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Question Number 181628 Answers: 1 Comments: 0

find the domain and range of y = (1/((x − 1)(x + 2))) restricted to 0 ≤ x ≤ 6

$$\mathrm{find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{and}\:\mathrm{range}\:\mathrm{of}\:\:\:\mathrm{y}\:\:=\:\:\frac{\mathrm{1}}{\left(\mathrm{x}\:\:−\:\:\mathrm{1}\right)\left(\mathrm{x}\:\:+\:\:\mathrm{2}\right)} \\ $$$$\mathrm{restricted}\:\mathrm{to}\:\:\:\mathrm{0}\:\:\leqslant\:\:\mathrm{x}\:\:\leqslant\:\:\mathrm{6} \\ $$

Question Number 181625 Answers: 0 Comments: 0

K-Lemoine′s , I-incenter in △ABC. Prove that: KA^4 +KB^4 +KC^4 ≥ IA^4 +IB^4 +IC^4

$$\mathrm{K}-\mathrm{Lemoine}'\mathrm{s}\:,\:\mathrm{I}-\mathrm{incenter}\:\mathrm{in}\:\bigtriangleup\mathrm{ABC}. \\ $$$$\mathrm{Prove}\:\mathrm{that}: \\ $$$$\mathrm{KA}^{\mathrm{4}} +\mathrm{KB}^{\mathrm{4}} +\mathrm{KC}^{\mathrm{4}} \:\geqslant\:\mathrm{IA}^{\mathrm{4}} +\mathrm{IB}^{\mathrm{4}} +\mathrm{IC}^{\mathrm{4}} \\ $$

Question Number 181627 Answers: 1 Comments: 1

Point E is marked on side AD in rhombus ABCD. If AC = 6 (√(10)) and BD = 2 (√(10)) . How many different integer values can a piece of BE take?

$$\mathrm{Point}\:\:\mathrm{E}\:\:\mathrm{is}\:\mathrm{marked}\:\mathrm{on}\:\mathrm{side}\:\:\mathrm{AD}\:\:\mathrm{in} \\ $$$$\mathrm{rhombus}\:\:\mathrm{ABCD}.\:\mathrm{If}\:\:\mathrm{AC}\:=\:\mathrm{6}\:\sqrt{\mathrm{10}}\:\:\mathrm{and} \\ $$$$\mathrm{BD}\:=\:\mathrm{2}\:\sqrt{\mathrm{10}}\:.\:\mathrm{How}\:\mathrm{many}\:\mathrm{different} \\ $$$$\mathrm{integer}\:\mathrm{values}\:\mathrm{can}\:\mathrm{a}\:\mathrm{piece}\:\mathrm{of}\:\:\mathrm{BE}\:\:\mathrm{take}? \\ $$

Question Number 181619 Answers: 2 Comments: 1

Question Number 181618 Answers: 2 Comments: 0

(dy/dx)+2xy=x^2 y(0)=3 Solve .

$$\frac{\mathrm{dy}}{\mathrm{dx}}+\mathrm{2xy}=\mathrm{x}^{\mathrm{2}} \:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(\mathrm{0}\right)=\mathrm{3} \\ $$$$ \\ $$$$\mathrm{Solve} \\ $$$$ \\ $$$$. \\ $$

Question Number 181617 Answers: 0 Comments: 0

Solve: x(dy/dx)+(x+1)y=e^x^2 .

$$\mathrm{Solve}: \\ $$$$\mathrm{x}\frac{\mathrm{dy}}{\mathrm{dx}}+\left(\mathrm{x}+\mathrm{1}\right)\mathrm{y}=\mathrm{e}^{\mathrm{x}^{\mathrm{2}} } \\ $$$$ \\ $$$$. \\ $$

Question Number 181615 Answers: 1 Comments: 0

Determine whether this is Homogenous or not (dy/dx)=(y/(y−2x)) .

