Question and Answers Forum

AllQuestion and Answers: Page 711

Question Number 147015 Answers: 0 Comments: 0

Question Number 147011 Answers: 2 Comments: 3

2x - (√(2x - 3)) - 9 = 0 if there′s a solution to equation, find 4a + 3 = ?

$$\mathrm{2}{x}\:-\:\sqrt{\mathrm{2}{x}\:-\:\mathrm{3}}\:-\:\mathrm{9}\:=\:\mathrm{0} \\ $$$${if}\:{there}'{s}\:\boldsymbol{{a}}\:{solution}\:{to}\:{equation}, \\ $$$${find}\:\:\mathrm{4}\boldsymbol{{a}}\:+\:\mathrm{3}\:=\:? \\ $$

Question Number 147010 Answers: 1 Comments: 1

if the radius of a circle touching parabola y^2 =4x at (4,4)and having directrix of y^2 =4x as its normal is r, then find [r]? (where [x] denote greatest integer lessthan or equal to x)

$${if}\:{the}\:{radius}\:{of}\:{a}\:{circle}\:{touching}\: \\ $$$${parabola}\:{y}^{\mathrm{2}} =\mathrm{4}{x}\:\:{at}\:\left(\mathrm{4},\mathrm{4}\right){and}\:{having} \\ $$$${directrix}\:{of}\:{y}^{\mathrm{2}} =\mathrm{4}{x}\:{as}\:{its}\:{normal}\: \\ $$$${is}\:{r},\:{then}\:{find}\:\left[{r}\right]? \\ $$$$\left({where}\:\left[{x}\right]\:{denote}\:{greatest}\:{integer}\:\right. \\ $$$$\left.{lessthan}\:{or}\:{equal}\:{to}\:{x}\right) \\ $$

Question Number 147009 Answers: 1 Comments: 0

a parabola y=x^2 −15x+36 cuts the x axis at P and Q. a circle is drawn through P and Q so that the origin is outside it. then find the length of tangent to the circle from (0,0)?

$${a}\:{parabola}\:{y}={x}^{\mathrm{2}} −\mathrm{15}{x}+\mathrm{36}\:{cuts}\:{the}\: \\ $$$${x}\:{axis}\:{at}\:{P}\:\:{and}\:{Q}.\:{a}\:{circle}\:{is}\:{drawn} \\ $$$${through}\:{P}\:{and}\:{Q}\:{so}\:{that}\:{the}\:{origin} \\ $$$${is}\:{outside}\:{it}.\:{then}\:{find}\:{the}\:{length}\: \\ $$$${of}\:{tangent}\:{to}\:{the}\:{circle}\:{from}\:\left(\mathrm{0},\mathrm{0}\right)? \\ $$

Question Number 147006 Answers: 1 Comments: 0

find I_n =∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)......(x^2 +n)))

$$\mathrm{find}\:\:\mathrm{I}_{\mathrm{n}} =\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{\mathrm{dx}}{\left(\mathrm{x}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{2}\right)......\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{n}\right)} \\ $$

Question Number 146996 Answers: 1 Comments: 0

∫ln(cht)dt

$$\int{ln}\left({cht}\right){dt} \\ $$

Question Number 146994 Answers: 3 Comments: 0

u_n =cos(√(n+1))−cos(√n) lim_(x→+∞) u_n =??

$${u}_{{n}} ={cos}\sqrt{{n}+\mathrm{1}}−{cos}\sqrt{{n}} \\ $$$$\underset{{x}\rightarrow+\infty} {\mathrm{lim}}{u}_{{n}} =?? \\ $$

Question Number 146989 Answers: 1 Comments: 2

Simplify: ((x^(1/2) + y^(1/2) )/(x^(1/6) + y^(1/6) )) - ((x^(1/2) - y^(1/2) )/(x^(1/6) - y^(1/6) )) = ?

$${Simplify}: \\ $$$$\frac{{x}^{\frac{\mathrm{1}}{\mathrm{2}}} \:+\:{y}^{\frac{\mathrm{1}}{\mathrm{2}}} }{{x}^{\frac{\mathrm{1}}{\mathrm{6}}} \:+\:{y}^{\frac{\mathrm{1}}{\mathrm{6}}} }\:\:-\:\:\frac{{x}^{\frac{\mathrm{1}}{\mathrm{2}}} \:-\:{y}^{\frac{\mathrm{1}}{\mathrm{2}}} }{{x}^{\frac{\mathrm{1}}{\mathrm{6}}} \:-\:{y}^{\frac{\mathrm{1}}{\mathrm{6}}} }\:=\:? \\ $$

