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AlgebraQuestion and Answers: Page 247

Question Number 107945 Answers: 3 Comments: 0

((○BeMath○)/(∧⌣∧)) { ((x^4 +(1/x^4 ) = 23)),((x^3 −(1/x^3 ) = ?)) :}

$$\:\:\:\:\:\:\frac{\circ\mathbb{B}{e}\mathbb{M}{ath}\circ}{\wedge\smile\wedge} \\ $$$$\:\:\:\begin{cases}{{x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }\:=\:\mathrm{23}}\\{{x}^{\mathrm{3}} −\frac{\mathrm{1}}{{x}^{\mathrm{3}} }\:=\:?}\end{cases} \\ $$

Question Number 107867 Answers: 0 Comments: 0

Question Number 107794 Answers: 2 Comments: 0

Question Number 107779 Answers: 1 Comments: 3

Question Number 107690 Answers: 1 Comments: 0

“BeMath“ Let the complex number z satisfies the equation 3(z−1)= i(z+1) (1) find z in the form a+bi where a,b ∈R (2) find the value of ∣z∣ and ∣z−z^∗ ∣

$$\:\:\:\:\:\:\:\:``\mathcal{B}{e}\mathcal{M}{ath}`` \\ $$$${Let}\:{the}\:{complex}\:{number}\:{z}\:{satisfies}\:{the} \\ $$$${equation}\:\mathrm{3}\left({z}−\mathrm{1}\right)=\:{i}\left({z}+\mathrm{1}\right)\: \\ $$$$\left(\mathrm{1}\right)\:{find}\:{z}\:{in}\:{the}\:{form}\:{a}+{bi}\:{where}\:{a},{b}\:\in\mathbb{R}\: \\ $$$$\left(\mathrm{2}\right)\:{find}\:{the}\:{value}\:{of}\:\mid{z}\mid\:{and}\:\mid{z}−{z}^{\ast} \mid\: \\ $$$$ \\ $$

Question Number 107674 Answers: 2 Comments: 0

f(x)=(√x)(√x) D_f =???

$${f}\left({x}\right)=\sqrt{{x}}\sqrt{{x}}\:\:\:\:\:\:\:{D}_{{f}} =??? \\ $$

Question Number 107673 Answers: 3 Comments: 0

Question Number 107486 Answers: 3 Comments: 1

∦BeMath∦ (2/5)+(5/(25))+(8/(125))+((11)/(625))+((14)/(3125))+... = ?

$$\:\:\:\:\:\:\nparallel\mathcal{B}{e}\mathcal{M}{ath}\nparallel \\ $$$$\frac{\mathrm{2}}{\mathrm{5}}+\frac{\mathrm{5}}{\mathrm{25}}+\frac{\mathrm{8}}{\mathrm{125}}+\frac{\mathrm{11}}{\mathrm{625}}+\frac{\mathrm{14}}{\mathrm{3125}}+...\:=\:? \\ $$

Question Number 107484 Answers: 2 Comments: 0

∦BeMath∦ (√(x+(√(x+(√(x+(√(x+...)))))))) = (√(4(√(4(√(4(√(4...)))))))) x=?

$$\:\:\:\:\:\nparallel\mathcal{B}{e}\mathcal{M}{ath}\nparallel \\ $$$$\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+\sqrt{{x}+...}}}}\:=\:\sqrt{\mathrm{4}\sqrt{\mathrm{4}\sqrt{\mathrm{4}\sqrt{\mathrm{4}...}}}} \\ $$$${x}=?\: \\ $$

Question Number 107483 Answers: 2 Comments: 0

⋇JS⋇ ∣1+(1/x) ∣−∣x−3∣ > 2 find solution set. (A) 3−(√(10)) < x < 2−(√3) ; x≠0 (B) 3−(√(10)) < x < 3+(√(10)) ; x≠0 (C) 3−(√(10)) < x < 2+(√(10)) ; x≠0 (D) 2+(√(10)) < x < 3+(√(10)) ; x≠0 (E) none of these

$$\:\:\:\:\:\:\:\:\divideontimes\mathcal{JS}\divideontimes \\ $$$$\:\:\:\:\:\mid\mathrm{1}+\frac{\mathrm{1}}{{x}}\:\mid−\mid{x}−\mathrm{3}\mid\:>\:\mathrm{2}\: \\ $$$${find}\:{solution}\:{set}. \\ $$$$\left({A}\right)\:\mathrm{3}−\sqrt{\mathrm{10}}\:<\:{x}\:<\:\mathrm{2}−\sqrt{\mathrm{3}}\:;\:{x}\neq\mathrm{0} \\ $$$$\left({B}\right)\:\mathrm{3}−\sqrt{\mathrm{10}}\:<\:{x}\:<\:\mathrm{3}+\sqrt{\mathrm{10}}\:;\:{x}\neq\mathrm{0} \\ $$$$\left({C}\right)\:\mathrm{3}−\sqrt{\mathrm{10}}\:<\:{x}\:<\:\mathrm{2}+\sqrt{\mathrm{10}}\:;\:{x}\neq\mathrm{0} \\ $$$$\left({D}\right)\:\mathrm{2}+\sqrt{\mathrm{10}}\:<\:{x}\:<\:\mathrm{3}+\sqrt{\mathrm{10}}\:;\:{x}\neq\mathrm{0} \\ $$$$\left({E}\right)\:{none}\:{of}\:{these}\: \\ $$

Question Number 107454 Answers: 2 Comments: 0

Given the function f(x) = ((x + 3)/(x−2)) and g(x) = (1/2)xe^x (1) Find the centre of symmetry of f. (2) Define the monotony of g and if possible draw a variation table for g(x). (3) Sketch the function g(x) (4) determine if f and g intersect.

$$\mathrm{Given}\:\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:=\:\frac{{x}\:+\:\mathrm{3}}{{x}−\mathrm{2}}\:\mathrm{and}\:\mathrm{g}\left({x}\right)\:=\:\frac{\mathrm{1}}{\mathrm{2}}{xe}^{{x}} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{centre}\:\mathrm{of}\:\mathrm{symmetry}\:\mathrm{of}\:{f}. \\ $$$$\left(\mathrm{2}\right)\:\mathrm{Define}\:\mathrm{the}\:\mathrm{monotony}\:\mathrm{of}\:\mathrm{g}\:\mathrm{and}\:\mathrm{if}\:\mathrm{possible}\:\mathrm{draw}\:\mathrm{a}\:\mathrm{variation} \\ $$$$\mathrm{table}\:\mathrm{for}\:\mathrm{g}\left({x}\right). \\ $$$$\left(\mathrm{3}\right)\:\mathrm{Sketch}\:\mathrm{the}\:\mathrm{function}\:\mathrm{g}\left({x}\right) \\ $$$$\left(\mathrm{4}\right)\:\mathrm{determine}\:\mathrm{if}\:{f}\:\mathrm{and}\:\mathrm{g}\:\mathrm{intersect}. \\ $$

Question Number 107438 Answers: 1 Comments: 0