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Question Number 96290 Answers: 0 Comments: 1

If : tan(x +iy) = a + bi then find a,b

$${If}\::\:\mathrm{tan}\left({x}\:+{iy}\right)\:=\:{a}\:+\:{bi}\: \\ $$$${then}\:{find}\:{a},{b} \\ $$

Question Number 96289 Answers: 0 Comments: 1

1010^x +2020^x =4040^x x=?

$$\mathrm{1010}^{{x}} +\mathrm{2020}^{{x}} =\mathrm{4040}^{{x}} \\ $$$${x}=? \\ $$

Question Number 96287 Answers: 1 Comments: 0

Consider the system in N^3 (S): { ((p^2 +q^2 =r^2 )),((q+p+r=24)),((r<p+q)) :} Show that the triplet (p:q:r) is solution to (S) if and only if r<12. p and q are solutions to the equation; n^2 −(24−r)n+24(12−r)=0 where n is an unknown.p

$$\mathcal{C}\mathrm{onsider}\:\mathrm{the}\:\mathrm{system}\:\mathrm{in}\:\mathbb{N}^{\mathrm{3}} \\ $$$$\left(\mathrm{S}\right):\:\begin{cases}{\mathrm{p}^{\mathrm{2}} +\mathrm{q}^{\mathrm{2}} =\mathrm{r}^{\mathrm{2}} }\\{\mathrm{q}+\mathrm{p}+\mathrm{r}=\mathrm{24}}\\{\mathrm{r}<\mathrm{p}+\mathrm{q}}\end{cases} \\ $$$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{triplet}\:\left(\mathrm{p}:\mathrm{q}:\mathrm{r}\right)\:\mathrm{is}\:\mathrm{solution}\:\mathrm{to}\:\left(\mathrm{S}\right)\:\mathrm{if} \\ $$$$\mathrm{and}\:\mathrm{only}\:\mathrm{if}\:\mathrm{r}<\mathrm{12}.\:\mathrm{p}\:\mathrm{and}\:\mathrm{q}\:\mathrm{are}\:\mathrm{solutions}\:\mathrm{to}\:\mathrm{the}\:\mathrm{equation}; \\ $$$$\mathrm{n}^{\mathrm{2}} −\left(\mathrm{24}−\mathrm{r}\right)\mathrm{n}+\mathrm{24}\left(\mathrm{12}−\mathrm{r}\right)=\mathrm{0}\:\mathrm{where}\:\mathrm{n}\:\mathrm{is}\:\mathrm{an}\:\mathrm{unknown}.\mathrm{p} \\ $$

Question Number 96282 Answers: 3 Comments: 0

Question Number 96280 Answers: 2 Comments: 1

Question Number 96279 Answers: 0 Comments: 0

Find P(x)=Π_2 (x)×Π_(2α) (x)

$$\mathcal{F}\mathfrak{ind}\:\mathcal{P}\left(\mathfrak{x}\right)=\prod_{\mathrm{2}} \left(\mathfrak{x}\right)×\prod_{\mathrm{2}\alpha} \left(\mathfrak{x}\right)\: \\ $$

Question Number 96276 Answers: 0 Comments: 5

Question Number 96260 Answers: 1 Comments: 0

tan ((π/9))+tan (((4π)/9))+tan (((7π)/9)) =?

$$\mathrm{tan}\:\left(\frac{\pi}{\mathrm{9}}\right)+\mathrm{tan}\:\left(\frac{\mathrm{4}\pi}{\mathrm{9}}\right)+\mathrm{tan}\:\left(\frac{\mathrm{7}\pi}{\mathrm{9}}\right)\:=? \\ $$

Question Number 96257 Answers: 1 Comments: 0

∫ x^3 (√(1−x^2 )) dx ?

$$\int\:{x}^{\mathrm{3}} \:\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\:{dx}\:?\: \\ $$

Question Number 96244 Answers: 1 Comments: 2

The line y = mx meets the parabola y = (x − a)(b − x) tangentially where 0 < a < b. Show that m = ((√b) − (√a))^2

$$ \\ $$$$\:\:\mathrm{The}\:\mathrm{line}\:{y}\:=\:{mx}\:\:\mathrm{meets}\:\mathrm{the}\:\mathrm{parabola} \\ $$$$\:\:{y}\:=\:\left({x}\:−\:{a}\right)\left({b}\:−\:{x}\right)\:\mathrm{tangentially}\:\mathrm{where} \\ $$$$\:\:\mathrm{0}\:<\:{a}\:<\:{b}.\:\mathrm{Show}\:\mathrm{that}\:{m}\:=\:\left(\sqrt{{b}}\:−\:\sqrt{{a}}\right)^{\mathrm{2}} \\ $$$$ \\ $$

Question Number 96242 Answers: 2 Comments: 0

find x if 4^x +6^x =9^x findx?

$$\mathrm{find}\:\mathrm{x}\:\mathrm{if}\:\mathrm{4}^{\mathrm{x}} +\mathrm{6}^{\mathrm{x}} =\mathrm{9}^{\mathrm{x}} \:\:\:\:\mathrm{findx}? \\ $$

Question Number 96241 Answers: 2 Comments: 0

find x^2 =2^× findx?

$$\mathrm{find}\:\mathrm{x}^{\mathrm{2}} =\mathrm{2}^{×} \:\:\:\mathrm{findx}? \\ $$

