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Question Number 157546    Answers: 1   Comments: 5

( _1 ^(2002) ) + ( _4 ^(2002) ) + ( _7 ^(2002) ) + …+ ( _(2002) ^(2002) ) = ? Thank you so much .

$$\left(\underset{\mathrm{1}} {\overset{\mathrm{2002}} {\:}}\right)\:+\:\left(\underset{\mathrm{4}} {\overset{\mathrm{2002}} {\:}}\right)\:+\:\left(\underset{\mathrm{7}} {\overset{\mathrm{2002}} {\:}}\right)\:+\:\ldots+\:\left(\underset{\mathrm{2002}} {\overset{\mathrm{2002}} {\:}}\right)\:\:=\:? \\ $$$${Thank}\:\:{you}\:\:{so}\:\:{much}\:. \\ $$

Question Number 157538    Answers: 1   Comments: 1

Question Number 157531    Answers: 2   Comments: 0

Question Number 157515    Answers: 0   Comments: 0

∫ ((x sin x)/(16x+9)) dx

$$\:\:\:\:\:\int\:\frac{{x}\:\mathrm{sin}\:{x}}{\mathrm{16}{x}+\mathrm{9}}\:{dx}\: \\ $$

Question Number 157508    Answers: 0   Comments: 1

Question Number 157494    Answers: 1   Comments: 0

Question Number 157487    Answers: 2   Comments: 0

Find the equation of the tangents drawn from the point (1,3) to the parabola y^2 =−16x.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tangents}\:\mathrm{drawn} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{1},\mathrm{3}\right)\:\mathrm{to}\:\mathrm{the}\:\mathrm{parabola} \\ $$$${y}^{\mathrm{2}} =−\mathrm{16}{x}. \\ $$

Question Number 157489    Answers: 2   Comments: 0

Solve for real numbers: tan(10x) = tan^5 (2x)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{real}\:\mathrm{numbers}: \\ $$$$\mathrm{tan}\left(\mathrm{10x}\right)\:=\:\mathrm{tan}^{\mathrm{5}} \left(\mathrm{2x}\right) \\ $$$$ \\ $$

Question Number 157478    Answers: 0   Comments: 12

Sir Tinku-Tara, I′ve been facing some difficulties eversince I changed my device 1• I can′t save my work as images to my new device. In case I have to upload my work to another plateform such as a whatsapp group, I′ll just have to send it directly from app. Whereas with my previous device I could save it as an image then send it from gallery while on another plateforme. 2• It′s impossible for me to send images after inserting page breaks. It has always been the case even with my previous device. The only difference being that, there, after launching the send process the images automatically get saved to my gallery. So I could send them from there.

