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Question Number 114511 Answers: 2 Comments: 3

Find numbers which are common terms of the two following arithmetic progression: 3,7,11,...,407 and 2,9,16,...,709

$$\mathrm{Find}\:\mathrm{numbers}\:\mathrm{which}\:\mathrm{are}\:\mathrm{common} \\ $$$$\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{following}\:\mathrm{arithmetic} \\ $$$$\mathrm{progression}: \\ $$$$\mathrm{3},\mathrm{7},\mathrm{11},...,\mathrm{407}\:\mathrm{and}\:\mathrm{2},\mathrm{9},\mathrm{16},...,\mathrm{709} \\ $$

Question Number 114485 Answers: 3 Comments: 0

Question Number 114482 Answers: 1 Comments: 0

Question Number 114480 Answers: 3 Comments: 1

Question Number 114475 Answers: 0 Comments: 5

Question Number 114472 Answers: 0 Comments: 2

... calculus... evaluate :: I=∫_0 ^( (π/2)) ((tan(2x))/( (√(sin^4 (x)+4cos^2 (x)))−(√(cos^4 (x)+4sin^2 (x) )))) dx= ??? ...m.n.july.1970....

$$\:\:\:\:\:\:\:\:\:...\:\:{calculus}... \\ $$$${evaluate}\::: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}=\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{tan}\left(\mathrm{2}{x}\right)}{\:\sqrt{{sin}^{\mathrm{4}} \left({x}\right)+\mathrm{4}{cos}^{\mathrm{2}} \left({x}\right)}−\sqrt{{cos}^{\mathrm{4}} \left({x}\right)+\mathrm{4}{sin}^{\mathrm{2}} \left({x}\right)\:}}\:{dx}=\:??? \\ $$$$\:\:\: \\ $$$$\:\:\:\:\:\:...{m}.{n}.{july}.\mathrm{1970}.... \\ $$$$ \\ $$

Question Number 114467 Answers: 1 Comments: 0

∫x sin^n (x) dx

$$\int{x}\:{sin}^{{n}} \left({x}\right)\:{dx} \\ $$

Question Number 114461 Answers: 1 Comments: 1

Question Number 114447 Answers: 4 Comments: 1

Question Number 114433 Answers: 1 Comments: 0

find sum of the series 1^2 −3^2 +5^2 −7^2 +9^2 −11^2 +...+(4n−3)^2 −(4n−1)^2

$${find}\:{sum}\:{of}\:{the}\:{series}\: \\ $$$$\mathrm{1}^{\mathrm{2}} −\mathrm{3}^{\mathrm{2}} +\mathrm{5}^{\mathrm{2}} −\mathrm{7}^{\mathrm{2}} +\mathrm{9}^{\mathrm{2}} −\mathrm{11}^{\mathrm{2}} +...+\left(\mathrm{4}{n}−\mathrm{3}\right)^{\mathrm{2}} −\left(\mathrm{4}{n}−\mathrm{1}\right)^{\mathrm{2}} \\ $$

Question Number 114422 Answers: 3 Comments: 3

The solution set of ∣((x+1)/x)∣+∣x+1∣=(((x+1)^2 )/(∣x∣)) is

$$\mathrm{The}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\: \\ $$$$\:\mid\frac{{x}+\mathrm{1}}{{x}}\mid+\mid{x}+\mathrm{1}\mid=\frac{\left({x}+\mathrm{1}\right)^{\mathrm{2}} }{\mid{x}\mid}\:\:\mathrm{is} \\ $$

Question Number 114420 Answers: 2 Comments: 4

Solution of ∣ x−1 ∣≥∣ x−3 ∣ is

$$\mathrm{Solution}\:\mathrm{of}\:\:\mid\:{x}−\mathrm{1}\:\mid\geqslant\mid\:{x}−\mathrm{3}\:\mid\:\mathrm{is} \\ $$

Question Number 114411 Answers: 2 Comments: 0

lim_(x→0) (((1+x)^(−(3/4)) −(1+x)^(−(1/4)) )/(2x)) =?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\left(\mathrm{1}+{x}\right)^{−\frac{\mathrm{3}}{\mathrm{4}}} −\left(\mathrm{1}+{x}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} }{\mathrm{2}{x}}\:=? \\ $$

Question Number 114409 Answers: 1 Comments: 0

find solution set of equation sin x = 2 , x ∈ C .

$${find}\:{solution}\:{set}\:{of}\:{equation} \\ $$$$\:\mathrm{sin}\:{x}\:=\:\mathrm{2}\:,\:{x}\:\in\:\mathbb{C}\:. \\ $$

Question Number 114405 Answers: 2 Comments: 0

lim_(x→0) ((x tan x)/( (√3) cos x−sin^2 x−(√3))) ?

$$\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{{x}\:\mathrm{tan}\:{x}}{\:\sqrt{\mathrm{3}}\:\mathrm{cos}\:{x}−\mathrm{sin}\:^{\mathrm{2}} {x}−\sqrt{\mathrm{3}}}\:? \\ $$

Question Number 114403 Answers: 1 Comments: 1

∫ ((ln (1+x^4 ))/x) dx

$$\:\:\:\:\:\:\:\:\:\int\:\frac{\mathrm{ln}\:\left(\mathrm{1}+{x}^{\mathrm{4}} \right)}{{x}}\:{dx} \\ $$$$ \\ $$

