers: 0 Comments: 0

Find the possible values for x and y if 10cosx + 12cos(x+y)=5 10sinx + 12sin(x+y)=20.66

$${Find}\:{the}\:{possible}\:{values}\:{for}\:{x}\:{and}\:{y}\:{if} \\ $$$$\mathrm{10}{cosx}\:+\:\mathrm{12}{cos}\left({x}+{y}\right)=\mathrm{5} \\ $$$$\mathrm{10}{sinx}\:+\:\mathrm{12}{sin}\left({x}+{y}\right)=\mathrm{20}.\mathrm{66} \\ $$

Question Number 204083 Answers: 2 Comments: 0

Given that tan(A + B) = 1 and tan(A - B) = 1/7 find tan A and tan B

Question Number 204082 Answers: 1 Comments: 3

(√(((√(x^2 +66^2 ))+x)/x))−(√(x(√(x^2 +66^2 ))−x^2 ))=5

$$\sqrt{\frac{\sqrt{{x}^{\mathrm{2}} +\mathrm{66}^{\mathrm{2}} }+{x}}{{x}}}−\sqrt{{x}\sqrt{{x}^{\mathrm{2}} +\mathrm{66}^{\mathrm{2}} }−{x}^{\mathrm{2}} }=\mathrm{5} \\ $$

Question Number 204081 Answers: 1 Comments: 0

what is the area of the largest square that can be enclosed in a triangle with an area of 1?

$${what}\:{is}\:{the}\:{area}\:{of}\:{the}\:{largest}\:{square} \\ $$$${that}\:{can}\:{be}\:{enclosed}\:{in}\:{a}\:{triangle} \\ $$$${with}\:{an}\:{area}\:{of}\:\mathrm{1}? \\ $$

Question Number 204078 Answers: 0 Comments: 1

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))=?

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

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