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Question Number 92219 Answers: 0 Comments: 5

Question Number 92214 Answers: 0 Comments: 1

Question Number 92211 Answers: 1 Comments: 1

4x = 2 (mod 3 )

$$\mathrm{4x}\:=\:\mathrm{2}\:\left(\mathrm{mod}\:\mathrm{3}\:\right)\: \\ $$

Question Number 92197 Answers: 0 Comments: 1

Given L(n) = { ((0 , if n = 1)),((L ⌊(n/2)⌋ +1 , if n > 1)) :} find L(25)

$$\mathrm{Given}\:\mathrm{L}\left(\mathrm{n}\right)\:=\:\begin{cases}{\mathrm{0}\:,\:\mathrm{if}\:\mathrm{n}\:=\:\mathrm{1}}\\{\mathrm{L}\:\lfloor\frac{\mathrm{n}}{\mathrm{2}}\rfloor\:+\mathrm{1}\:,\:\mathrm{if}\:\mathrm{n}\:>\:\mathrm{1}}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{L}\left(\mathrm{25}\right)\: \\ $$

Question Number 92196 Answers: 0 Comments: 4

2^x + 3^y = 72 2^y + 3^(x ) = 108 Please am not getting correct answer for this question using a method proposed .

$$\mathrm{2}^{\mathrm{x}} \:\:+\:\:\mathrm{3}^{\mathrm{y}} \:\:=\:\:\mathrm{72} \\ $$$$\mathrm{2}^{\mathrm{y}} \:\:+\:\:\mathrm{3}^{\mathrm{x}\:\:} =\:\:\mathrm{108} \\ $$$$\mathrm{Please}\:\mathrm{am}\:\mathrm{not}\:\mathrm{getting}\:\mathrm{correct}\:\mathrm{answer}\:\mathrm{for} \\ $$$$\mathrm{this}\:\mathrm{question}\:\mathrm{using}\:\mathrm{a}\:\mathrm{method}\:\mathrm{proposed}\:. \\ $$

Question Number 92191 Answers: 0 Comments: 1

⌈ ((30))^(1/(3 )) ⌉ ⌊ ((30))^(1/(3 )) ⌋ ⌈ ((1256 ))^(1/(6 )) ⌉

$$\lceil\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{30}}\:\rceil\: \\ $$$$\lfloor\:\sqrt[{\mathrm{3}\:\:}]{\mathrm{30}}\:\rfloor\: \\ $$$$\lceil\:\sqrt[{\mathrm{6}\:\:}]{\mathrm{1256}\:}\:\rceil\: \\ $$

Question Number 92188 Answers: 0 Comments: 0

let a,b,c be three digits all different of zero Prove that ((ac)/(cb))=(a/b) ⇔ ∀ n≥1 ((accc...cc)/(ccc...ccb)) =(a/b) the number accc...cc has the digit c n times

$${let}\:{a},{b},{c}\:{be}\:{three}\:{digits}\:{all}\:{different}\:{of}\:{zero} \\ $$$${Prove}\:{that}\:\frac{{ac}}{{cb}}=\frac{{a}}{{b}}\:\Leftrightarrow\:\forall\:{n}\geqslant\mathrm{1}\:\:\:\:\frac{{accc}...{cc}}{{ccc}...{ccb}}\:=\frac{{a}}{{b}}\:\:\: \\ $$$${the}\:{number}\:{accc}...{cc}\:\:\:{has}\:{the}\:{digit}\:{c}\:\:{n}\:{times} \\ $$

Question Number 92187 Answers: 1 Comments: 1

4x = 6 (mod 10 )

$$\mathrm{4x}\:=\:\mathrm{6}\:\left(\mathrm{mod}\:\mathrm{10}\:\right) \\ $$

Question Number 92182 Answers: 0 Comments: 4

Question Number 92179 Answers: 0 Comments: 12

((x/(12)))^(log_(√3) x) =((x/(18)))^(log_(√2) x) find x

$$\left(\frac{\mathrm{x}}{\mathrm{12}}\right)^{\mathrm{log}_{\sqrt{\mathrm{3}}} \mathrm{x}} =\left(\frac{\mathrm{x}}{\mathrm{18}}\right)^{\mathrm{log}_{\sqrt{\mathrm{2}}} \mathrm{x}} \\ $$$$\mathrm{find}\:\mathrm{x} \\ $$

Question Number 92170 Answers: 0 Comments: 3

Question Number 92167 Answers: 1 Comments: 1

lim_(x→∞) x−x^2 ln (1+(1/x)) ?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\mathrm{x}−\mathrm{x}^{\mathrm{2}} \mathrm{ln}\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{x}}\right)\:? \\ $$