$$\mathrm{Sir}\:\mathrm{Tinku}-\mathrm{Tara}, \\ $$$$\mathrm{I}'\mathrm{ve}\:\mathrm{been}\:\mathrm{facing}\:\mathrm{some}\:\mathrm{difficulties}\:\mathrm{eversince}\:\mathrm{I}\:\mathrm{changed}\:\mathrm{my}\:\mathrm{device} \\ $$$$\mathrm{1}\bullet\:\mathrm{I}\:\mathrm{can}'\mathrm{t}\:\mathrm{save}\:\mathrm{my}\:\mathrm{work}\:\mathrm{as}\:\mathrm{images}\:\mathrm{to}\:\mathrm{my}\:\mathrm{new}\:\mathrm{device}. \\ $$$$\:\:\:\:\:\mathrm{In}\:\mathrm{case}\:\mathrm{I}\:\mathrm{have}\:\mathrm{to}\:\mathrm{upload}\:\mathrm{my}\:\mathrm{work}\:\mathrm{to}\:\mathrm{another}\:\mathrm{plateform}\:\mathrm{such}\:\mathrm{as}\:\mathrm{a}\: \\ $$$$\:\:\:\:\:\mathrm{whatsapp}\:\mathrm{group},\:\mathrm{I}'\mathrm{ll}\:\mathrm{just}\:\mathrm{have}\:\mathrm{to}\:\mathrm{send}\:\mathrm{it}\:\mathrm{directly}\:\mathrm{from}\:\mathrm{app}.\:\mathrm{Whereas} \\ $$$$\:\:\:\:\:\mathrm{with}\:\mathrm{my}\:\mathrm{previous}\:\mathrm{device}\:\mathrm{I}\:\mathrm{could}\:\mathrm{save}\:\mathrm{it}\:\mathrm{as}\:\mathrm{an}\:\mathrm{image}\:\mathrm{then}\:\mathrm{send}\:\mathrm{it}\:\mathrm{from} \\ $$$$\:\:\:\:\:\mathrm{gallery}\:\mathrm{while}\:\mathrm{on}\:\mathrm{another}\:\mathrm{plateforme}. \\ $$$$\mathrm{2}\bullet\:\mathrm{It}'\mathrm{s}\:\mathrm{impossible}\:\mathrm{for}\:\mathrm{me}\:\mathrm{to}\:\mathrm{send}\:\mathrm{images}\:\mathrm{after}\:\mathrm{inserting}\:\mathrm{page}\:\mathrm{breaks}.\:\mathrm{It}\:\mathrm{has} \\ $$$$\:\:\:\:\:\:\mathrm{always}\:\mathrm{been}\:\mathrm{the}\:\mathrm{case}\:\mathrm{even}\:\mathrm{with}\:\mathrm{my}\:\mathrm{previous}\:\mathrm{device}.\:\mathrm{The}\:\mathrm{only}\:\mathrm{difference} \\ $$$$\:\:\:\:\:\mathrm{being}\:\mathrm{that},\:\mathrm{there},\:\mathrm{after}\:\mathrm{launching}\:\mathrm{the}\:\mathrm{send}\:\mathrm{process}\:\mathrm{the}\:\mathrm{images}\: \\ $$$$\:\:\:\:\:\:\mathrm{automatically}\:\mathrm{get}\:\mathrm{saved}\:\mathrm{to}\:\mathrm{my}\:\mathrm{gallery}.\:\mathrm{So}\:\mathrm{I}\:\mathrm{could}\:\mathrm{send}\:\mathrm{them}\:\mathrm{from}\:\mathrm{there}. \\ $$

Question Number 157469    Answers: 1   Comments: 0

calculate : Ω:= ∫_(0 ) ^( 1) (( ln(1+x).ln(1−x))/(1+x)) dx =?

$$ \\ $$$$\:\:\:\:{calculate}\:: \\ $$$$\:\Omega:=\:\int_{\mathrm{0}\:} ^{\:\mathrm{1}} \frac{\:{ln}\left(\mathrm{1}+{x}\right).{ln}\left(\mathrm{1}−{x}\right)}{\mathrm{1}+{x}}\:{dx}\:=? \\ $$$$\:\:\:\: \\ $$

Question Number 157457    Answers: 3   Comments: 0

xy^′ + y = y^2 ln x

$$\mathrm{xy}^{'} \:+\:\mathrm{y}\:=\:\mathrm{y}^{\mathrm{2}} \:\mathrm{ln}\:\mathrm{x} \\ $$$$ \\ $$

Question Number 157456    Answers: 4   Comments: 0

∫ 5^(3−2x) dx =?

$$\:\int\:\mathrm{5}^{\mathrm{3}−\mathrm{2}{x}} \:{dx}\:=? \\ $$

Question Number 157455    Answers: 1   Comments: 0

Question Number 157454    Answers: 2   Comments: 0

Given 1+(3/y)+(5/y^2 )+(7/y^3 )+(9/y^4 )+...= 71 then 1+(4/y)+(9/y^2 )+((16)/y^3 )+((25)/y^4 )+... =?

$$\:{Given}\:\mathrm{1}+\frac{\mathrm{3}}{{y}}+\frac{\mathrm{5}}{{y}^{\mathrm{2}} }+\frac{\mathrm{7}}{{y}^{\mathrm{3}} }+\frac{\mathrm{9}}{{y}^{\mathrm{4}} }+...=\:\mathrm{71} \\ $$$$\:{then}\:\mathrm{1}+\frac{\mathrm{4}}{{y}}+\frac{\mathrm{9}}{{y}^{\mathrm{2}} }+\frac{\mathrm{16}}{{y}^{\mathrm{3}} }+\frac{\mathrm{25}}{{y}^{\mathrm{4}} }+...\:=? \\ $$

Question Number 157453    Answers: 1   Comments: 0

Question Number 157452    Answers: 0   Comments: 1

solve tan x=cos 3x

$$\:{solve}\:\mathrm{tan}\:{x}=\mathrm{cos}\:\mathrm{3}{x}\: \\ $$

Question Number 157442    Answers: 2   Comments: 0

∫ (dx/(x−(√(x^2 +2x+2))))