Question Number 96240 Answers: 3 Comments: 0

Find the shortest distance from the point P(2,−3,5) to the line L ((x+3)/2)=((y−1)/(−3))=((z−2)/4)

$${Find}\:{the}\:{shortest}\:{distance}\:{from}\:{the} \\ $$$${point}\:{P}\left(\mathrm{2},−\mathrm{3},\mathrm{5}\right)\:{to}\:{the}\:{line}\:{L} \\ $$$$\frac{{x}+\mathrm{3}}{\mathrm{2}}=\frac{{y}−\mathrm{1}}{−\mathrm{3}}=\frac{{z}−\mathrm{2}}{\mathrm{4}} \\ $$

Question Number 96232 Answers: 3 Comments: 1

lim_(x→∞) ((cos (√x)−cos x)/(1−cos (√x)))=

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{cos}\:\sqrt{{x}}−\mathrm{cos}\:{x}}{\mathrm{1}−\mathrm{cos}\:\sqrt{{x}}}= \\ $$

Question Number 96231 Answers: 0 Comments: 1

Question Number 96222 Answers: 1 Comments: 2

If for nonzero x ; 2f (x^2 )+3f ((1/x^2 )) = x^2 −1 then f (x^2 ) = ?

$$\mathrm{If}\:\mathrm{for}\:\mathrm{nonzero}\:{x}\:;\:\mathrm{2}{f}\:\left({x}^{\mathrm{2}} \right)+\mathrm{3}{f}\:\left(\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\right)\:=\:{x}^{\mathrm{2}} −\mathrm{1} \\ $$$${then}\:{f}\:\left({x}^{\mathrm{2}} \right)\:=\:? \\ $$

Question Number 96220 Answers: 0 Comments: 0

∫((tan(x))/x)dx ∫x tan(x) dx

$$\int\frac{{tan}\left({x}\right)}{{x}}{dx} \\ $$$$\int{x}\:{tan}\left({x}\right)\:{dx} \\ $$

Question Number 96217 Answers: 1 Comments: 0

(dy/dx) = (((y^2 −x^2 +y)/x))

$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\left(\frac{\mathrm{y}^{\mathrm{2}} −\mathrm{x}^{\mathrm{2}} +\mathrm{y}}{\mathrm{x}}\right)\: \\ $$

Question Number 96211 Answers: 3 Comments: 0

solve inside C (x−(1/x))^3 +(x−(1/x))^2 +(x−(1/x))+1 =0

$$\mathrm{solve}\:\mathrm{inside}\:\mathrm{C}\:\:\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{3}} \:+\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)^{\mathrm{2}} \:+\left(\mathrm{x}−\frac{\mathrm{1}}{\mathrm{x}}\right)+\mathrm{1}\:=\mathrm{0} \\ $$

Question Number 96497 Answers: 2 Comments: 0

Question Number 96200 Answers: 2 Comments: 0

solve y^(′′) +y^′ −2y =xcosx with y^((2)) (0)=1 and y^′ (0) =−2

$$\mathrm{solve}\:\:\mathrm{y}^{''} \:+\mathrm{y}^{'} \:−\mathrm{2y}\:=\mathrm{xcosx}\:\:\mathrm{with}\:\mathrm{y}^{\left(\mathrm{2}\right)} \left(\mathrm{0}\right)=\mathrm{1}\:\mathrm{and}\:\mathrm{y}^{'} \left(\mathrm{0}\right)\:=−\mathrm{2} \\ $$

Question Number 96198 Answers: 1 Comments: 0

calculate f(a) =∫_0 ^∞ ((cos(sh(2x)))/(x^2 +a^2 ))dx and g(a) =∫_0 ^∞ ((cos(sh(2x)))/((x^2 +a^2 )^2 )) (a>0)

$$\mathrm{calculate}\:\mathrm{f}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{cos}\left(\mathrm{sh}\left(\mathrm{2x}\right)\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{a}^{\mathrm{2}} }\mathrm{dx}\:\mathrm{and}\:\mathrm{g}\left(\mathrm{a}\right)\:=\int_{\mathrm{0}} ^{\infty} \:\frac{\mathrm{cos}\left(\mathrm{sh}\left(\mathrm{2x}\right)\right)}{\left(\mathrm{x}^{\mathrm{2}} \:+\mathrm{a}^{\mathrm{2}} \right)^{\mathrm{2}} }\:\:\:\left(\mathrm{a}>\mathrm{0}\right) \\ $$

Question Number 96197 Answers: 1 Comments: 0

calculate ∫_0 ^∞ ((ch(cosx−sinx))/(x^2 +4))dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{ch}\left(\mathrm{cosx}−\mathrm{sinx}\right)}{\mathrm{x}^{\mathrm{2}} \:+\mathrm{4}}\mathrm{dx} \\ $$

Question Number 96196 Answers: 1 Comments: 0

let g(x) =ln(sinx) developp g at fourier serie

$$\mathrm{let}\:\mathrm{g}\left(\mathrm{x}\right)\:=\mathrm{ln}\left(\mathrm{sinx}\right)\:\:\mathrm{developp}\:\mathrm{g}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

Question Number 96195 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (arctan((1/x)))^2 dx

$$\mathrm{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\left(\mathrm{arctan}\left(\frac{\mathrm{1}}{\mathrm{x}}\right)\right)^{\mathrm{2}} \:\mathrm{dx} \\ $$

Question Number 96194 Answers: 2 Comments: 0

let f(x) =ln(cosx) developp f at fourier serie

$$\mathrm{let}\:\mathrm{f}\left(\mathrm{x}\right)\:=\mathrm{ln}\left(\mathrm{cosx}\right)\:\mathrm{developp}\:\mathrm{f}\:\mathrm{at}\:\mathrm{fourier}\:\mathrm{serie} \\ $$

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