Question and Answers Forum

AllQuestion and Answers: Page 1330

Question Number 75468 Answers: 0 Comments: 2

lim_(n→∞) (√((2n^2 −5n+3)/(n^5 +1)))

$$\underset{{n}\rightarrow\infty} {{lim}}\sqrt{\frac{\mathrm{2}{n}^{\mathrm{2}} −\mathrm{5}{n}+\mathrm{3}}{{n}^{\mathrm{5}} +\mathrm{1}}} \\ $$

Question Number 75465 Answers: 0 Comments: 1

Question Number 75463 Answers: 2 Comments: 0

Question Number 75457 Answers: 2 Comments: 5

Question Number 75456 Answers: 2 Comments: 0

Find the domain and range of relation (a)R={(x,y):y=(√(x^2 −6)) } (b)R={(x,y):x^2 −y^2 =1 }

$${Find}\:{the}\:{domain}\:{and}\: \\ $$$${range}\:{of}\:{relation} \\ $$$$\left({a}\right){R}=\left\{\left({x},{y}\right):{y}=\sqrt{{x}^{\mathrm{2}} −\mathrm{6}}\:\right\} \\ $$$$\left({b}\right){R}=\left\{\left({x},{y}\right):{x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{1}\:\right\} \\ $$

Question Number 75453 Answers: 0 Comments: 3

Question Number 75509 Answers: 1 Comments: 0

Give the exponentional form of the complex Z=((1−cosθ+itanθ)/(1+cosθ−isinθ))

$$\mathrm{Give}\:\mathrm{the}\:\mathrm{exponentional}\:\mathrm{form}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{complex}\:\mathrm{Z}=\frac{\mathrm{1}−\mathrm{cos}\theta+\mathrm{itan}\theta}{\mathrm{1}+\mathrm{cos}\theta−\mathrm{isin}\theta} \\ $$

Question Number 75446 Answers: 1 Comments: 0

∫(1/(x^5 −1))dx

$$\int\frac{\mathrm{1}}{{x}^{\mathrm{5}} −\mathrm{1}}{dx} \\ $$

Question Number 75445 Answers: 3 Comments: 0

If a variable line in two adjacent positions has direction cosines l,m, n and l+δl, m+δm, n+δn , show that the small angle δθ b/w the two positions is given by δθ^2 = δl^2 + δm^2 + δn^2 ??

$$\mathrm{If}\:\mathrm{a}\:\mathrm{variable}\:\mathrm{line}\:\mathrm{in}\:\mathrm{two}\:\mathrm{adjacent} \\ $$$$\mathrm{positions}\:\mathrm{has}\:\mathrm{direction}\:\mathrm{cosines} \\ $$$${l},{m},\:{n}\:\mathrm{and}\:{l}+\delta{l},\:{m}+\delta{m},\:{n}+\delta{n} \\ $$$$,\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{small}\:\mathrm{angle}\:\delta\theta\: \\ $$$$\mathrm{b}/\mathrm{w}\:\mathrm{the}\:\mathrm{two}\:\mathrm{positions}\:\mathrm{is}\:\mathrm{given}\:\mathrm{by} \\ $$$$\delta\theta^{\mathrm{2}} \:=\:\delta{l}^{\mathrm{2}} \:+\:\delta{m}^{\mathrm{2}} \:+\:\delta{n}^{\mathrm{2}} \:\:?? \\ $$

Question Number 75444 Answers: 0 Comments: 1

Find the angle b/w the lines whose direction cosines are given by the equations l + m + n = 0 , l^2 + m^2 − n^2 = 0 ??

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{b}/\mathrm{w}\:\mathrm{the}\:\mathrm{lines} \\ $$$$\mathrm{whose}\:\mathrm{direction}\:\mathrm{cosines}\:\mathrm{are}\:\mathrm{given} \\ $$$$\mathrm{by}\:\mathrm{the}\:\mathrm{equations}\:{l}\:+\:{m}\:+\:{n}\:=\:\mathrm{0} \\ $$$$,\:{l}^{\mathrm{2}} \:+\:{m}^{\mathrm{2}} \:−\:{n}^{\mathrm{2}} \:=\:\mathrm{0}\:?? \\ $$$$ \\ $$

