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Question Number 190625 Answers: 1 Comments: 0

solve in R : ⌊ (1/x) ⌋ + ⌊ x ⌋ = 2

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\mathrm{solve}\:\mathrm{in}\:\:\:\mathbb{R}\:\:\:: \\ $$$$\:\:\:\:\:\:\:\:\lfloor\:\frac{\mathrm{1}}{{x}}\:\rfloor\:\:+\:\lfloor\:{x}\:\rfloor\:=\:\mathrm{2}\:\:\:\:\: \\ $$$$ \\ $$

Question Number 190624 Answers: 2 Comments: 0

Question Number 190623 Answers: 2 Comments: 0

calculate : Σ_(n=1) ^∞ (( (−1)^( n−1) )/n) cos ((( nπ)/3) ) =?

$$ \\ $$$$\:\:\:\:\:\:\mathrm{calculate}\:: \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\:\left(−\mathrm{1}\right)^{\:{n}−\mathrm{1}} }{{n}}\:\mathrm{cos}\:\left(\frac{\:{n}\pi}{\mathrm{3}}\:\right)\:=? \\ $$$$ \\ $$

Question Number 190639 Answers: 1 Comments: 0

The points A, B and C have position vectors i−j , 5i−3j and 11i−6j respectively . Show that A, B and C are collinear.

$$\:{The}\:{points}\:{A},\:{B}\:{and}\:{C}\:{have}\:{position} \\ $$$$\:{vectors}\:{i}−{j}\:,\:\mathrm{5}{i}−\mathrm{3}{j}\:{and}\:\mathrm{11}{i}−\mathrm{6}{j}\: \\ $$$${respectively}\:.\:{Show}\:{that}\:{A},\:{B}\:{and}\:{C} \\ $$$${are}\:{collinear}. \\ $$

Question Number 190622 Answers: 1 Comments: 0

prove : ∫_(−∞) ^( ∞) ((( x)/( cosh(x))))^2 dx= Σ_(k=1) ^∞ (1/( k^2 ))

$$ \\ $$$$\:\:\:{prove}\:: \\ $$$$\:\:\int_{−\infty} ^{\:\infty} \:\:\:\left(\frac{\:{x}}{ {cosh}\left({x}\right)}\right)^{\mathrm{2}} \mathrm{d}{x}=\:\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\:{k}\:^{\mathrm{2}} }\:\: \: \\ $$$$ \\ $$

Question Number 190618 Answers: 1 Comments: 0

f(x−f(x))=x ,f(5)=−1 f(−1)=?

$$\mathrm{f}\left(\mathrm{x}−\mathrm{f}\left(\mathrm{x}\right)\right)=\mathrm{x}\:\:,\mathrm{f}\left(\mathrm{5}\right)=−\mathrm{1} \\ $$$$\mathrm{f}\left(−\mathrm{1}\right)=? \\ $$

Question Number 190615 Answers: 1 Comments: 1

Question Number 190611 Answers: 0 Comments: 2

Montrer que: 1•c^2 =a^2 +b^2 2• rayon r=(c/(1+(√2)))−((a+b)/(2+(√2)))

$$\mathrm{Montrer}\:\mathrm{que}: \\ $$$$\mathrm{1}\bullet\boldsymbol{\mathrm{c}}^{\mathrm{2}} =\boldsymbol{\mathrm{a}}^{\mathrm{2}} +\boldsymbol{\mathrm{b}}^{\mathrm{2}} \\ $$$$\mathrm{2}\bullet\:\mathrm{rayon}\:\:\:\:\:\boldsymbol{\mathrm{r}}=\frac{\boldsymbol{\mathrm{c}}}{\mathrm{1}+\sqrt{\mathrm{2}}}−\frac{\boldsymbol{\mathrm{a}}+\boldsymbol{\mathrm{b}}}{\mathrm{2}+\sqrt{\mathrm{2}}} \\ $$$$ \\ $$

Question Number 190607 Answers: 0 Comments: 0

Question Number 190602 Answers: 1 Comments: 0

let S={a,b,c,d,e,f} if we take any subset S (same subset is allowed), it also can be S, which will form S if we join them, order of operation does not matter ({a,b,c,d},{d,e,f}) is the same as ({d,e,f},{a,b,c,d}) how many ways can we choose?

