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Question Number 144460    Answers: 1   Comments: 0

If C=226k find the least integal value of k that will make C a perfect square

$$ \\ $$$$\mathrm{If}\:\mathrm{C}=\mathrm{226}{k}\:\mathrm{find}\:\mathrm{the}\:\mathrm{least} \\ $$$$\mathrm{integal}\:\mathrm{value}\:\mathrm{of}\:{k}\:\mathrm{that}\:\mathrm{will} \\ $$$$\mathrm{make}\:\mathrm{C}\:\mathrm{a}\:\mathrm{perfect}\:\mathrm{square} \\ $$

Question Number 144479    Answers: 0   Comments: 0

Consider the followinge statments P: All students with measles stay in the sick bay. T: All students in the sick bay do not do homework. Which of the following is/are valid deductions from the two statements a) Kofi does not have measles so Kofi does his homework. b)George has done his homework therefore he does not stay in the sick bay c) Jane does not have measles so she does not stay in the sick bay

$$ \\ $$$$\mathrm{Consider}\:\mathrm{the}\:\mathrm{followinge} \\ $$$$\mathrm{statments} \\ $$$$\mathrm{P}:\:\mathrm{All}\:\mathrm{students}\:\mathrm{with}\:\mathrm{measles} \\ $$$$\:\mathrm{stay}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sick}\:\mathrm{bay}. \\ $$$$\mathrm{T}:\:\mathrm{All}\:\mathrm{students}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sick} \\ $$$$\:\mathrm{bay}\:\mathrm{do}\:\mathrm{not}\:\mathrm{do}\:\mathrm{homework}. \\ $$$$\mathrm{Which}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\:\mathrm{is}/\mathrm{are}\:\mathrm{valid}\:\mathrm{deductions} \\ $$$$\:\mathrm{from}\:\mathrm{the}\:\mathrm{two}\:\mathrm{statements} \\ $$$$\left.\mathrm{a}\right)\:\mathrm{Kofi}\:\mathrm{does}\:\mathrm{not}\:\mathrm{have}\: \\ $$$$\mathrm{measles}\:\mathrm{so}\:\mathrm{Kofi}\:\mathrm{does}\:\mathrm{his} \\ $$$$\:\mathrm{homework}. \\ $$$$\left.\mathrm{b}\right)\mathrm{George}\:\mathrm{has}\:\mathrm{done}\:\mathrm{his}\: \\ $$$$\mathrm{homework}\:\mathrm{therefore}\:\mathrm{he} \\ $$$$\mathrm{does}\:\mathrm{not}\:\mathrm{stay}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sick}\:\mathrm{bay} \\ $$$$\left.\:\mathrm{c}\right)\:\mathrm{Jane}\:\mathrm{does}\:\mathrm{not}\:\mathrm{have} \\ $$$$\mathrm{measles}\:\mathrm{so}\:\mathrm{she}\:\mathrm{does}\:\mathrm{not}\: \\ $$$$\mathrm{stay}\:\mathrm{in}\:\mathrm{the}\:\mathrm{sick}\:\mathrm{bay} \\ $$

Question Number 144452    Answers: 2   Comments: 0

Find minimum value of f(x)=sin (x+3)−sin (x+1)−2cos (x+2) where xεR

$$\:\mathrm{Find}\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\: \\ $$$$\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{sin}\:\left(\mathrm{x}+\mathrm{3}\right)−\mathrm{sin}\:\left(\mathrm{x}+\mathrm{1}\right)−\mathrm{2cos}\:\left(\mathrm{x}+\mathrm{2}\right) \\ $$$$\mathrm{where}\:\mathrm{x}\epsilon\mathrm{R} \\ $$

Question Number 144450    Answers: 3   Comments: 0

.........Calculus(I)......... Lim_( x → 0) ((1 −cos(xcos((x/2)).cos((x/4))cos((x/8))))/x^( 2) )=?

$$ \\ $$$$\:\:\:\:\:\:\:\:.........\mathrm{C}{alculus}\left(\mathrm{I}\right)......... \\ $$$$\:\:\mathrm{Lim}_{\:\:{x}\:\rightarrow\:\mathrm{0}} \frac{\mathrm{1}\:−{cos}\left({xcos}\left(\frac{{x}}{\mathrm{2}}\right).{cos}\left(\frac{{x}}{\mathrm{4}}\right){cos}\left(\frac{{x}}{\mathrm{8}}\right)\right)}{{x}^{\:\mathrm{2}} }=? \\ $$

