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Question Number 104536    Answers: 1   Comments: 1

The sum of two numbers is 384 and their GCD is 48. What is the LCM of the numbers ?

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{numbers}}\:\boldsymbol{\mathrm{is}}\:\mathrm{384}\:\boldsymbol{\mathrm{and}} \\ $$$$\mathrm{t}\boldsymbol{\mathrm{heir}}\:\boldsymbol{\mathrm{GCD}}\:\boldsymbol{\mathrm{is}}\:\mathrm{48}.\:\boldsymbol{\mathrm{What}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{LCM}}\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{numbers}}\:? \\ $$

Question Number 104533    Answers: 3   Comments: 0

find : lim_(x→1) (((x+2)^2 +(x+1)^3 −17)/((√(x+3))−((x+7))^(1/3) ))

$${find}\:: \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\left({x}+\mathrm{2}\right)^{\mathrm{2}} +\left({x}+\mathrm{1}\right)^{\mathrm{3}} −\mathrm{17}}{\sqrt{{x}+\mathrm{3}}−\sqrt[{\mathrm{3}}]{{x}+\mathrm{7}}} \\ $$

Question Number 105006    Answers: 2   Comments: 0

Miranda did market in 3 day. The monday, she bought 3kg of fish^ ,2kg of meat ,1kg of rice at 10000 $. The wednesday she bought 1kg of fish, 3kg of meat, 2kg of rice at 10000$. And the thursday she bought 4kg of fish, 2kg of meat,3 kg of rice at 12500$. 1) Which price(sum) will spend Miranda if she she go to the market at saturday to buy at the same price 3kg of fish, 1kg of meat and 1.5kg of rice?

$$ \\ $$$${Miranda}\:{did}\:{market}\:{in}\:\mathrm{3}\:{day}. \\ $$$${The}\:{monday},\:{she}\:{bought}\:\mathrm{3}{kg}\:{of}\:{fis}\bar {{h}} \\ $$$$,\mathrm{2}{kg}\:{of}\:{meat}\:,\mathrm{1}{kg}\:{of}\:{rice}\:{at}\:\mathrm{10000}\:\$. \\ $$$${The}\:{wednesday}\:{she}\:{bought}\:\mathrm{1}{kg}\:{of} \\ $$$${fish},\:\mathrm{3}{kg}\:{of}\:{meat},\:\mathrm{2}{kg}\:{of}\:{rice}\:{at} \\ $$$$\mathrm{10000\$}. \\ $$$${And}\:{the}\:{thursday}\:{she}\:{bought}\:\mathrm{4}{kg}\:{of} \\ $$$${fish},\:\mathrm{2}{kg}\:{of}\:{meat},\mathrm{3}\:{kg}\:{of}\:{rice}\:{at} \\ $$$$\mathrm{12500\$}. \\ $$$$\left.\mathrm{1}\right)\:{Which}\:{price}\left({sum}\right)\:{will}\:{spend}\:{Miranda} \\ $$$${if}\:{she}\:{she}\:{go}\:{to}\:{the}\:{market}\:{at} \\ $$$${saturday}\:{to}\:{buy}\:{at}\:{the}\:{same}\:{price} \\ $$$$\mathrm{3}{kg}\:{of}\:{fish},\:\mathrm{1}{kg}\:{of}\:{meat}\:{and}\:\mathrm{1}.\mathrm{5}{kg}\:{of} \\ $$$${rice}? \\ $$

Question Number 105001    Answers: 1   Comments: 1

Question Number 104998    Answers: 2   Comments: 2

Question Number 104997    Answers: 0   Comments: 0

Question Number 104523    Answers: 0   Comments: 0

∫((xdx)/((x^3 +x+1)^2 ))

$$\int\frac{\mathrm{xdx}}{\left(\mathrm{x}^{\mathrm{3}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 104517    Answers: 2   Comments: 0

Question Number 104516    Answers: 1   Comments: 1

Question Number 104509    Answers: 2   Comments: 0

(1) (d^2 y/dx^2 ) −7 (dy/dx) +12y = 0 (2) y′′′−3y′′+4y′−2y= e^x −cos x (3)y′′′+3y′′+5y′+3y=0 (4) lim_(x→0) ((cot 4x−1)/(2x^2 ))

$$\left(\mathrm{1}\right)\:\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }\:−\mathrm{7}\:\frac{{dy}}{{dx}}\:+\mathrm{12}{y}\:=\:\mathrm{0} \\ $$$$\left(\mathrm{2}\right)\:{y}'''−\mathrm{3}{y}''+\mathrm{4}{y}'−\mathrm{2}{y}=\:{e}^{{x}} −\mathrm{cos}\:{x} \\ $$$$\left(\mathrm{3}\right){y}'''+\mathrm{3}{y}''+\mathrm{5}{y}'+\mathrm{3}{y}=\mathrm{0} \\ $$$$\left(\mathrm{4}\right)\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cot}\:\mathrm{4}{x}−\mathrm{1}}{\mathrm{2}{x}^{\mathrm{2}} } \\ $$

Question Number 104505    Answers: 1   Comments: 0

calculate ∫_0 ^∞ (dx/((x+1)^2 (x+2)^2 (x+3)^2 ))

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} \left(\mathrm{x}+\mathrm{2}\right)^{\mathrm{2}} \left(\mathrm{x}+\mathrm{3}\right)^{\mathrm{2}} } \\ $$