$$\mathrm{Determine}\:\mathrm{whether}\:\mathrm{this}\:\mathrm{is}\:\mathrm{Homogenous} \\ $$$$\mathrm{or}\:\mathrm{not} \\ $$$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{y}}{\mathrm{y}−\mathrm{2x}} \\ $$$$ \\ $$$$. \\ $$

Question Number 181613 Answers: 1 Comments: 0

(dy/dx)=((xy+y^2 )/x^2 ) y(−1)=2 .

$$\frac{\mathrm{dy}}{\mathrm{dx}}=\frac{\mathrm{xy}+\mathrm{y}^{\mathrm{2}} }{\mathrm{x}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{y}\left(−\mathrm{1}\right)=\mathrm{2} \\ $$$$ \\ $$$$. \\ $$

Question Number 181607 Answers: 0 Comments: 0

Question Number 181605 Answers: 0 Comments: 1

Question Number 181599 Answers: 1 Comments: 0

f(x) is a strictly monotonic function in its domain (0, +∞) such that ∀x>0, f(f(x)−(1/x))=2. Find f(x).

$${f}\left({x}\right)\:\mathrm{is}\:\mathrm{a}\:\mathrm{strictly}\:\mathrm{monotonic}\:\mathrm{function}\:\mathrm{in}\:\mathrm{its}\:\mathrm{domain}\:\left(\mathrm{0},\:+\infty\right) \\ $$$$\mathrm{such}\:\mathrm{that}\:\forall{x}>\mathrm{0},\:{f}\left({f}\left({x}\right)−\frac{\mathrm{1}}{{x}}\right)=\mathrm{2}. \\ $$$$\mathrm{Find}\:{f}\left({x}\right). \\ $$

Question Number 181595 Answers: 2 Comments: 0

Question Number 181593 Answers: 2 Comments: 0

I f , a^( 2) +5 b^( 2) + 4c^( 2) = 4b (a +c ) then , find the value of : E = (( ( b+ c −a )^( 3) )/( abc)) = ? ( abc ≠ 0 )

$$ \\ $$$$\:\:\:\:\:\:\:\mathrm{I}\:\mathrm{f}\:,\:\:\:\:{a}^{\:\mathrm{2}} \:+\mathrm{5}\:{b}^{\:\mathrm{2}} \:+\:\mathrm{4}{c}^{\:\mathrm{2}} =\:\mathrm{4}{b}\:\left({a}\:+{c}\:\right) \\ $$$$\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\mathrm{then}\:,\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:: \\ $$$$\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\mathrm{E}\:=\:\frac{\:\left(\:{b}+\:{c}\:−{a}\:\right)^{\:\mathrm{3}} }{\:{abc}}\:=\:?\:\:\:\:\left(\:{abc}\:\neq\:\mathrm{0}\:\right)\:\:\:\:\:\:\: \\ $$

Question Number 181592 Answers: 1 Comments: 0

prove that (1/(cos0 cos1 ))+(1/(cos1 cos2))+......+(1/(cos88 cos89))=((cos1)/(sin^2 1))

$${prove}\:{that} \\ $$$$\frac{\mathrm{1}}{{cos}\mathrm{0}\:{cos}\mathrm{1}\:}+\frac{\mathrm{1}}{{cos}\mathrm{1}\:{cos}\mathrm{2}}+......+\frac{\mathrm{1}}{{cos}\mathrm{88}\:{cos}\mathrm{89}}=\frac{{cos}\mathrm{1}}{{sin}^{\mathrm{2}} \mathrm{1}} \\ $$

Question Number 181590 Answers: 1 Comments: 0

Mr. Jibril is four times as old as his son. Four years ago, he was seven times as old as his son. In how many years will Mr Jibril′s age be twice his son′s age?