Question Number 144447    Answers: 1   Comments: 1

Question Number 144446    Answers: 2   Comments: 0

Question Number 144439    Answers: 1   Comments: 4

Question Number 144432    Answers: 1   Comments: 0

∫_0 ^∝ t^(n−2) costdt

$$\int_{\mathrm{0}} ^{\propto} {t}^{{n}−\mathrm{2}} {costdt} \\ $$

Question Number 144431    Answers: 1   Comments: 0

∫tan x sin^2 x cos^3 x cot^4 x dx =?

$$\:\:\:\int\mathrm{tan}\:\mathrm{x}\:\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:\mathrm{cos}\:^{\mathrm{3}} \mathrm{x}\:\mathrm{cot}\:^{\mathrm{4}} \mathrm{x}\:\mathrm{dx}\:=? \\ $$

Question Number 144429    Answers: 0   Comments: 0

Set a,b∈[−Π Π] be such that cos (a−b)=1 and cos (a+b)=(1/e). Then find the number of pairs of a,b satisfying the above system of equations?

$$\mathrm{Set}\:\mathrm{a},\mathrm{b}\in\left[−\Pi\:\Pi\right]\:\mathrm{be}\:\mathrm{such}\:\mathrm{that}\: \\ $$$$\mathrm{cos}\:\left(\mathrm{a}−\mathrm{b}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{cos}\:\left(\mathrm{a}+\mathrm{b}\right)=\frac{\mathrm{1}}{\mathrm{e}}. \\ $$$$\mathrm{Then}\:\mathrm{find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{pairs} \\ $$$$\mathrm{of}\:\mathrm{a},\mathrm{b}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{above}\: \\ $$$$\mathrm{system}\:\mathrm{of}\:\mathrm{equations}? \\ $$

Question Number 144427    Answers: 0   Comments: 0

Determiner l′original de laplace... F(p)=(1/((p^2 +p+1)^2 ))

$${Determiner}\:{l}'{original}\:{de}\:{laplace}... \\ $$$${F}\left({p}\right)=\frac{\mathrm{1}}{\left({p}^{\mathrm{2}} +{p}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 144424    Answers: 2   Comments: 0

make c the subject in S=(1/(2(a+b+c)))

$${make}\:{c}\:{the}\:{subject}\:{in}\:{S}=\frac{\mathrm{1}}{\mathrm{2}\left({a}+{b}+{c}\right)} \\ $$

Question Number 144422    Answers: 1   Comments: 0

make n the subject of the formular if A=p(1+(r/(100)))^n

$${make}\:{n}\:{the}\:{subject}\:{of}\:{the}\:{formular} \\ $$$${if}\:{A}={p}\left(\mathrm{1}+\frac{{r}}{\mathrm{100}}\right)^{{n}} \\ $$

Question Number 144421    Answers: 0   Comments: 0

Let a,b,c > 0 and a+b+c = 3. Prove that ((a^(2021) +b^(2021) +c^(2021) )/3) ≥ 1+((4042)/3)(1−((ab+bc+ca)/3))

$$\mathrm{Let}\:{a},{b},{c}\:>\:\mathrm{0}\:\mathrm{and}\:{a}+{b}+{c}\:=\:\mathrm{3}.\:\mathrm{Prove}\:\mathrm{that} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\frac{{a}^{\mathrm{2021}} +{b}^{\mathrm{2021}} +{c}^{\mathrm{2021}} }{\mathrm{3}}\:\geqslant\:\mathrm{1}+\frac{\mathrm{4042}}{\mathrm{3}}\left(\mathrm{1}−\frac{{ab}+{bc}+{ca}}{\mathrm{3}}\right)\:\:\:\:\:\:\:\:\:\:\: \\ $$

Question Number 144420    Answers: 2   Comments: 1

Question Number 144419    Answers: 1   Comments: 0

...Advanced ....Calculus... Without using the Feynman′s trick , Find the value of :: I :=∫_0 ^( 1) ((Log (1+ x^( 2) ))/(1 +x)) dx=? m.n...

$$\:\:\:\:\:...{Advanced}\:....{Calculus}... \\ $$$${Without}\:{using}\:{the}\:{Feynman}'{s}\:{trick}\:, \\ $$$$\:\:\:\:\:{Find}\:{the}\:{value}\:{of}\:\:\::: \\ $$$$\:\:\:\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\int_{\mathrm{0}} ^{\:\mathrm{1}} \frac{{Log}\:\left(\mathrm{1}+\:\mathrm{x}^{\:\mathrm{2}} \right)}{\mathrm{1}\:+\mathrm{x}}\:\mathrm{dx}=? \\ $$$$\:\:\:\:\mathrm{m}.\mathrm{n}... \\ $$

