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Question Number 203468 Answers: 0 Comments: 0

let A B and C be sets prove using venn diagrams and by first principle a)A×(B∪C)=(A×B)∪(A×C) b)A×(B∩C)=(A×B)∩(A×C) c)(A−B)∩(A∩B)∩(B−A)={}

Question Number 203474 Answers: 5 Comments: 0

((z^4 +4z^3 −6z^2 −4z+1)/(z^4 −4z^3 −6z^2 +4z+1))=((z+1)/(z−1)) Find z∈R.

$$\frac{{z}^{\mathrm{4}} +\mathrm{4}{z}^{\mathrm{3}} −\mathrm{6}{z}^{\mathrm{2}} −\mathrm{4}{z}+\mathrm{1}}{{z}^{\mathrm{4}} −\mathrm{4}{z}^{\mathrm{3}} −\mathrm{6}{z}^{\mathrm{2}} +\mathrm{4}{z}+\mathrm{1}}=\frac{{z}+\mathrm{1}}{{z}−\mathrm{1}} \\ $$$${Find}\:{z}\in\mathbb{R}. \\ $$

Question Number 203465 Answers: 2 Comments: 0

Focus and vertex of a parabola are at (3, 4) and (0,0). Find the equation of the directrix.

$$\mathrm{Focus}\:\mathrm{and}\:\mathrm{vertex}\:\mathrm{of}\:\mathrm{a}\:\mathrm{parabola}\:\mathrm{are}\:\mathrm{at}\:\left(\mathrm{3},\:\mathrm{4}\right)\:\mathrm{and}\:\left(\mathrm{0},\mathrm{0}\right). \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{directrix}. \\ $$

Question Number 203457 Answers: 1 Comments: 0

Question Number 203454 Answers: 1 Comments: 0

(√5)+(√5)=x x×5π=? find all answers until 24.01.2024

$$\sqrt{\mathrm{5}}+\sqrt{\mathrm{5}}={x} \\ $$$${x}×\mathrm{5}\pi=?\:{find}\:{all}\:{answers}\:{until}\:\mathrm{24}.\mathrm{01}.\mathrm{2024} \\ $$

Question Number 203445 Answers: 0 Comments: 1

Question Number 203417 Answers: 1 Comments: 1

If ∣−z + iz^(−) ∣ = 2 (√(13)) and z = 1 + (x + 1)∙i Find: mun(x) = ?

$$\mathrm{If} \\ $$$$\mid\overline {−\mathrm{z}\:+\:\boldsymbol{\mathrm{i}}\mathrm{z}}\mid\:=\:\mathrm{2}\:\sqrt{\mathrm{13}}\:\:\:\mathrm{and}\:\:\:\mathrm{z}\:=\:\mathrm{1}\:+\:\left(\mathrm{x}\:+\:\mathrm{1}\right)\centerdot\boldsymbol{\mathrm{i}} \\ $$$$ \\ $$$$\mathrm{Find}:\:\:\:\mathrm{mun}\left(\mathrm{x}\right)\:=\:? \\ $$

Question Number 203416 Answers: 2 Comments: 0

Question Number 203434 Answers: 2 Comments: 0

Question Number 203448 Answers: 2 Comments: 1

y = sin3x−ln(3x+1)+3^(2x) find: y^′ = ?

$$\mathrm{y}\:=\:\mathrm{sin3x}−\mathrm{ln}\left(\mathrm{3x}+\mathrm{1}\right)+\mathrm{3}^{\mathrm{2}\boldsymbol{\mathrm{x}}} \\ $$$$\mathrm{find}:\:\:\:\mathrm{y}^{'} \:=\:? \\ $$

Question Number 203396 Answers: 0 Comments: 0

State the completness axioms of the real number

$$\mathrm{State}\:\mathrm{the}\:\mathrm{completness}\:\mathrm{axioms}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{real}\:\mathrm{number} \\ $$

