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Question Number 171314 Answers: 1 Comments: 0

If C_r , C_s are cyclic groups such that g.c.d(r,s)=1, then show that C_r ×C_s is a cyclic group. Mastermind

$${If}\:{C}_{{r}} ,\:{C}_{{s}} \:{are}\:{cyclic}\:{groups}\:{such}\:{that} \\ $$$${g}.{c}.{d}\left({r},{s}\right)=\mathrm{1},\:{then}\:{show}\:{that}\:{C}_{{r}} ×{C}_{{s}} \:{is} \\ $$$${a}\:{cyclic}\:{group}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171179 Answers: 1 Comments: 0

Question Number 171161 Answers: 1 Comments: 0

Question Number 171153 Answers: 1 Comments: 0

An aeroplane covers a certain distance at a speed of 240kmph in 5 hours. to cover the same distance in 1(2/3) hrs, it must travel at a speed of: A) 300kmph B) 360kmph C) 600kmph D) 700kmph Mastermind

$${An}\:{aeroplane}\:{covers}\:{a}\:{certain}\:{distance} \\ $$$${at}\:{a}\:{speed}\:{of}\:\mathrm{240}{kmph}\:{in}\:\mathrm{5}\:{hours}. \\ $$$${to}\:{cover}\:{the}\:{same}\:{distance}\:{in}\:\mathrm{1}\frac{\mathrm{2}}{\mathrm{3}}\:{hrs}, \\ $$$${it}\:{must}\:{travel}\:{at}\:{a}\:{speed}\:{of}: \\ $$$$\left.{A}\right)\:\mathrm{300}{kmph} \\ $$$$\left.{B}\right)\:\mathrm{360}{kmph} \\ $$$$\left.{C}\right)\:\mathrm{600}{kmph} \\ $$$$\left.{D}\right)\:\mathrm{700}{kmph} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171152 Answers: 1 Comments: 0

The average ages of three person is 27 years. Their ages are in the propor tion of 1:3:5. What is the age in years of the youngest one among them? Mastermind

$${The}\:{average}\:{ages}\:{of}\:{three}\:{person}\:{is} \\ $$$$\mathrm{27}\:{years}.\:{Their}\:{ages}\:{are}\:{in}\:{the}\:{propor} \\ $$$${tion}\:{of}\:\mathrm{1}:\mathrm{3}:\mathrm{5}.\:{What}\:{is}\:{the}\:{age}\:{in}\:{years} \\ $$$${of}\:{the}\:{youngest}\:{one}\:{among}\:{them}? \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171107 Answers: 0 Comments: 0

Please help lim_(x→−∞) (x−1)e^(x−1) −1=? lim_(x→+∞) (x−1)e^(x−1) −1=? g(x)=(x−1)e^(x−1) −1 g(x)′=?

$${Please}\:{help} \\ $$$${li}\underset{{x}\rightarrow−\infty} {{m}}\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1}=? \\ $$$${li}\underset{{x}\rightarrow+\infty} {{m}}\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1}=? \\ $$$${g}\left({x}\right)=\left({x}−\mathrm{1}\right){e}^{{x}−\mathrm{1}} −\mathrm{1} \\ $$$${g}\left({x}\right)'=? \\ $$$$ \\ $$

Question Number 171094 Answers: 0 Comments: 0

prove that: 𝛀=Σ_(n=0) ^∞ ((((n!)^2 )/((2n)!)))^2 (2^(4n) /((2n+1)^3 ))=^? (7/2)𝛇(3)−πG G−Catalan′s constant

Question Number 171032 Answers: 1 Comments: 0

Find the domain and range of the function, f(x)=((x^2 +2)/(2x+1)) Mastermind

$${Find}\:{the}\:{domain}\:{and}\:{range}\:{of}\:{the} \\ $$$${function},\:{f}\left({x}\right)=\frac{{x}^{\mathrm{2}} +\mathrm{2}}{\mathrm{2}{x}+\mathrm{1}} \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171025 Answers: 2 Comments: 0

