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Question Number 189123 Answers: 2 Comments: 0

Question Number 189132 Answers: 1 Comments: 0

Find the value of a+b+c+d+e in the system of equations: { ((13a+2b+c+6d+2e=96)),((5a+9b+2c+7d+3e=75)),((7a+8b+17c+11d+7e=99)),((3a+3b+3c+d+8e=55)),((a+7b+6c+4d+9e=79)) :}

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\:\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{d}+\mathrm{e} \\ $$$$\mathrm{in}\:\mathrm{the}\:\mathrm{system}\:\mathrm{of}\:\mathrm{equations}: \\ $$$$\begin{cases}{\mathrm{13a}+\mathrm{2b}+\mathrm{c}+\mathrm{6d}+\mathrm{2e}=\mathrm{96}}\\{\mathrm{5a}+\mathrm{9b}+\mathrm{2c}+\mathrm{7d}+\mathrm{3e}=\mathrm{75}}\\{\mathrm{7a}+\mathrm{8b}+\mathrm{17c}+\mathrm{11d}+\mathrm{7e}=\mathrm{99}}\\{\mathrm{3a}+\mathrm{3b}+\mathrm{3c}+\mathrm{d}+\mathrm{8e}=\mathrm{55}}\\{\mathrm{a}+\mathrm{7b}+\mathrm{6c}+\mathrm{4d}+\mathrm{9e}=\mathrm{79}}\end{cases} \\ $$

Question Number 189114 Answers: 2 Comments: 0

Question Number 189112 Answers: 0 Comments: 3

Question Number 189110 Answers: 0 Comments: 1

Question Number 189101 Answers: 0 Comments: 1

Question Number 189079 Answers: 1 Comments: 0

Question Number 189077 Answers: 0 Comments: 0

Question Number 189070 Answers: 1 Comments: 0

Question Number 189066 Answers: 2 Comments: 0

Given f(x)+∫_0 ^1 (x+y)^2 f(y) dy=2x^2 −3x+1 find f(x).

$$\:\mathrm{Given}\:\mathrm{f}\left(\mathrm{x}\right)+\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\left(\mathrm{x}+\mathrm{y}\right)^{\mathrm{2}} \:\mathrm{f}\left(\mathrm{y}\right)\:\mathrm{dy}=\mathrm{2x}^{\mathrm{2}} −\mathrm{3x}+\mathrm{1} \\ $$$$\:\mathrm{find}\:\mathrm{f}\left(\mathrm{x}\right). \\ $$

Question Number 189057 Answers: 0 Comments: 6

Help! Evaluate the following integral usings Green theorem: ∮4xydx + x^2 dy Where C is the square of vertices (0,0), (0,2), (2,0) and (2,2).

$$\: \\ $$$$\:\mathrm{Help}! \\ $$$$\: \\ $$$$\:\mathrm{Evaluate}\:\:\mathrm{the}\:\:\mathrm{following}\:\:\mathrm{integral}\:\:\mathrm{usings}\:\:\mathrm{Green}\:\mathrm{theorem}: \\ $$$$\: \\ $$$$\:\oint\mathrm{4xy}{d}\mathrm{x}\:\:+\:\:\mathrm{x}^{\mathrm{2}} {d}\mathrm{y} \\ $$$$\: \\ $$$$\:\mathrm{Where}\:\:{C}\:\:\mathrm{is}\:\:\mathrm{the}\:\:\mathrm{square}\:\:\mathrm{of}\:\:\mathrm{vertices}\:\:\left(\mathrm{0},\mathrm{0}\right),\:\left(\mathrm{0},\mathrm{2}\right),\:\left(\mathrm{2},\mathrm{0}\right)\:\:\mathrm{and}\:\:\left(\mathrm{2},\mathrm{2}\right). \\ $$$$\: \\ $$

Question Number 189054 Answers: 1 Comments: 0

Question Number 189053 Answers: 3 Comments: 0

find f(x) 1:f(((x+1)/(x−1)))=x+3; x≠1 2:f(((2x+1)/(x−1)))=x^2 +2x ;x≠1 3:f(x+1)+f(x−y)=2f(x)cosy ∀x,y f(0)=f((π/2))=1

$${find}\:{f}\left({x}\right) \\ $$$$\mathrm{1}:{f}\left(\frac{{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)={x}+\mathrm{3};\:{x}\neq\mathrm{1} \\ $$$$\mathrm{2}:{f}\left(\frac{\mathrm{2}{x}+\mathrm{1}}{{x}−\mathrm{1}}\right)={x}^{\mathrm{2}} +\mathrm{2}{x}\:;{x}\neq\mathrm{1} \\ $$$$\mathrm{3}:{f}\left({x}+\mathrm{1}\right)+{f}\left({x}−{y}\right)=\mathrm{2}{f}\left({x}\right){cosy}\:\forall{x},{y} \\ $$$${f}\left(\mathrm{0}\right)={f}\left(\frac{\pi}{\mathrm{2}}\right)=\mathrm{1} \\ $$