$$ \\ $$$$\: \\ $$$$\:{let}\:{S}=\left\{{a},{b},{c},{d},{e},{f}\right\} \\ $$$$\:{if}\:{we}\:{take}\:{any}\:{subset}\:{S}\:\left({same}\:{subset}\:{is}\:{allowed}\right), \\ $$$$\:{it}\:{also}\:{can}\:{be}\:{S},\:{which}\:{will}\:{form}\:{S}\:{if}\:{we}\:{join}\:{them}, \\ $$$${order}\:{of}\:{operation}\:{does}\:{not}\:{matter} \\ $$$$\:\left(\left\{{a},{b},{c},{d}\right\},\left\{{d},{e},{f}\right\}\right)\:{is}\:{the}\:{same}\:{as} \\ $$$$\:\left(\left\{{d},{e},{f}\right\},\left\{{a},{b},{c},{d}\right\}\right) \\ $$$$\:{how}\:{many}\:{ways}\:{can}\:{we}\:{choose}? \\ $$$$\: \\ $$$$ \\ $$

Question Number 190644 Answers: 1 Comments: 0

Question Number 190583 Answers: 1 Comments: 0

Question Number 190580 Answers: 1 Comments: 0

Question Number 190579 Answers: 1 Comments: 0

Question Number 190578 Answers: 1 Comments: 0

Question Number 190573 Answers: 1 Comments: 3

a^ 2+2ab+b^ 2

$$\hat {{a}}\mathrm{2}+\mathrm{2}{ab}+\hat {{b}}\mathrm{2} \\ $$

Question Number 190568 Answers: 0 Comments: 1

Question Number 190569 Answers: 1 Comments: 0

The number of 4−digit numbers that contain the number 6 and are divisible by 3 is ___

$$\:\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{4}−\mathrm{digit}\: \\ $$$$\:\mathrm{numbers}\:\mathrm{that}\:\mathrm{contain}\:\mathrm{the} \\ $$$$\:\mathrm{number}\:\mathrm{6}\:\mathrm{and}\:\mathrm{are}\:\mathrm{divisible}\: \\ $$$$\:\mathrm{by}\:\mathrm{3}\:\mathrm{is}\:\_\_\_ \\ $$

Question Number 190565 Answers: 1 Comments: 0

Question Number 190564 Answers: 2 Comments: 0

Question Number 190563 Answers: 1 Comments: 0

Question Number 190557 Answers: 2 Comments: 0

Question Number 190552 Answers: 1 Comments: 1

∫_(1/2) ^2 ln(((ln(x+(1/x)))/(ln(x^2 −x+((17)/6)))))dx=?

$$\int_{\frac{\mathrm{1}}{\mathrm{2}}} ^{\mathrm{2}} {ln}\left(\frac{{ln}\left({x}+\frac{\mathrm{1}}{{x}}\right)}{{ln}\left({x}^{\mathrm{2}} −{x}+\frac{\mathrm{17}}{\mathrm{6}}\right)}\right){dx}=? \\ $$

Question Number 190546 Answers: 2 Comments: 0

Given x,y,z>0 and x^2 +y^2 +z^2 +x+2y+3z=23 find maximum of x+y+z.

$$\:\mathrm{Given}\:\mathrm{x},\mathrm{y},\mathrm{z}>\mathrm{0}\:\mathrm{and}\: \\ $$$$\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} +\mathrm{z}^{\mathrm{2}} +\mathrm{x}+\mathrm{2y}+\mathrm{3z}=\mathrm{23}\: \\ $$$$\:\mathrm{find}\:\mathrm{maximum}\:\mathrm{of}\:\mathrm{x}+\mathrm{y}+\mathrm{z}. \\ $$

Question Number 190544 Answers: 1 Comments: 1

Given p,q,r,s sre distinc prime numbers such that pq−rs divisible by 30. minimum value of p+q+r+s =?

$$\mathrm{Given}\:\mathrm{p},\mathrm{q},\mathrm{r},\mathrm{s}\:\mathrm{sre}\:\mathrm{distinc}\:\mathrm{prime}\:\mathrm{numbers} \\ $$$$\:\mathrm{such}\:\mathrm{that}\:\mathrm{pq}−\mathrm{rs}\:\mathrm{divisible}\:\mathrm{by}\:\mathrm{30}. \\ $$$$\:\mathrm{minimum}\:\mathrm{value}\:\mathrm{of}\:\mathrm{p}+\mathrm{q}+\mathrm{r}+\mathrm{s}\:=? \\ $$

Question Number 190542 Answers: 0 Comments: 0

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