$$\mathrm{Mr}.\:\mathrm{Jibril}\:\mathrm{is}\:\mathrm{four}\:\mathrm{times}\:\mathrm{as}\:\mathrm{old}\:\mathrm{as}\:\mathrm{his}\:\mathrm{son}. \\ $$$$\mathrm{Four}\:\mathrm{years}\:\mathrm{ago},\:\mathrm{he}\:\mathrm{was}\:\mathrm{seven}\:\mathrm{times}\:\mathrm{as}\:\mathrm{old} \\ $$$$\mathrm{as}\:\mathrm{his}\:\mathrm{son}.\:\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{years}\:\mathrm{will}\:\mathrm{Mr} \\ $$$$\mathrm{Jibril}'\mathrm{s}\:\mathrm{age}\:\mathrm{be}\:\mathrm{twice}\:\mathrm{his}\:\mathrm{son}'\mathrm{s}\:\mathrm{age}? \\ $$

Question Number 181573 Answers: 0 Comments: 1

25^x − 4^x = 9^x fimd x

$$\mathrm{25}^{{x}} \:−\:\mathrm{4}^{{x}} \:=\:\mathrm{9}^{{x}} \\ $$$${fimd}\:{x} \\ $$

Question Number 181570 Answers: 1 Comments: 0

prove that:xε]−1,1[ Σ_(n=1) ^(+oo) (x^n /n)=−ln(1−x)

$$\left.{prove}\:{that}:{x}\epsilon\right]−\mathrm{1},\mathrm{1}\left[\right. \\ $$$$\underset{{n}=\mathrm{1}} {\overset{+{oo}} {\sum}}\frac{{x}^{{n}} }{{n}}=−{ln}\left(\mathrm{1}−{x}\right) \\ $$

Question Number 181323 Answers: 2 Comments: 1

{ ((U_0 =1 et U_1 =2)),((U_(n+2) =(√(U_n U_(n+1) )))) :} determiner le terme generale et sa nature besoin d′aide avp

$$\begin{cases}{{U}_{\mathrm{0}} =\mathrm{1}\:{et}\:{U}_{\mathrm{1}} =\mathrm{2}}\\{{U}_{{n}+\mathrm{2}} =\sqrt{{U}_{{n}} {U}_{{n}+\mathrm{1}} }}\end{cases} \\ $$$${determiner}\:{le}\:{terme}\:{generale}\:{et}\:{sa}\:{nature} \\ $$$${besoin}\:{d}'{aide}\:{avp} \\ $$

Question Number 181319 Answers: 1 Comments: 0

Determiner 1. ∫(x/(x^4 +x^2 +1))dx 2. ∫((x^4 +1)/(x^4 +x^2 +1))dx

$${Determiner} \\ $$$$\mathrm{1}.\:\:\:\int\frac{{x}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$$$\mathrm{2}.\:\:\:\int\frac{{x}^{\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{4}} +{x}^{\mathrm{2}} +\mathrm{1}}{dx} \\ $$

Question Number 181318 Answers: 2 Comments: 1

if x+y+z=0, find the maximum of ((∣x+2y+3z∣)/( (√(x^2 +y^2 +z^2 )))).

$${if}\:{x}+{y}+{z}=\mathrm{0},\:{find}\:{the}\:{maximum}\:{of} \\ $$$$\frac{\mid{x}+\mathrm{2}{y}+\mathrm{3}{z}\mid}{\:\sqrt{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} }}. \\ $$

Question Number 181313 Answers: 2 Comments: 0

Montrer que 3^(2n+1) +2^(n+2) est divisible par 7

$${Montrer}\:{que} \\ $$$$\mathrm{3}^{\mathrm{2}{n}+\mathrm{1}} +\mathrm{2}^{{n}+\mathrm{2}} \:\:\:{est}\:{divisible}\:{par}\:\mathrm{7} \\ $$

Question Number 181296 Answers: 1 Comments: 0

Question Number 181312 Answers: 0 Comments: 0

Question Number 181280 Answers: 1 Comments: 0

Question Number 181279 Answers: 3 Comments: 0

Question Number 181275 Answers: 1 Comments: 7

what is the sum of all even factors of 1000?

$${what}\:{is}\:{the}\:{sum}\:{of}\:{all} \\ $$$${even}\:{factors}\:{of}\:\mathrm{1000}? \\ $$

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