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Question Number 199135 Answers: 7 Comments: 0

a + (1/a) = 3 find: a^5 + (1/a^5 ) = ?

$$\mathrm{a}\:+\:\frac{\mathrm{1}}{\mathrm{a}}\:=\:\mathrm{3} \\ $$$$\mathrm{find}:\:\:\:\mathrm{a}^{\mathrm{5}} \:+\:\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{5}} }\:\:=\:\:? \\ $$

Question Number 199133 Answers: 1 Comments: 0

a^2 b − 1 = 1999 how many natural solutions of the equation (a,b) have?

$$\mathrm{a}^{\mathrm{2}} \mathrm{b}\:−\:\mathrm{1}\:=\:\mathrm{1999} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{natural}\:\mathrm{solutions}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation}\:\left(\mathrm{a},\mathrm{b}\right)\:\mathrm{have}? \\ $$

Question Number 199149 Answers: 3 Comments: 1

Question Number 199353 Answers: 0 Comments: 4

What is the probability that in a class of 18 people, there exists exactly a group of exactly 3 people born on the same day of the week?

$${What}\:{is}\:{the}\:{probability}\:{that}\:{in}\:{a}\:{class}\: \\ $$$${of}\:\mathrm{18}\:{people},\:{there}\:{exists}\:{exactly}\:{a}\: \\ $$$${group}\:{of}\:{exactly}\:\mathrm{3}\:{people}\:{born}\:{on}\:{the} \\ $$$${same}\:{day}\:{of}\:{the}\:{week}? \\ $$

Question Number 199351 Answers: 1 Comments: 0

Question Number 199112 Answers: 2 Comments: 0

{ ((a^2 − b = 73)),((b^2 − a = 73)) :} find: a,b = ?

$$\begin{cases}{\mathrm{a}^{\mathrm{2}} \:−\:\mathrm{b}\:=\:\mathrm{73}}\\{\mathrm{b}^{\mathrm{2}} \:−\:\mathrm{a}\:=\:\mathrm{73}}\end{cases}\:\:\:\:\:\mathrm{find}:\:\mathrm{a},\mathrm{b}\:=\:? \\ $$

Question Number 199109 Answers: 2 Comments: 1

Q: α , β ,γ are the roots of the following equation . find the value of: Eq^( n) : x^( 3) −2x^2 + x + 2=0 E = (α/(β +γ)) +(β/(α +γ)) +(γ/(α+ β))

$$ \\ $$$$\:{Q}:\:\:\:\:\alpha\:,\:\beta\:,\gamma\:{are}\:{the}\:{roots}\:{of}\:{the}\:{following} \\ $$$$\:\:\:\:\:{equation}\:.\:{find}\:{the}\:{value}\:{of}: \\ $$$$ \\ $$$$\:\:\:\:\:{Eq}^{\:{n}} \::\:\:\:{x}^{\:\mathrm{3}} −\mathrm{2}{x}^{\mathrm{2}} \:+\:{x}\:+\:\mathrm{2}=\mathrm{0} \\ $$$$\:\:\:{E}\:=\:\frac{\alpha}{\beta\:+\gamma}\:+\frac{\beta}{\alpha\:+\gamma}\:+\frac{\gamma}{\alpha+\:\beta} \\ $$$$ \\ $$

Question Number 199103 Answers: 1 Comments: 2

Question Number 199101 Answers: 3 Comments: 0

Question Number 199093 Answers: 0 Comments: 0

Question Number 199084 Answers: 1 Comments: 0

lim_(n→∞) ∫_0 ^(√n) (1−(x^2 /n))^n dx = ???

$$\:\:\:\:\:\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\int_{\mathrm{0}} ^{\sqrt{\mathrm{n}}} \:\left(\mathrm{1}−\frac{\mathrm{x}^{\mathrm{2}} }{\mathrm{n}}\right)^{\mathrm{n}} \mathrm{dx}\:\:\:=\:\:\:\:??? \\ $$

Question Number 199073 Answers: 1 Comments: 0

∣3−3x∣>9 solve fir x ss

$$\mid\mathrm{3}−\mathrm{3x}\mid>\mathrm{9} \\ $$$$ \\ $$$$\mathrm{solve}\:\mathrm{fir}\:\mathrm{x} \\ $$$$ \\ $$$$\mathrm{ss} \\ $$$$ \\ $$