Question Number 171038 Answers: 2 Comments: 0

Question Number 171009 Answers: 1 Comments: 0

Find the inverse, y^(−1) of the function y=x^3 +4. Mastermind

$${Find}\:{the}\:{inverse},\:{y}^{−\mathrm{1}} \:{of}\:{the}\:{function} \\ $$$${y}={x}^{\mathrm{3}} +\mathrm{4}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171008 Answers: 0 Comments: 1

Find the maximum and minimum values of h(x)=(4/3)x^3 +(9/2)x^2 +5x+8. Mastermind

$${Find}\:{the}\:{maximum}\:{and}\:{minimum} \\ $$$${values}\:{of}\:{h}\left({x}\right)=\frac{\mathrm{4}}{\mathrm{3}}{x}^{\mathrm{3}} +\frac{\mathrm{9}}{\mathrm{2}}{x}^{\mathrm{2}} +\mathrm{5}{x}+\mathrm{8}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171006 Answers: 0 Comments: 1

Find the area enclosed by the curve y=4−3x^2 and the x−axis between x_1 =−1 and x_2 =1. Mastermind

$${Find}\:{the}\:{area}\:{enclosed}\:{by}\:{the}\:{curve} \\ $$$${y}=\mathrm{4}−\mathrm{3}{x}^{\mathrm{2}} \:{and}\:{the}\:{x}−{axis}\:{between} \\ $$$${x}_{\mathrm{1}} =−\mathrm{1}\:{and}\:{x}_{\mathrm{2}} =\mathrm{1}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 171005 Answers: 0 Comments: 0

The distance S metre travelled in time t seconds by an object released from rest and allow to fall freely under the force of gravity is given by s(t)=4.5t^2 . find a) the average speed of the object during the time interval from 2 to 2.5 seconds. b) the instantaneous velocity of the object after 4 seconds. Mastermind

$${The}\:{distance}\:{S}\:{metre}\:{travelled}\:{in}\:{time} \\ $$$${t}\:{seconds}\:{by}\:{an}\:{object}\:{released}\:{from} \\ $$$${rest}\:{and}\:{allow}\:{to}\:{fall}\:{freely}\:{under}\:{the} \\ $$$${force}\:{of}\:{gravity}\:{is}\:{given}\:{by}\:{s}\left({t}\right)=\mathrm{4}.\mathrm{5}{t}^{\mathrm{2}} . \\ $$$${find}\: \\ $$$$\left.{a}\right)\:{the}\:{average}\:{speed}\:{of}\:{the}\:{object} \\ $$$${during}\:{the}\:{time}\:{interval}\:{from}\:\mathrm{2}\:{to} \\ $$$$\mathrm{2}.\mathrm{5}\:{seconds}. \\ $$$$\left.{b}\right)\:{the}\:{instantaneous}\:{velocity}\:{of}\:{the} \\ $$$${object}\:{after}\:\mathrm{4}\:{seconds}. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170997 Answers: 1 Comments: 0

Find the equation of the tangent to the curve x^2 +y^2 −4x+6y−12=0 at the point (2, 3). Mastermind

$${Find}\:{the}\:{equation}\:{of}\:{the}\:{tangent}\:{to}\:{the} \\ $$$${curve}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{6}{y}−\mathrm{12}=\mathrm{0}\:{at}\:{the} \\ $$$${point}\:\left(\mathrm{2},\:\mathrm{3}\right). \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170996 Answers: 1 Comments: 0

Find the volume of the solid obtained by rotating about x−axis of the curve y=(√x) on the interval [0, 2]. Mastermind

$${Find}\:{the}\:{volume}\:{of}\:{the}\:{solid}\:{obtained} \\ $$$${by}\:{rotating}\:{about}\:{x}−{axis}\:{of}\:{the}\:{curve} \\ $$$${y}=\sqrt{{x}}\:{on}\:{the}\:{interval}\:\left[\mathrm{0},\:\mathrm{2}\right]. \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170995 Answers: 0 Comments: 1

Approximate sin46° by “differentials” Mastermind

$${Approximate}\:{sin}\mathrm{46}°\:{by}\:``{differentials}'' \\ $$$$ \\ $$$${Mastermind} \\ $$

Question Number 170994 Answers: 1 Comments: 0

Show that the function h(x)=x^5 −2x is an odd function Mastermind