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AlgebraQuestion and Answers: Page 242

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

Question Number 107761 Answers: 0 Comments: 2

Question Number 107385 Answers: 0 Comments: 7

⋰BeMath⋰ Given 6x^2 −6px+14p−2=0 has the roots are u & v where u,v ∉Z If u,v ≥ 1 , then the value of ∣u−v∣ . (a)14 (b)15 (c)16 (d)17 (e) 18

$$\:\:\:\:\:\iddots\mathcal{B}{e}\mathcal{M}{ath}\iddots \\ $$$${Given}\:\mathrm{6}{x}^{\mathrm{2}} −\mathrm{6}{px}+\mathrm{14}{p}−\mathrm{2}=\mathrm{0} \\ $$$${has}\:{the}\:{roots}\:{are}\:\:{u}\:\&\:{v}\:{where}\:{u},{v}\:\notin\mathbb{Z} \\ $$$${If}\:{u},{v}\:\geqslant\:\mathrm{1}\:,\:{then}\:{the}\:{value}\:{of}\:\mid{u}−{v}\mid\:. \\ $$$$\left({a}\right)\mathrm{14}\:\:\:\:\:\left({b}\right)\mathrm{15}\:\:\:\:\:\left({c}\right)\mathrm{16}\:\:\:\:\:\left({d}\right)\mathrm{17}\:\:\:\left({e}\right)\:\mathrm{18} \\ $$

Question Number 107352 Answers: 5 Comments: 0

⊚BeMath⊚ (1)1−(1/(√2)) +(1/(√3))−(1/(√4))+(1/(√5))−(1/(√6))+...=? (2) lim_(x→0) (1+sin x)^(1/x) ?

$$\:\:\:\:\:\:\:\:\circledcirc\mathcal{B}{e}\mathcal{M}{ath}\circledcirc \\ $$$$\left(\mathrm{1}\right)\mathrm{1}−\frac{\mathrm{1}}{\sqrt{\mathrm{2}}}\:+\frac{\mathrm{1}}{\sqrt{\mathrm{3}}}−\frac{\mathrm{1}}{\sqrt{\mathrm{4}}}+\frac{\mathrm{1}}{\sqrt{\mathrm{5}}}−\frac{\mathrm{1}}{\sqrt{\mathrm{6}}}+...=? \\ $$$$\left(\mathrm{2}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left(\mathrm{1}+\mathrm{sin}\:{x}\right)^{\frac{\mathrm{1}}{{x}}} \:? \\ $$

Question Number 107313 Answers: 2 Comments: 0

{ ((x+y(√x) = ((95)/8))),((y+x(√y) = ((93)/8))) :} . Find (√(xy))

$$\begin{cases}{{x}+{y}\sqrt{{x}}\:=\:\frac{\mathrm{95}}{\mathrm{8}}}\\{{y}+{x}\sqrt{{y}}\:=\:\frac{\mathrm{93}}{\mathrm{8}}}\end{cases}\:.\:\mathcal{F}{ind}\:\sqrt{{xy}} \\ $$

Question Number 107262 Answers: 0 Comments: 0

What is the requirement of last axioms i.e. 1v=v ∀ v∈V in the definition of vector space?

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{requirement}\:\mathrm{of}\:\mathrm{last} \\ $$$$\mathrm{axioms}\:\mathrm{i}.\mathrm{e}.\:\mathrm{1}{v}={v}\:\forall\:{v}\in{V}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{definition}\:\mathrm{of}\:\mathrm{vector}\:\mathrm{space}? \\ $$

Question Number 107242 Answers: 4 Comments: 0

...question... prove that: if a,b,c∈R^+ then: ♣ (√a) +(√b)+(√c)> (√(a+b+c)) ♣ ....sincerly yours... ... M.N...

$$\:\:\:\:\:...{question}... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:{prove}\:{that}: \\ $$$$\:{if}\:\:{a},{b},{c}\in\mathbb{R}^{+} \:{then}: \\ $$$$\:\:\:\:\:\clubsuit\:\:\:\sqrt{{a}}\:+\sqrt{{b}}+\sqrt{{c}}>\:\sqrt{{a}+{b}+{c}}\:\clubsuit\: \\ $$$$\:\:\:\:\:\:\:....{sincerly}\:{yours}... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:...\:\mathscr{M}.\mathscr{N}... \\ $$$$\:\: \\ $$

