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AllQuestion and Answers: Page 1224

Question Number 92255 Answers: 2 Comments: 0

7x = 3 (mod 18 )

$$\mathrm{7x}\:=\:\mathrm{3}\:\left(\mathrm{mod}\:\mathrm{18}\:\right)\: \\ $$

Question Number 92252 Answers: 1 Comments: 0

{ ((x(√y) +y(√x) = 6)),((x+y = 5 )) :} find x^3 + (1/y) =

$$\begin{cases}{\mathrm{x}\sqrt{\mathrm{y}}\:+\mathrm{y}\sqrt{\mathrm{x}}\:=\:\mathrm{6}}\\{\mathrm{x}+\mathrm{y}\:=\:\mathrm{5}\:}\end{cases} \\ $$$$\mathrm{find}\:\mathrm{x}^{\mathrm{3}} +\:\frac{\mathrm{1}}{\mathrm{y}}\:=\: \\ $$

Question Number 92248 Answers: 0 Comments: 4

Question Number 92247 Answers: 0 Comments: 1

How to convert the non−linear equations to linear form? y=(x/(c+mx)) y=ce^(mx)

$$\mathrm{How}\:\mathrm{to}\:\mathrm{convert}\:\mathrm{the}\:\mathrm{non}−\mathrm{linear}\:\mathrm{equation}{s} \\ $$$$\mathrm{to}\:\mathrm{linear}\:\mathrm{form}? \\ $$$$ \\ $$$${y}=\frac{{x}}{{c}+{mx}} \\ $$$$ \\ $$$${y}={ce}^{{mx}} \\ $$

Question Number 92242 Answers: 0 Comments: 2

((8^x +27^x )/(12^x +18^x )) = (7/6) x = ?

$$\frac{\mathrm{8}^{{x}} +\mathrm{27}^{{x}} }{\mathrm{12}^{{x}} +\mathrm{18}^{{x}} }\:=\:\frac{\mathrm{7}}{\mathrm{6}}\: \\ $$$${x}\:=\:? \\ $$

Question Number 92239 Answers: 0 Comments: 5

lim_(x→0) ((1−∣cos 7x∣)/(1−∣tan 5x∣)) =

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{1}−\mid\mathrm{cos}\:\mathrm{7x}\mid}{\mathrm{1}−\mid\mathrm{tan}\:\mathrm{5x}\mid}\:=\: \\ $$

Question Number 92235 Answers: 0 Comments: 0

let 0<p<1 and x>0 prove that x^2 ≤ (1−p)( ^((1−p)) (√x) ) +p (^p (√x))

$${let}\:\:\mathrm{0}<{p}<\mathrm{1}\:\:{and}\:\:{x}>\mathrm{0} \\ $$$${prove}\:{that}\:\:\:\:{x}^{\mathrm{2}} \leqslant\:\left(\mathrm{1}−{p}\right)\left(\:\:\:^{\left(\mathrm{1}−{p}\right)} \sqrt{{x}}\:\right)\:+{p}\:\left(\:^{{p}} \sqrt{{x}}\right) \\ $$$$ \\ $$$$ \\ $$

Question Number 92231 Answers: 0 Comments: 0

Question Number 92232 Answers: 0 Comments: 1

Question Number 92228 Answers: 0 Comments: 0

Are there infinite prime number p such as p!≡1[p+2]

$$\:{Are}\:{there}\:{infinite}\:{prime}\:{number}\:{p}\:{such}\:{as} \\ $$$$\:\:\:{p}!\equiv\mathrm{1}\left[{p}+\mathrm{2}\right]\: \\ $$

Question Number 92226 Answers: 0 Comments: 6

Question Number 92225 Answers: 1 Comments: 0

if tanh(x)=((72)/(161))(√5) prove that sinh(x)∈Q Q={rational numbdrs}

$${if}\:\:\:{tanh}\left({x}\right)=\frac{\mathrm{72}}{\mathrm{161}}\sqrt{\mathrm{5}} \\ $$$${prove}\:{that}\:{sinh}\left({x}\right)\in{Q}\: \\ $$$$ \\ $$$$ \\ $$$${Q}=\left\{{rational}\:{numbdrs}\right\} \\ $$$$ \\ $$

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

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

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