Question Number 146988 Answers: 0 Comments: 3

if ((z^2 + 4)/(z - 2i)) = −5 + 10i find Re(Z) + Im(Z) = ?

$${if}\:\:\:\frac{\boldsymbol{{z}}^{\mathrm{2}} \:+\:\mathrm{4}}{\boldsymbol{{z}}\:-\:\mathrm{2}\boldsymbol{{i}}}\:=\:−\mathrm{5}\:+\:\mathrm{10}\boldsymbol{{i}} \\ $$$${find}\:\:\:{Re}\left({Z}\right)\:+\:{Im}\left({Z}\right)\:=\:? \\ $$

Question Number 146987 Answers: 1 Comments: 0

Question Number 146979 Answers: 1 Comments: 1

If there just were 0,±1,±2,±3,±4,±i in place of the decimal or binary equivalets..

$${If}\:{there}\:{just}\:{were} \\ $$$$\:\:\mathrm{0},\pm\mathrm{1},\pm\mathrm{2},\pm\mathrm{3},\pm\mathrm{4},\pm{i} \\ $$$${in}\:{place}\:{of}\:{the}\:{decimal}\:{or} \\ $$$${binary}\:{equivalets}.. \\ $$

Question Number 146977 Answers: 2 Comments: 0

find (1) ∫_C (e^z^2 /(z^2 +4z+3))dz ,C:∣z−2∣=5 (2)∫_(−∞) ^( ∞) ((cosx)/(x^2 +2x+2))dx

$${find} \\ $$$$\left(\mathrm{1}\right)\:\int_{{C}} \:\frac{{e}^{{z}^{\mathrm{2}} } }{{z}^{\mathrm{2}} +\mathrm{4}{z}+\mathrm{3}}{dz}\:\:,{C}:\mid{z}−\mathrm{2}\mid=\mathrm{5} \\ $$$$ \\ $$$$\left(\mathrm{2}\right)\int_{−\infty} ^{\:\infty} \frac{{cosx}}{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}}{dx} \\ $$

Question Number 146975 Answers: 1 Comments: 0

find laurant series f(z)=((z^2 −2z+3)/(z−2)) ,∣z−1∣>1

$${find}\:{laurant}\:{series}\:{f}\left({z}\right)=\frac{{z}^{\mathrm{2}} −\mathrm{2}{z}+\mathrm{3}}{{z}−\mathrm{2}}\:,\mid{z}−\mathrm{1}\mid>\mathrm{1} \\ $$

Question Number 146964 Answers: 1 Comments: 0

Simplify: (((√2) ∙ (√(2 + (√2))) ∙ (√(2 - (√2))))/( (√(2(√2))))) = ?

$${Simplify}: \\ $$$$\frac{\sqrt{\mathrm{2}}\:\centerdot\:\sqrt{\mathrm{2}\:+\:\sqrt{\mathrm{2}}}\:\centerdot\:\sqrt{\mathrm{2}\:-\:\sqrt{\mathrm{2}}}}{\:\sqrt{\mathrm{2}\sqrt{\mathrm{2}}}}\:=\:? \\ $$

Question Number 146962 Answers: 1 Comments: 0

Question Number 146961 Answers: 1 Comments: 0

(√(sin(x))) ∙ cos(x) < 0

$$\sqrt{{sin}\left({x}\right)}\:\centerdot\:{cos}\left({x}\right)\:<\:\mathrm{0} \\ $$

Question Number 146960 Answers: 2 Comments: 0

Question Number 146959 Answers: 1 Comments: 0

∫ln(1+(√(x^2 +2x+4)))dx

$$\int{ln}\left(\mathrm{1}+\sqrt{{x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{4}}\right){dx} \\ $$

Question Number 147764 Answers: 1 Comments: 0

Question Number 146943 Answers: 3 Comments: 0

b_(n+2) ∙ b_(n+3) ∙ b_(n+4) = 3^(3n+3) geometric series b_8 = ?

$${b}_{\boldsymbol{{n}}+\mathrm{2}} \:\centerdot\:{b}_{\boldsymbol{{n}}+\mathrm{3}} \:\centerdot\:{b}_{\boldsymbol{{n}}+\mathrm{4}} \:=\:\mathrm{3}^{\mathrm{3}\boldsymbol{{n}}+\mathrm{3}} \\ $$$${geometric}\:{series}\:\:\boldsymbol{{b}}_{\mathrm{8}} \:=\:? \\ $$