Question Number 189049 Answers: 1 Comments: 2

Question Number 189026 Answers: 3 Comments: 0

Question Number 189025 Answers: 0 Comments: 0

Question Number 189024 Answers: 0 Comments: 0

Question Number 189023 Answers: 0 Comments: 3

Question Number 189022 Answers: 3 Comments: 0

if ((√(1+x^2 ))+x)((√(1+y^2 ))+y)=1 with x,y ∈R, find (x+y)^2 =?

$${if}\:\left(\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }+{x}\right)\left(\sqrt{\mathrm{1}+{y}^{\mathrm{2}} }+{y}\right)=\mathrm{1}\: \\ $$$${with}\:{x},{y}\:\in{R},\:{find}\:\left({x}+{y}\right)^{\mathrm{2}} =? \\ $$

Question Number 189021 Answers: 2 Comments: 4

How many non−similar triangles have integer angles in °?

$${How}\:{many}\:{non}−{similar}\:{triangles} \\ $$$${have}\:{integer}\:{angles}\:{in}\:°? \\ $$

Question Number 189013 Answers: 2 Comments: 0

Suppose (G, ∙ ) and (H, ∗ ) are groups. Take homomorphism φ : G → H. Suppose ∃g∈G : ∣g∣ = n, then ∣φ(g)∣ ≤ n. Does ∀g∈G, ∣g∣ = ∣φ(g)∣ ⇒ G ≅ H ?

$$\mathrm{Suppose}\:\left({G},\:\centerdot\:\right)\:\mathrm{and}\:\left({H},\:\ast\:\right)\:\mathrm{are}\:\mathrm{groups}. \\ $$$$\mathrm{Take}\:\mathrm{homomorphism}\:\phi\::\:{G}\:\rightarrow\:{H}. \\ $$$$\mathrm{Suppose}\:\exists{g}\in{G}\::\:\mid{g}\mid\:=\:{n},\:\mathrm{then}\:\mid\phi\left({g}\right)\mid\:\leqslant\:{n}. \\ $$$$\: \\ $$$$\mathrm{Does}\:\forall{g}\in{G},\:\mid{g}\mid\:=\:\mid\phi\left({g}\right)\mid\:\Rightarrow\:{G}\:\cong\:{H}\:? \\ $$

Question Number 189012 Answers: 0 Comments: 0

Triangle ABC have: sin2A+sin2B+sin2C=(√3)(cosA+cosB+cosC) => Prove that ABC is equilateral triangle

$${Triangle}\:{ABC}\:{have}:\: \\ $$$${sin}\mathrm{2}{A}+{sin}\mathrm{2}{B}+{sin}\mathrm{2}{C}=\sqrt{\mathrm{3}}\left({cosA}+{cosB}+{cosC}\right) \\ $$$$=>\:{Prove}\:{that}\:{ABC}\:{is}\:{equilateral}\:{triangle} \\ $$

Question Number 189000 Answers: 1 Comments: 0

Question Number 188998 Answers: 2 Comments: 3

Question Number 188985 Answers: 1 Comments: 1

Lim_(x→∼) ((4x^3 −2x^2 −5x+4)/(9x^3 −4x^2 +9)) = ??

$$ \\ $$$$\:\:\:\boldsymbol{\mathrm{Lim}}_{\boldsymbol{{x}}\rightarrow\sim} \:\:\frac{\mathrm{4}\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{5}\boldsymbol{{x}}+\mathrm{4}}{\mathrm{9}\boldsymbol{{x}}^{\mathrm{3}} −\mathrm{4}\boldsymbol{{x}}^{\mathrm{2}} +\mathrm{9}}\:=\:??\: \\ $$

Question Number 188984 Answers: 1 Comments: 4

Lim_(x→∼) (√(16x^2 −2x−1))−4x−5 = ??

$$ \\ $$$$\:\:\boldsymbol{\mathrm{Lim}}_{\boldsymbol{{x}}\rightarrow\sim} \:\sqrt{\mathrm{16}\boldsymbol{{x}}^{\mathrm{2}} −\mathrm{2}\boldsymbol{{x}}−\mathrm{1}}−\mathrm{4}\boldsymbol{{x}}−\mathrm{5}\:=\:??\:\:\:\: \\ $$$$ \\ $$

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