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

Question Number 157441    Answers: 2   Comments: 0

(7 ((6x−10))^(1/5) )^2 = ((49)/( ((1/x^2 ))^(1/5) ))

$$\:\left(\mathrm{7}\:\sqrt[{\mathrm{5}}]{\mathrm{6x}−\mathrm{10}}\right)^{\mathrm{2}} \:=\:\frac{\mathrm{49}}{\:\sqrt[{\mathrm{5}}]{\frac{\mathrm{1}}{\mathrm{x}^{\mathrm{2}} }}}\: \\ $$

Question Number 157425    Answers: 1   Comments: 0

Question Number 157420    Answers: 2   Comments: 0

∫(1/(u^4 +(1−u)^4 ))du

$$\int\frac{\mathrm{1}}{\boldsymbol{{u}}^{\mathrm{4}} +\left(\mathrm{1}−\boldsymbol{{u}}\right)^{\mathrm{4}} }\boldsymbol{{du}} \\ $$

Question Number 157418    Answers: 0   Comments: 0

Question Number 157417    Answers: 1   Comments: 0

if a;b>0 then prove that: (((a + b)^6 (a^(15) + b^(15) ) (a^(21) + b^(21) ))/((a^3 + b^3 )^2 (a^5 + b^5 )^3 (a^7 + b^7 )^3 )) ≥ 1

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b}>\mathrm{0}\:\:\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\frac{\left(\mathrm{a}\:+\:\mathrm{b}\right)^{\mathrm{6}} \:\left(\mathrm{a}^{\mathrm{15}} \:+\:\mathrm{b}^{\mathrm{15}} \right)\:\left(\mathrm{a}^{\mathrm{21}} \:+\:\mathrm{b}^{\mathrm{21}} \right)}{\left(\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{b}^{\mathrm{3}} \right)^{\mathrm{2}} \:\left(\mathrm{a}^{\mathrm{5}} \:+\:\mathrm{b}^{\mathrm{5}} \right)^{\mathrm{3}} \:\left(\mathrm{a}^{\mathrm{7}} \:+\:\mathrm{b}^{\mathrm{7}} \right)^{\mathrm{3}} }\:\geqslant\:\mathrm{1} \\ $$$$ \\ $$

Question Number 157416    Answers: 3   Comments: 3

If 2x^2 +11x+5 is a factor of ax^3 −17x^2 +bx−15 , then what is a and b ?

$$\:{If}\:\mathrm{2}{x}^{\mathrm{2}} +\mathrm{11}{x}+\mathrm{5}\:{is}\:{a}\:{factor}\:{of} \\ $$$$\:{ax}^{\mathrm{3}} −\mathrm{17}{x}^{\mathrm{2}} +{bx}−\mathrm{15}\:,\:{then}\:{what} \\ $$$${is}\:{a}\:{and}\:{b}\:? \\ $$

Question Number 157412    Answers: 2   Comments: 0

∫_( 0) ^( (π/2)) (x/(sin^8 x+cos^8 x)) dx ?

$$\:\int_{\:\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \:\frac{{x}}{\mathrm{sin}\:^{\mathrm{8}} {x}+\mathrm{cos}\:^{\mathrm{8}} {x}}\:{dx}\:? \\ $$

Question Number 157392    Answers: 1   Comments: 2

Question Number 157389    Answers: 0   Comments: 0

lim_(x→∞) (((6e^x^2 −20ln ∣x∣)/(6e^x^2 −20ln ∣x∣+3)))^(3e^(2x^2 ) sin (((6k)/e^x^2 ))) =26 k=?

$$\:\underset{{x}\rightarrow\infty} {\mathrm{lim}}\left(\frac{\mathrm{6}{e}^{{x}^{\mathrm{2}} } −\mathrm{20ln}\:\mid{x}\mid}{\mathrm{6}{e}^{{x}^{\mathrm{2}} } −\mathrm{20ln}\:\mid{x}\mid+\mathrm{3}}\right)^{\mathrm{3}{e}^{\mathrm{2}{x}^{\mathrm{2}} } \:\mathrm{sin}\:\left(\frac{\mathrm{6}{k}}{{e}^{{x}^{\mathrm{2}} } }\right)} =\mathrm{26} \\ $$$$\:{k}=? \\ $$$$ \\ $$

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