Question Number 92193 Answers: 0 Comments: 2

−2345 (mod 6) −5400 ( mod 11)

$$−\mathrm{2345}\:\left(\mathrm{mod}\:\mathrm{6}\right)\: \\ $$$$−\mathrm{5400}\:\left(\:\mathrm{mod}\:\mathrm{11}\right)\: \\ $$

Question Number 92156 Answers: 0 Comments: 1

find ∫_0 ^1 xe^(−x^2 ) ln(1+x)dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:{xe}^{−{x}^{\mathrm{2}} } {ln}\left(\mathrm{1}+{x}\right){dx} \\ $$

Question Number 92151 Answers: 0 Comments: 1

If p and q are positive integers such that the value pq + 2p+2q = 217 find p+q

$$\mathrm{If}\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{are}\:\mathrm{positive}\:\mathrm{integers}\: \\ $$$$\mathrm{such}\:\mathrm{that}\:\mathrm{the}\:\mathrm{value}\: \\ $$$$\mathrm{pq}\:+\:\mathrm{2p}+\mathrm{2q}\:=\:\mathrm{217}\: \\ $$$$\mathrm{find}\:\mathrm{p}+\mathrm{q}\: \\ $$

Question Number 92146 Answers: 1 Comments: 1

how do i find integers that satisfy x^2 −y^2 =2017

$${how}\:{do}\:{i}\:{find}\:{integers}\:{that}\:{satisfy} \\ $$$${x}^{\mathrm{2}} −{y}^{\mathrm{2}} =\mathrm{2017} \\ $$

Question Number 92143 Answers: 0 Comments: 1

fond∫((2x)/(1+x^2 ))dx

$${fond}\int\frac{\mathrm{2}{x}}{\mathrm{1}+{x}^{\mathrm{2}} }{dx} \\ $$

Question Number 92138 Answers: 2 Comments: 0

∫(dx/(1+x^2 ))

$$\int\frac{{dx}}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$

Question Number 92137 Answers: 0 Comments: 2

∫((2x)/(1+x))

$$\int\frac{\mathrm{2}{x}}{\mathrm{1}+{x}} \\ $$

Question Number 92135 Answers: 0 Comments: 5

a^x = log _a (x) a=?

$${a}^{{x}} \:=\:\mathrm{log}\:_{{a}} \:\left({x}\right) \\ $$$${a}=? \\ $$

Question Number 92134 Answers: 0 Comments: 1

find ∫_(−1) ^1 (e^x /(√(1−x^2 )))dx

$${find}\:\int_{−\mathrm{1}} ^{\mathrm{1}} \:\frac{{e}^{{x}} }{\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }}{dx}\: \\ $$

Question Number 92133 Answers: 0 Comments: 0

1) decompose F(x) =(1/(x^5 −1)) 2) calculate ∫_2 ^(+∞) (dx/(x^5 −1))

$$\left.\mathrm{1}\right)\:{decompose}\:{F}\left({x}\right)\:=\frac{\mathrm{1}}{{x}^{\mathrm{5}} −\mathrm{1}} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{2}} ^{+\infty} \:\frac{{dx}}{{x}^{\mathrm{5}} −\mathrm{1}} \\ $$

Question Number 92126 Answers: 0 Comments: 0

∫ (√((x^2 +2x−1)/(x+1))) dx

$$\int\:\sqrt{\frac{{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{1}}{{x}+\mathrm{1}}}\:{dx}\: \\ $$

Question Number 92120 Answers: 0 Comments: 0

∫_(−3) ^4 ⌊x.⌈x^2 ⌉⌋ dx

$$\int_{−\mathrm{3}} ^{\mathrm{4}} \lfloor{x}.\lceil{x}^{\mathrm{2}} \rceil\rfloor\:{dx} \\ $$

Question Number 92119 Answers: 0 Comments: 3

show that ∫_1 ^∞ (1/(⌊x⌋^2 ))dx=∫_0 ^1 ∫_0 ^1 ((dx dy)/(1−xy))

$${show}\:{that}\: \\ $$$$\int_{\mathrm{1}} ^{\infty} \frac{\mathrm{1}}{\lfloor{x}\rfloor^{\mathrm{2}} }{dx}=\int_{\mathrm{0}} ^{\mathrm{1}} \int_{\mathrm{0}} ^{\mathrm{1}} \frac{{dx}\:{dy}}{\mathrm{1}−{xy}} \\ $$

Question Number 92118 Answers: 1 Comments: 3

If 9^(2x+1 ) = ((81^(x−2) )/(3x)) . find x

$$\mathrm{If}\:\:\mathrm{9}^{\mathrm{2x}+\mathrm{1}\:\:\:} =\:\:\frac{\mathrm{81}^{\mathrm{x}−\mathrm{2}} }{\mathrm{3x}}\:\:.\:\:\:\:\:\:\:\:\:\:\:\mathrm{find}\:\mathrm{x} \\ $$

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