Question Number 107234 Answers: 1 Comments: 0

Question Number 107117 Answers: 2 Comments: 0

Question Number 107073 Answers: 0 Comments: 0

Question Number 107033 Answers: 0 Comments: 0

Question Number 106941 Answers: 1 Comments: 0

Find the maximum value of Σ_(i=1) ^n sin^5 θ_i with Σ_(i=1) ^n sin θ_i =0.

$${Find}\:{the}\:{maximum}\:{value}\:{of}\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{sin}^{\mathrm{5}} \:\theta_{{i}} \\ $$$${with}\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}\mathrm{sin}\:\theta_{{i}} =\mathrm{0}. \\ $$

Question Number 106943 Answers: 3 Comments: 1

Question Number 106907 Answers: 1 Comments: 0

Question Number 106906 Answers: 2 Comments: 0

Question Number 106816 Answers: 2 Comments: 1

prove by mathematical induction (1) n^2 ≤ 2^n ; n ≥ 4 (2) (n+1)^2 < 2n^2 ; n ≥ 3 (3) 2^n −3 ≥ 2^(n−2) ; n ≥ 5 @bemath@

$$\mathrm{prove}\:\mathrm{by}\:\mathrm{mathematical}\:\mathrm{induction} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{n}^{\mathrm{2}} \:\leqslant\:\mathrm{2}^{\mathrm{n}} \:;\:\mathrm{n}\:\geqslant\:\mathrm{4} \\ $$$$\left(\mathrm{2}\right)\:\left(\mathrm{n}+\mathrm{1}\right)^{\mathrm{2}} \:<\:\mathrm{2n}^{\mathrm{2}} \:;\:\mathrm{n}\:\geqslant\:\mathrm{3} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{2}^{\mathrm{n}} −\mathrm{3}\:\geqslant\:\mathrm{2}^{\mathrm{n}−\mathrm{2}} \:;\:\mathrm{n}\:\geqslant\:\mathrm{5} \\ $$$$\:\:\:\:\:\:@\mathrm{bemath}@ \\ $$

Question Number 106794 Answers: 3 Comments: 0

repost old question unanswer Given → { ((((4x^2 )/(1+4x^2 )) = y)),((((4y^2 )/(1+4y^2 )) = z)),((((4z^2 )/(1+4z^2 )) = x)) :}

$$\mathrm{repost}\:\mathrm{old}\:\mathrm{question}\:\mathrm{unanswer} \\ $$$$\mathcal{G}\mathrm{iven}\:\rightarrow\begin{cases}{\frac{\mathrm{4x}^{\mathrm{2}} }{\mathrm{1}+\mathrm{4x}^{\mathrm{2}} }\:=\:\mathrm{y}}\\{\frac{\mathrm{4y}^{\mathrm{2}} }{\mathrm{1}+\mathrm{4y}^{\mathrm{2}} }\:=\:\mathrm{z}}\\{\frac{\mathrm{4z}^{\mathrm{2}} }{\mathrm{1}+\mathrm{4z}^{\mathrm{2}} }\:=\:\mathrm{x}}\end{cases} \\ $$

Question Number 106745 Answers: 2 Comments: 8

Question Number 106730 Answers: 1 Comments: 0

Question Number 106727 Answers: 2 Comments: 0

Question Number 106774 Answers: 4 Comments: 0

^(@bemath@) (1) 3^x + 3^((√x) ) = 90. find x ? (2) x (dy/dx)−(1+x)y = xy^2

$$\:\:\:\:\overset{@\mathrm{bemath}@} {\:} \\ $$$$\:\left(\mathrm{1}\right)\:\:\:\:\mathrm{3}^{{x}} \:+\:\mathrm{3}^{\sqrt{{x}}\:} =\:\mathrm{90}.\:\mathrm{find}\:{x}\:?\: \\ $$$$\:\:\left(\mathrm{2}\right)\:\mathrm{x}\:\frac{\mathrm{dy}}{\mathrm{dx}}−\left(\mathrm{1}+\mathrm{x}\right)\mathrm{y}\:=\:\mathrm{xy}^{\mathrm{2}} \\ $$

Question Number 106659 Answers: 1 Comments: 0

How many terms has the polynomial; (X_1 +2X_2 −X_3 +34)^(10) ?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{terms}\:\mathrm{has}\:\mathrm{the}\:\mathrm{polynomial}; \\ $$$$\left(\mathrm{X}_{\mathrm{1}} +\mathrm{2X}_{\mathrm{2}} −\mathrm{X}_{\mathrm{3}} +\mathrm{34}\right)^{\mathrm{10}} \:? \\ $$

Question Number 106655 Answers: 0 Comments: 1

Question Number 106378 Answers: 2 Comments: 0

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