Question Number 104497    Answers: 1   Comments: 2

Question Number 104494    Answers: 0   Comments: 0

Question Number 104486    Answers: 1   Comments: 0

If A = [(3,(−4),2),((−2),1,0),((−1),(−1),1) ]and B = [(1,2,(−2)),(2,5,(−4)),(3,7,(−5)) ]then show that AB = BA = I_3 .

$$\boldsymbol{\mathrm{If}}\:\boldsymbol{\mathrm{A}}\:=\:\begin{bmatrix}{\mathrm{3}}&{−\mathrm{4}}&{\mathrm{2}}\\{−\mathrm{2}}&{\mathrm{1}}&{\mathrm{0}}\\{−\mathrm{1}}&{−\mathrm{1}}&{\mathrm{1}}\end{bmatrix}\boldsymbol{\mathrm{and}}\: \\ $$$$\boldsymbol{\mathrm{B}}\:=\:\begin{bmatrix}{\mathrm{1}}&{\mathrm{2}}&{−\mathrm{2}}\\{\mathrm{2}}&{\mathrm{5}}&{−\mathrm{4}}\\{\mathrm{3}}&{\mathrm{7}}&{−\mathrm{5}}\end{bmatrix}\boldsymbol{\mathrm{then}}\: \\ $$$$\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{AB}}\:=\:\boldsymbol{\mathrm{BA}}\:=\:\boldsymbol{\mathrm{I}}_{\mathrm{3}} \:. \\ $$

Question Number 104485    Answers: 1   Comments: 0

If a^2 +b^2 = ab+bc+ca then a:b:c = ?

$$\mathrm{If}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} \:=\:{ab}+{bc}+{ca}\:\mathrm{then}\: \\ $$$${a}:{b}:{c}\:=\:?\: \\ $$

Question Number 104475    Answers: 2   Comments: 0

Solve 2^(2x) + 42^x −32=0

$$\mathrm{Solve}\:\mathrm{2}^{\mathrm{2x}} \:+\:\mathrm{42}^{\mathrm{x}} −\mathrm{32}=\mathrm{0} \\ $$

Question Number 104471    Answers: 1   Comments: 0

Σ_(n=1) ^∞ ((e^n n!)/n^n )

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{{e}^{{n}} {n}!}{{n}^{{n}} } \\ $$

Question Number 104468    Answers: 1   Comments: 7

Question Number 104461    Answers: 1   Comments: 0

Question Number 104460    Answers: 1   Comments: 0

The number of reading books is 1248 in a library. The number of story books is 936. The librarians bought more reading books. Now ((The number of Reading books)/(The number of story books )) = ((11)/5). How many reading books were bought ?

$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{reading}\:\mathrm{books}\:\mathrm{is}\:\mathrm{1248} \\ $$$$\mathrm{in}\:\mathrm{a}\:\mathrm{library}.\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{story} \\ $$$$\mathrm{books}\:\mathrm{is}\:\mathrm{936}.\:\mathrm{The}\:\mathrm{librarians}\:\mathrm{bought} \\ $$$$\mathrm{more}\:\mathrm{reading}\:\mathrm{books}.\:\mathrm{Now}\:\frac{\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{Reading}\:\mathrm{books}}{\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{story}\:\mathrm{books}\:} \\ $$$$=\:\frac{\mathrm{11}}{\mathrm{5}}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{reading}\:\mathrm{books}\:\mathrm{were} \\ $$$$\mathrm{bought}\:? \\ $$

Question Number 104459    Answers: 1   Comments: 1

∫ (dx/(√(Acos x+B)))

$$\int\:\frac{{dx}}{\sqrt{{A}\mathrm{cos}\:{x}+{B}}} \\ $$

Question Number 104452    Answers: 3   Comments: 0

If A:B = 3:4, B:C = 6:7 then A:B:C = ? A:C = ?

$$\mathrm{If}\:\mathrm{A}:\mathrm{B}\:=\:\mathrm{3}:\mathrm{4},\:\mathrm{B}:\mathrm{C}\:=\:\mathrm{6}:\mathrm{7}\:\mathrm{then} \\ $$$$\mathrm{A}:\mathrm{B}:\mathrm{C}\:=\:?\:\mathrm{A}:\mathrm{C}\:=\:?\: \\ $$

Question Number 104450    Answers: 1   Comments: 0

(4/(99)) + (7/(999)) + ((11)/(999999)) = ? Can you solve this?

$$\frac{\mathrm{4}}{\mathrm{99}}\:+\:\frac{\mathrm{7}}{\mathrm{999}}\:+\:\frac{\mathrm{11}}{\mathrm{999999}}\:=\:? \\ $$$$\boldsymbol{\mathrm{Can}}\:\boldsymbol{\mathrm{you}}\:\boldsymbol{\mathrm{solve}}\:\boldsymbol{\mathrm{this}}? \\ $$

Question Number 104445    Answers: 0   Comments: 2

Question Number 104428    Answers: 4   Comments: 0

given a_(n+1) =a_(n−1) +2a_n if a_3 = 0 & a_5 = −1 find a_n

$${given}\:{a}_{{n}+\mathrm{1}} ={a}_{{n}−\mathrm{1}} +\mathrm{2}{a}_{{n}} \\ $$$${if}\:{a}_{\mathrm{3}} =\:\mathrm{0}\:\&\:{a}_{\mathrm{5}} \:=\:−\mathrm{1} \\ $$$${find}\:{a}_{{n}} \\ $$

Question Number 104426    Answers: 0   Comments: 0

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