Question Number 144414    Answers: 1   Comments: 0

find Lourant series of f(z)=(1/(1−z+z^2 )) ,0<∣z−1∣<1

$${find}\:{Lourant}\:{series}\:{of}\: \\ $$$$ \\ $$$${f}\left({z}\right)=\frac{\mathrm{1}}{\mathrm{1}−{z}+{z}^{\mathrm{2}} }\:\:\:\:,\mathrm{0}<\mid{z}−\mathrm{1}\mid<\mathrm{1} \\ $$

Question Number 144413    Answers: 2   Comments: 0

lim_(x→1) [ (1/(4−4(√x)))−(1/(5−5(x)^(1/5) )) ] =?

$$\:\:\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\left[\:\frac{\mathrm{1}}{\mathrm{4}−\mathrm{4}\sqrt{\mathrm{x}}}−\frac{\mathrm{1}}{\mathrm{5}−\mathrm{5}\sqrt[{\mathrm{5}}]{\mathrm{x}}}\:\right]\:=? \\ $$

Question Number 144403    Answers: 1   Comments: 0

A=lim_(x→0) ((∫_(2x) ^(4x) ((sint)/t)dt)/(e^x −1)) =?

$$\mathrm{A}=\underset{\mathrm{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\int_{\mathrm{2x}} ^{\mathrm{4x}} \frac{\mathrm{sint}}{\mathrm{t}}\mathrm{dt}}{\mathrm{e}^{\mathrm{x}} −\mathrm{1}}\:=? \\ $$

Question Number 144402    Answers: 1   Comments: 2

Question Number 144406    Answers: 0   Comments: 0

Question Number 144409    Answers: 2   Comments: 0

∫ (dx/((x+3)(√(1−x^2 )))) ?

$$\:\:\:\:\int\:\frac{\mathrm{dx}}{\left(\mathrm{x}+\mathrm{3}\right)\sqrt{\mathrm{1}−\mathrm{x}^{\mathrm{2}} }}\:? \\ $$

Question Number 144408    Answers: 3   Comments: 0

lg(2)=x lg(7)=y lg_5 (9,8)=?

$$\boldsymbol{{lg}}\left(\mathrm{2}\right)=\boldsymbol{{x}} \\ $$$$\boldsymbol{{lg}}\left(\mathrm{7}\right)=\boldsymbol{{y}} \\ $$$$\boldsymbol{{lg}}_{\mathrm{5}} \left(\mathrm{9},\mathrm{8}\right)=? \\ $$

Question Number 144396    Answers: 1   Comments: 1

L=lim_(n→+∝) ((1/(n^2 +1^2 )) + (2/(n^2 +2^2 )) +..+ (n/(n^2 +n^2 )))=?

$$\mathrm{L}=\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{2}} +\mathrm{1}^{\mathrm{2}} }\:+\:\frac{\mathrm{2}}{\mathrm{n}^{\mathrm{2}} +\mathrm{2}^{\mathrm{2}} }\:+..+\:\frac{\mathrm{n}}{\mathrm{n}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} }\right)=? \\ $$

Question Number 144395    Answers: 0   Comments: 0

L=lim_(n→+∝) ((n+n^2 +n^3 +n^4 +...+n^n )/(1^n +2^n +3^n +4^n +...+n^n )) =?

$$\mathrm{L}=\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\frac{\mathrm{n}+\mathrm{n}^{\mathrm{2}} +\mathrm{n}^{\mathrm{3}} +\mathrm{n}^{\mathrm{4}} +...+\mathrm{n}^{\mathrm{n}} }{\mathrm{1}^{\mathrm{n}} +\mathrm{2}^{\mathrm{n}} +\mathrm{3}^{\mathrm{n}} +\mathrm{4}^{\mathrm{n}} +...+\mathrm{n}^{\mathrm{n}} }\:=? \\ $$

Question Number 144394    Answers: 0   Comments: 1

L=lim_(n→+∝) ((1/(n+1)) + (1/(n+2)) +...+ (1/(n+n)))=?

$$\mathrm{L}=\underset{\mathrm{n}\rightarrow+\propto} {\mathrm{lim}}\left(\frac{\mathrm{1}}{\mathrm{n}+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{2}}\:+...+\:\frac{\mathrm{1}}{\mathrm{n}+\mathrm{n}}\right)=? \\ $$

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