Question Number 114401 Answers: 1 Comments: 0

What is reminder when 4^(29) divided by 17

$${What}\:{is}\:{reminder}\:{when}\:\mathrm{4}^{\mathrm{29}} \\ $$$${divided}\:{by}\:\mathrm{17} \\ $$

Question Number 114395 Answers: 1 Comments: 0

find ∫_0 ^∞ (((1+x)^(−(3/4)) −(1+x)^(−(1/4)) )/x)dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\infty} \:\frac{\left(\mathrm{1}+\mathrm{x}\right)^{−\frac{\mathrm{3}}{\mathrm{4}}} −\left(\mathrm{1}+\mathrm{x}\right)^{−\frac{\mathrm{1}}{\mathrm{4}}} }{\mathrm{x}}\mathrm{dx} \\ $$

Question Number 114388 Answers: 0 Comments: 2

Developed the formula for the cubic equation when it has three real roots and Cardano is just not suitable as discriminant gets negative.. Given x^3 −bx−c=0 with b>0 , c>0 (t/b)=1+((15)/2)((c^2 /b^3 ))+(√(((c^2 /b^3 ))[49−((75)/4)((c^2 /b^3 ))])) x=(√(t+((4c^2 )/b^2 ))) −((3c)/b) ★ mrW Sir, MjS Sir please check!

$${Developed}\:{the}\:{formula}\:{for}\:{the}\:{cubic} \\ $$$${equation}\:{when}\:{it}\:{has}\:{three}\:{real}\:{roots} \\ $$$${and}\:{Cardano}\:{is}\:{just}\:{not}\:{suitable}\:{as} \\ $$$${discriminant}\:{gets}\:{negative}.. \\ $$$$\:\:\:{Given}\:\:\:\:\boldsymbol{{x}}^{\mathrm{3}} −\boldsymbol{{bx}}−\boldsymbol{{c}}=\mathrm{0} \\ $$$$\:\:{with}\:\:\boldsymbol{{b}}>\mathrm{0}\:,\:\boldsymbol{{c}}>\mathrm{0} \\ $$$$\:\frac{\boldsymbol{{t}}}{\boldsymbol{{b}}}=\mathrm{1}+\frac{\mathrm{15}}{\mathrm{2}}\left(\frac{\boldsymbol{{c}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{3}} }\right)+\sqrt{\left(\frac{\boldsymbol{{c}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{3}} }\right)\left[\mathrm{49}−\frac{\mathrm{75}}{\mathrm{4}}\left(\frac{\boldsymbol{{c}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{3}} }\right)\right]} \\ $$$$\:\:\:\:\:\boldsymbol{{x}}=\sqrt{\boldsymbol{{t}}+\frac{\mathrm{4}\boldsymbol{{c}}^{\mathrm{2}} }{\boldsymbol{{b}}^{\mathrm{2}} }}\:−\frac{\mathrm{3}\boldsymbol{{c}}}{\boldsymbol{{b}}}\:\:\bigstar \\ $$$${mrW}\:{Sir},\:{MjS}\:{Sir}\:\:{please}\:{check}! \\ $$

Question Number 114443 Answers: 1 Comments: 1

Question Number 114379 Answers: 1 Comments: 1

Question Number 114375 Answers: 1 Comments: 3

Question Number 114374 Answers: 1 Comments: 0

if the sum of three consecutive num ber in a geometric progression(G.P) is 19 and their multiple is 216.find the number

$${if}\:{the}\:{sum}\:{of}\:{three}\:{consecutive}\:{num} \\ $$$${ber}\:{in}\:{a}\:{geometric}\:{progression}\left({G}.{P}\right) \\ $$$${is}\:\mathrm{19}\:{and}\:{their}\:{multiple}\:{is}\:\mathrm{216}.{find} \\ $$$${the}\:{number} \\ $$

Question Number 114353 Answers: 1 Comments: 1

Question Number 114347 Answers: 1 Comments: 0

if (x^2 −(h+1)x+6i−6=0) then find the value of h if you know that one of the roots of the equation is three times the square of the other root (h∈ complex number)

$$\:{if}\:\left({x}^{\mathrm{2}} −\left({h}+\mathrm{1}\right){x}+\mathrm{6}{i}−\mathrm{6}=\mathrm{0}\right)\:{then}\:{find}\:{the}\:{value}\:{of}\:{h} \\ $$$${if}\:{you}\:{know}\:{that}\:{one}\:{of}\:{the}\:{roots}\:{of}\:{the}\:{equation}\:{is}\:{three}\: \\ $$$${times}\:{the}\:{square}\:{of}\:{the}\:{other}\:{root}\: \\ $$$$\left({h}\in\:{complex}\:{number}\right) \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 114343 Answers: 0 Comments: 4

How many ways can we place 5 identical books and another 6 identical books on a shelf?

$$\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{we}\:\mathrm{place}\:\mathrm{5}\:\mathrm{identical} \\ $$$$\mathrm{books}\:\mathrm{and}\:\mathrm{another}\:\mathrm{6}\:\mathrm{identical}\:\mathrm{books} \\ $$$$\mathrm{on}\:\mathrm{a}\:\mathrm{shelf}? \\ $$

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