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AllQuestion and Answers: Page 218

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)) = ....?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{sin}\:\mathrm{3x}}{\mathrm{tan}\:\mathrm{6x}}\:=\:....? \\ $$

Question Number 198951 Answers: 0 Comments: 1

(√(8+(√(48)) ))=....?

$$\sqrt{\mathrm{8}+\sqrt{\mathrm{48}}\:}=....? \\ $$

Question Number 198950 Answers: 1 Comments: 0

3x+2y=6 2x+3y=6 → x and y =...?

$$\mathrm{3x}+\mathrm{2y}=\mathrm{6} \\ $$$$\mathrm{2x}+\mathrm{3y}=\mathrm{6}\:\rightarrow\:\mathrm{x}\:\mathrm{and}\:\mathrm{y}\:=...? \\ $$

Question Number 198949 Answers: 1 Comments: 0

((5!×4!)/(3!×2!)) = ....

$$\:\:\frac{\mathrm{5}!×\mathrm{4}!}{\mathrm{3}!×\mathrm{2}!}\:=\:....\:\: \\ $$

Question Number 198941 Answers: 0 Comments: 1

Question Number 198939 Answers: 1 Comments: 0

Question Number 198933 Answers: 1 Comments: 2

Question Number 198932 Answers: 1 Comments: 0

Find the value of m given that the roots of x^4 −15x^3 +70x^2 −120x+m=0 form a geometric progression.

$${Find}\:{the}\:{value}\:{of}\:{m}\:{given}\:{that}\:{the} \\ $$$${roots}\:{of}\:{x}^{\mathrm{4}} −\mathrm{15}{x}^{\mathrm{3}} +\mathrm{70}{x}^{\mathrm{2}} −\mathrm{120}{x}+{m}=\mathrm{0} \\ $$$${form}\:{a}\:{geometric}\:{progression}. \\ $$

Question Number 198931 Answers: 2 Comments: 0

Find the value of t: t = (1/3)+(2/9)+(3/(27))+.......+(n/3^n )+.....

$${Find}\:{the}\:{value}\:{of}\:{t}:\: \\ $$$${t}\:=\:\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{2}}{\mathrm{9}}+\frac{\mathrm{3}}{\mathrm{27}}+.......+\frac{{n}}{\mathrm{3}^{{n}} }+..... \\ $$

Question Number 198929 Answers: 0 Comments: 0

Question Number 198919 Answers: 1 Comments: 1

Find the sum of the fourth powers of the roots of equation: 7x^3 −21x^2 +9x+2=0

$${Find}\:{the}\:{sum}\:{of}\:{the}\:{fourth}\:{powers}\:{of} \\ $$$${the}\:{roots}\:{of}\:{equation}: \\ $$$$\mathrm{7}{x}^{\mathrm{3}} −\mathrm{21}{x}^{\mathrm{2}} +\mathrm{9}{x}+\mathrm{2}=\mathrm{0} \\ $$

Question Number 198913 Answers: 3 Comments: 1

Question Number 198907 Answers: 0 Comments: 2

find the Area betwen Circle 1 and Circle2.

$$\mathrm{find}\:\mathrm{the}\:\mathrm{Area}\:\mathrm{betwen}\:\mathrm{Circle}\:\mathrm{1}\:\mathrm{and}\: \\ $$$$\mathrm{Circle2}. \\ $$

Question Number 198903 Answers: 1 Comments: 1

Find the minimum value of (a/(b+c))+(b/(c+a))+(c/(a+b)) for all positive real numbers

$${Find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$$\frac{{a}}{{b}+{c}}+\frac{{b}}{{c}+{a}}+\frac{{c}}{{a}+{b}}\:{for}\:{all}\:{positive}\:{real} \\ $$$${numbers} \\ $$

Question Number 198902 Answers: 2 Comments: 0

Given that k^2 −3k+5=0, determine the value of k^4 −6k^3 +9k^2 −7

$${Given}\:{that}\:{k}^{\mathrm{2}} −\mathrm{3}{k}+\mathrm{5}=\mathrm{0},\:{determine} \\ $$$${the}\:{value}\:{of}\:{k}^{\mathrm{4}} −\mathrm{6}{k}^{\mathrm{3}} +\mathrm{9}{k}^{\mathrm{2}} −\mathrm{7} \\ $$

Question Number 198901 Answers: 1 Comments: 0

Question Number 198900 Answers: 0 Comments: 0

((2sin2°+4sin4°+...+180sin180°)/(90))=? calculate.help me pleas.

$$\frac{\mathrm{2}{sin}\mathrm{2}°+\mathrm{4}{sin}\mathrm{4}°+...+\mathrm{180}{sin}\mathrm{180}°}{\mathrm{90}}=? \\ $$$${calculate}.{help}\:{me}\:{pleas}. \\ $$

Question Number 198879 Answers: 0 Comments: 0

Question Number 198869 Answers: 1 Comments: 2

Question Number 198862 Answers: 2 Comments: 0

Question Number 198860 Answers: 1 Comments: 0

Question Number 198855 Answers: 1 Comments: 0

prove : lim_(n→∞) ((n!)/(n^x (n−x)!)) = 1

$${prove}\::\:\underset{{n}\rightarrow\infty} {{lim}}\:\frac{{n}!}{{n}^{{x}} \left({n}−{x}\right)!}\:=\:\mathrm{1}\: \\ $$

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