Question Number 75440 Answers: 0 Comments: 3

Question Number 75439 Answers: 1 Comments: 0

A man left his office in a car at 10am to restaurant 30km away. He expected to arrive at 11:10am but had to stop 15km from the office for 15 minutes . He arrived at the restaurant 5 minutes late. a. Find the initial speed b. Draw a travel graph for the whole journey

$$\mathrm{A}\:\mathrm{man}\:\mathrm{left}\:\mathrm{his}\:\mathrm{office}\:\mathrm{in}\:\mathrm{a}\:\mathrm{car}\:\mathrm{at}\:\mathrm{10am} \\ $$$$\mathrm{to}\:\mathrm{restaurant}\:\mathrm{30km}\:\mathrm{away}.\:\mathrm{He}\:\mathrm{expected} \\ $$$$\mathrm{to}\:\mathrm{arrive}\:\mathrm{at}\:\mathrm{11}:\mathrm{10am}\:\mathrm{but}\:\mathrm{had}\:\mathrm{to}\:\mathrm{stop}\: \\ $$$$\mathrm{15km}\:\mathrm{from}\:\mathrm{the}\:\mathrm{office}\:\mathrm{for}\:\mathrm{15}\:\mathrm{minutes}\:. \\ $$$$\mathrm{He}\:\mathrm{arrived}\:\mathrm{at}\:\mathrm{the}\:\mathrm{restaurant}\:\mathrm{5}\:\mathrm{minutes}\: \\ $$$$\mathrm{late}. \\ $$$$\mathrm{a}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{initial}\:\mathrm{speed} \\ $$$$\mathrm{b}.\:\mathrm{Draw}\:\mathrm{a}\:\mathrm{travel}\:\mathrm{graph}\:\mathrm{for}\:\mathrm{the}\:\mathrm{whole}\:\mathrm{journey} \\ $$

Question Number 75437 Answers: 1 Comments: 6

Question Number 75435 Answers: 0 Comments: 4

solve the integral with Residue theorem. ∫_0 ^(2π) ((3 dθ)/(9 +sin^2 θ))

$${solve}\:{the}\:{integral}\:{with}\:{Residue}\:{theorem}. \\ $$$$\underset{\mathrm{0}} {\overset{\mathrm{2}\pi} {\int}}\frac{\mathrm{3}\:{d}\theta}{\mathrm{9}\:+\mathrm{sin}^{\mathrm{2}} \theta} \\ $$

Question Number 75426 Answers: 1 Comments: 0

A boy has to cover 4km to catch a bus. He walks part of the distance as 3km/h and run the rest at 5km/h if he takes 1hour to complete the distance. For how many kilometres does he walk

$$\mathrm{A}\:\mathrm{boy}\:\mathrm{has}\:\mathrm{to}\:\mathrm{cover}\:\:\mathrm{4km}\:\:\mathrm{to}\: \\ $$$$\mathrm{catch}\:\mathrm{a}\:\mathrm{bus}.\:\mathrm{He}\:\mathrm{walks}\:\mathrm{part}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{distance}\:\mathrm{as}\:\mathrm{3km}/\mathrm{h}\:\mathrm{and}\:\mathrm{run}\:\mathrm{the}\:\mathrm{rest}\:\mathrm{at} \\ $$$$\mathrm{5km}/\mathrm{h}\:\mathrm{if}\:\mathrm{he}\:\mathrm{takes}\:\mathrm{1hour}\:\mathrm{to}\:\mathrm{complete}\: \\ $$$$\mathrm{the}\:\mathrm{distance}.\:\mathrm{For}\:\mathrm{how}\:\mathrm{many}\:\mathrm{kilometres} \\ $$$$\mathrm{does}\:\mathrm{he}\:\mathrm{walk} \\ $$

Question Number 75421 Answers: 0 Comments: 3

If p is a point in the base AB of a triangle ABC such that AP :PB=P:Q prove that (p+q)cot θ=qcot A−pcot B

$${If}\:{p}\:{is}\:{a}\:{point}\:{in}\:{the}\:{base} \\ $$$${AB}\:{of}\:\:{a}\:\:{triangle}\:\:{ABC} \\ $$$${such}\:{that}\:{AP}\:\::{PB}={P}:{Q} \\ $$$${prove}\:{that} \\ $$$$\left({p}+{q}\right)\mathrm{cot}\:\theta={q}\mathrm{cot}\:{A}−{p}\mathrm{cot}\:{B} \\ $$

Question Number 75403 Answers: 1 Comments: 0