Question Number 199054 Answers: 2 Comments: 0

$$\:\:\boldsymbol{{x}} \\ $$

Question Number 199046 Answers: 2 Comments: 1

Question Number 199625 Answers: 1 Comments: 0

Given Fibonacci series F_1 =F_2 = 1 and F_(n+2) = F_(n+1) +F_n for n>0. Find the remainder F_(2022) divides by 5

$$\mathrm{Given}\:\mathrm{Fibonacci}\:\mathrm{series}\: \\ $$$$\:\mathrm{F}_{\mathrm{1}} =\mathrm{F}_{\mathrm{2}} =\:\mathrm{1}\:\mathrm{and}\:\mathrm{F}_{\mathrm{n}+\mathrm{2}} =\:\mathrm{F}_{\mathrm{n}+\mathrm{1}} +\mathrm{F}_{\mathrm{n}} \\ $$$$\:\mathrm{for}\:\mathrm{n}>\mathrm{0}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\: \\ $$$$\:\mathrm{F}_{\mathrm{2022}} \:\mathrm{divides}\:\mathrm{by}\:\mathrm{5}\: \\ $$

Question Number 199033 Answers: 1 Comments: 3

Question Number 199032 Answers: 0 Comments: 2

Please how can I search for old questions and answers? I need to see some things from my past accounts.

$${Please}\:{how}\:{can}\:{I}\:{search}\:{for}\:{old}\:{questions} \\ $$$${and}\:{answers}?\:{I}\:{need}\:{to}\:{see}\:{some}\:{things}\:{from} \\ $$$${my}\:{past}\:{accounts}. \\ $$

Question Number 199031 Answers: 1 Comments: 0

Question Number 199023 Answers: 1 Comments: 1

Question Number 200304 Answers: 2 Comments: 0

Question Number 199015 Answers: 2 Comments: 0

Question Number 199012 Answers: 0 Comments: 0

lim_(x→∞) ((log n)/n)^( n) (√(Σ_(k=1) ^∞ (k^n /(k!)))) = ????

$$\:\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{log}\:{n}}{{n}}\:^{\:\:{n}} \sqrt{\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{k}^{{n}} }{{k}!}}\:\:\:=\:\:\:???? \\ $$

Question Number 199011 Answers: 1 Comments: 1

Sum of two irrational numbers is 1 less than their product, and 8 less than their sum of squares. Find the larger of the two numbers.

$${Sum}\:{of}\:{two}\:{irrational}\:{numbers}\:{is}\:\mathrm{1} \\ $$$${less}\:{than}\:{their}\:{product},\:{and}\:\mathrm{8}\:{less}\:{than} \\ $$$${their}\:{sum}\:{of}\:{squares}.\:{Find}\:{the}\:{larger} \\ $$$${of}\:{the}\:{two}\:{numbers}. \\ $$

Question Number 199006 Answers: 0 Comments: 0

Given that ABCD is a trapezium such that AD//BC. The centroid of △ABD lies on the bisector of ∠BCD. Show that the centroid of △ABC lies on the bisector of ∠ADC.

$$\mathrm{Given}\:\mathrm{that}\:{ABCD}\:\mathrm{is}\:\mathrm{a}\:\mathrm{trapezium}\:\mathrm{such}\:\mathrm{that}\:{AD}//{BC}. \\ $$$$\mathrm{The}\:\mathrm{centroid}\:\mathrm{of}\:\bigtriangleup{ABD}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{bisector}\:\mathrm{of}\:\angle{BCD}. \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{centroid}\:\mathrm{of}\:\bigtriangleup{ABC}\:\mathrm{lies}\:\mathrm{on}\:\mathrm{the}\:\mathrm{bisector}\:\mathrm{of}\:\angle{ADC}. \\ $$

Question Number 199005 Answers: 0 Comments: 4

Question Number 199001 Answers: 1 Comments: 0

If ,A ∈ M_(n×n) , A^( 2) = A ,1≠ k ∈R. Find ( I − kA )^( −1) = ?

$$ \\ $$$$\:\mathrm{I}{f}\:,\mathrm{A}\:\in\:\mathrm{M}_{{n}×{n}} \:\:\:,\:\:\mathrm{A}^{\:\mathrm{2}} \:=\:\mathrm{A}\:,\mathrm{1}\neq\:{k}\:\in\mathbb{R}. \\ $$$$\:\:\:\mathrm{F}{ind}\:\:\:\:\left(\:\:\:\mathrm{I}\:−\:{k}\mathrm{A}\:\right)^{\:−\mathrm{1}} \:=\:?\: \\ $$

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