Question Number 203394 Answers: 1 Comments: 0

Question Number 203393 Answers: 0 Comments: 0

Question Number 203392 Answers: 0 Comments: 2

Question Number 203389 Answers: 1 Comments: 0

Question Number 203387 Answers: 1 Comments: 0

Question Number 203379 Answers: 0 Comments: 0

If a,b,c ∈R^+ with a+b+c=3 prove that (1/(a^6 +b^6 +3c^3 +4))+(1/(b^6 +c^6 +3a^3 +4))+(1/(c^6 +a^6 +3b^3 +4))≤(3/(3+2((√(ab))+(√(bc))+(√(ac)))))

$$\mathrm{If}\:{a},{b},{c}\:\in\mathbb{R}^{+} \:\mathrm{with}\:{a}+{b}+{c}=\mathrm{3}\:\mathrm{prove}\:\mathrm{that} \\ $$$$\frac{\mathrm{1}}{{a}^{\mathrm{6}} +{b}^{\mathrm{6}} +\mathrm{3}{c}^{\mathrm{3}} +\mathrm{4}}+\frac{\mathrm{1}}{{b}^{\mathrm{6}} +{c}^{\mathrm{6}} +\mathrm{3}{a}^{\mathrm{3}} +\mathrm{4}}+\frac{\mathrm{1}}{{c}^{\mathrm{6}} +{a}^{\mathrm{6}} +\mathrm{3}{b}^{\mathrm{3}} +\mathrm{4}}\leqslant\frac{\mathrm{3}}{\mathrm{3}+\mathrm{2}\left(\sqrt{{ab}}+\sqrt{{bc}}+\sqrt{{ac}}\right)} \\ $$

Question Number 203378 Answers: 0 Comments: 0

Question Number 203385 Answers: 2 Comments: 0

Question Number 203401 Answers: 2 Comments: 0

Question Number 203375 Answers: 0 Comments: 4

valeur x? (∡ECA =90)

$$\:\mathrm{valeur}\:\boldsymbol{\mathrm{x}}? \\ $$$$\left(\measuredangle\mathrm{ECA}\:\:=\mathrm{90}\right) \\ $$

Question Number 203374 Answers: 3 Comments: 0

Question Number 203370 Answers: 1 Comments: 1

Question Number 203367 Answers: 2 Comments: 0

if a+b=198, what is the largest integer root which the equation x^2 +ax+b=0 may have?

$${if}\:\boldsymbol{{a}}+\boldsymbol{{b}}=\mathrm{198},\:{what}\:{is}\:{the}\:{largest} \\ $$$$\boldsymbol{{integer}}\:{root}\:{which}\:{the}\:{equation} \\ $$$$\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{ax}}+\boldsymbol{{b}}=\mathrm{0}\:{may}\:{have}? \\ $$

Question Number 203357 Answers: 1 Comments: 0

For the series 5−(5/2)+(5/4)−(5/8)+∙∙∙+(((−1)^(n−1) 5)/2^(n−1) ) find an expression for the sum of the first n terms. Also if the series converges, find the sum to ∞.

$$\boldsymbol{{For}}\:\boldsymbol{{the}}\:\boldsymbol{{series}}\:\mathrm{5}−\frac{\mathrm{5}}{\mathrm{2}}+\frac{\mathrm{5}}{\mathrm{4}}−\frac{\mathrm{5}}{\mathrm{8}}+\centerdot\centerdot\centerdot+\frac{\left(−\mathrm{1}\right)^{\boldsymbol{{n}}−\mathrm{1}} \mathrm{5}}{\mathrm{2}^{\boldsymbol{{n}}−\mathrm{1}} } \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{an}}\:\boldsymbol{{expression}}\:\boldsymbol{{for}}\:\boldsymbol{{the}}\:\boldsymbol{{sum}}\:\boldsymbol{{of}}\:\boldsymbol{{the}}\:\boldsymbol{{first}} \\ $$$$\boldsymbol{{n}}\:\boldsymbol{{terms}}.\:\boldsymbol{{Also}}\:\boldsymbol{{if}}\:\boldsymbol{{the}}\:\boldsymbol{{series}}\:\boldsymbol{{converges}}, \\ $$$$\boldsymbol{{find}}\:\boldsymbol{{the}}\:\boldsymbol{{sum}}\:\boldsymbol{{to}}\:\infty. \\ $$$$ \\ $$$$ \\ $$

Question Number 203354 Answers: 1 Comments: 0

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