Question Number 146938 Answers: 0 Comments: 0

Question Number 146936 Answers: 3 Comments: 0

{ ((x^2 +2y^2 +xy=37)),((y^2 +2x^2 +2xy=26)) :} ⇒ x^2 +y^2 =?

$$\begin{cases}{{x}^{\mathrm{2}} +\mathrm{2}{y}^{\mathrm{2}} +{xy}=\mathrm{37}}\\{{y}^{\mathrm{2}} +\mathrm{2}{x}^{\mathrm{2}} +\mathrm{2}{xy}=\mathrm{26}}\end{cases}\:\Rightarrow\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} =? \\ $$

Question Number 146933 Answers: 0 Comments: 0

.....# advanced calculu#...... I := ∫_(−∞) ^( +∞) sin(cosh(x).cos(sinhx))dx=? ....solution .... I:=(1/2) ∫_(−∞) ^( +∞) {sin (cosh(x)+sinh(x))+sin(cosh(x)−sinh (x))} :=_(sinh(x)=((e^( x) −e^( −x) )/2)) ^(cosh(x)=((e^( x) +e^( −x) )/2)) (1/2) ∫_(−∞) ^( +∞) {sin(e^x )+sin (e^( −x) )}dx := (1/2) ∫_(−∞) ^( ∞) sin(e^( x) )dx +[(1/2)∫_(−∞) ^( +∞) sin(e^( x) )dx :: x=^(sub) −x] := ∫_(−∞) ^( +∞) sin(e^( x) ) dx =^(e^( x) =y) ∫_0 ^( ∞) ((sin(t))/t) dt ...... I:= (π/2) ..... ...m.n.1970...

$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:.....#\:{advanced}\:\:{calculu}#...... \\ $$$$\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{I}\::=\:\int_{−\infty} ^{\:+\infty} {sin}\left({cosh}\left({x}\right).{cos}\left({sinhx}\right)\right){dx}=? \\ $$$$\:\:\:\:\:....{solution}\:.... \\ $$$$\:\:\:\:\:\:\:\mathrm{I}:=\frac{\mathrm{1}}{\mathrm{2}}\:\int_{−\infty} ^{\:+\infty} \left\{{sin}\:\left({cosh}\left({x}\right)+{sinh}\left({x}\right)\right)+{sin}\left({cosh}\left({x}\right)−{sinh}\:\left({x}\right)\right)\right\} \\ $$$$\:\:\:\:\:\:\:\:\::\underset{{sinh}\left({x}\right)=\frac{{e}^{\:{x}} −{e}^{\:−{x}} }{\mathrm{2}}} {\overset{{cosh}\left({x}\right)=\frac{{e}^{\:{x}} +{e}^{\:−{x}} }{\mathrm{2}}} {=}}\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\int_{−\infty} ^{\:+\infty} \left\{{sin}\left({e}^{{x}} \right)+{sin}\:\left({e}^{\:−{x}} \right)\right\}{dx} \\ $$$$\:\:\:\:\:\:\:\:\::=\:\:\frac{\mathrm{1}}{\mathrm{2}}\:\int_{−\infty} ^{\:\infty} {sin}\left({e}^{\:{x}} \right){dx}\:+\left[\frac{\mathrm{1}}{\mathrm{2}}\int_{−\infty} ^{\:+\infty} {sin}\left({e}^{\:{x}} \right){dx}\:::\:\:{x}\overset{{sub}} {=}−{x}\right] \\ $$$$\:\:\:\:\:\:\:\::=\:\int_{−\infty} ^{\:+\infty} {sin}\left({e}^{\:{x}} \:\right)\:{dx}\:\overset{{e}^{\:{x}} ={y}} {=}\:\int_{\mathrm{0}} ^{\:\infty} \frac{{sin}\left({t}\right)}{{t}}\:{dt}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:......\:\mathrm{I}:=\:\frac{\pi}{\mathrm{2}}\:..... \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:...{m}.{n}.\mathrm{1970}... \\ $$$$\: \\ $$$$ \\ $$

Question Number 146929 Answers: 1 Comments: 5

Question Number 146927 Answers: 1 Comments: 0

Question Number 146926 Answers: 1 Comments: 0

Pg 706 Pg 707 Pg 708 Pg 709 Pg 710 Pg 711 Pg 712 Pg 713 Pg 714 Pg 715

Contact: info@tinkutara.com