Question and Answers Forum

AllQuestion and Answers: Page 212

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) = ?

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

Question Number 198989 Answers: 0 Comments: 1

Calcul : determinant ((3,(16),(24),(33)),(1,5,7,9),(5,(27),(36),(55)),(7,(38),(51),(78)))

$$ \\ $$$$ \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{Calcul}\:: \\ $$$$\begin{vmatrix}{\mathrm{3}}&{\mathrm{16}}&{\mathrm{24}}&{\mathrm{33}}\\{\mathrm{1}}&{\mathrm{5}}&{\mathrm{7}}&{\mathrm{9}}\\{\mathrm{5}}&{\mathrm{27}}&{\mathrm{36}}&{\mathrm{55}}\\{\mathrm{7}}&{\mathrm{38}}&{\mathrm{51}}&{\mathrm{78}}\end{vmatrix} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 198988 Answers: 1 Comments: 0

Question Number 198982 Answers: 0 Comments: 0

Question Number 198975 Answers: 0 Comments: 7

60 students of a school must take at least one of the three courses for mathematics, physics and chemistry respectively. if a student is randomly picked, what is the probability that he/she takes only one course?

$$\mathrm{60}\:{students}\:{of}\:{a}\:{school}\:{must}\:{take} \\ $$$${at}\:{least}\:{one}\:{of}\:{the}\:{three}\:{courses}\:{for} \\ $$$${mathematics},\:{physics}\:{and}\:{chemistry} \\ $$$${respectively}. \\ $$$${if}\:{a}\:{student}\:{is}\:{randomly}\:{picked},\:{what} \\ $$$${is}\:{the}\:{probability}\:{that}\:{he}/{she}\:{takes} \\ $$$${only}\:{one}\:{course}? \\ $$

Question Number 198973 Answers: 0 Comments: 0

calculate the symmetrical components.V_(a0) ,V_(a1) ,V_(a2) and V_(b0) , V_(b1) ,V_(b2) of the unbalanced three-phase system. with V_a =90∠90° , V_b =117∠0° , V_c =81∠225°

$$\mathrm{calculate}\:\mathrm{the}\:\:\mathrm{symmetrical}\: \\ $$$$\mathrm{components}.\mathrm{V}_{\mathrm{a0}} \:,\mathrm{V}_{\mathrm{a1}} ,\mathrm{V}_{\mathrm{a2}} \:\:\mathrm{and}\:\mathrm{V}_{\mathrm{b0}} , \\ $$$$\mathrm{V}_{\mathrm{b1}} \:,\mathrm{V}_{\mathrm{b2}} \:\:\mathrm{of}\:\mathrm{the}\:\mathrm{unbalanced} \\ $$$$\mathrm{three}-\mathrm{phase}\:\mathrm{system}.\:\mathrm{with} \\ $$$$\:\mathrm{V}_{\mathrm{a}} =\mathrm{90}\angle\mathrm{90}°\:,\:\mathrm{V}_{\mathrm{b}} =\mathrm{117}\angle\mathrm{0}°\:, \\ $$$$\mathrm{V}_{\mathrm{c}} =\mathrm{81}\angle\mathrm{225}° \\ $$

Question Number 198968 Answers: 2 Comments: 0

Find the polynomial with roots that exceed the roots of f(x)=3x^3 −14x^2 +x+62=0 by 3. Hence determine the value of (1/(a+3))+(1/(b+3))+(1/(c+3)), where a,b and c are roots.

$${Find}\:{the}\:{polynomial}\:{with}\:{roots}\:{that} \\ $$$${exceed}\:{the}\:{roots}\:{of}\: \\ $$$${f}\left({x}\right)=\mathrm{3}{x}^{\mathrm{3}} −\mathrm{14}{x}^{\mathrm{2}} +{x}+\mathrm{62}=\mathrm{0}\:{by}\:\mathrm{3}.\:{Hence} \\ $$$${determine}\:{the}\:{value}\:{of}\:\frac{\mathrm{1}}{{a}+\mathrm{3}}+\frac{\mathrm{1}}{{b}+\mathrm{3}}+\frac{\mathrm{1}}{{c}+\mathrm{3}}, \\ $$$${where}\:{a},{b}\:{and}\:{c}\:{are}\:{roots}. \\ $$

Question Number 198954 Answers: 1 Comments: 0

Convert this decimal number to praction number 1. 0.3333... =... 2. 2.1111...=... 3. 0.1313....=...

$$\:\mathrm{Convert}\:\mathrm{this}\:\mathrm{decimal}\:\mathrm{number}\:\mathrm{to}\: \\ $$$$\:\:\mathrm{praction}\:\mathrm{number} \\ $$$$\mathrm{1}.\:\mathrm{0}.\mathrm{3333}...\:=... \\ $$$$\mathrm{2}.\:\:\mathrm{2}.\mathrm{1111}...=... \\ $$$$\mathrm{3}.\:\mathrm{0}.\mathrm{1313}....=... \\ $$

Question Number 198953 Answers: 1 Comments: 0

f(x)= ((3x−5)/(2x+1)) →f^′ (x)=....?

$$\mathrm{f}\left(\mathrm{x}\right)=\:\frac{\mathrm{3x}−\mathrm{5}}{\mathrm{2x}+\mathrm{1}}\:\rightarrow\mathrm{f}^{'} \left(\mathrm{x}\right)=....? \\ $$

Question Number 198948 Answers: 2 Comments: 0

∫_1 ^3 ((x−2)/(x^2 −4x)) dx= ....

$$\int_{\mathrm{1}} ^{\mathrm{3}} \frac{\mathrm{x}−\mathrm{2}}{\mathrm{x}^{\mathrm{2}} −\mathrm{4x}}\:\mathrm{dx}=\:.... \\ $$

Question Number 198952 Answers: 3 Comments: 0

lim_(x→0) ((sin 3x)/(tan 6x)) = ....?