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Question Number 8050    Answers: 1   Comments: 0

The value of ((18^3 +7^3 +3 ∙ 18 ∙ 7 ∙ 25)/(3^6 +6∙243∙2+15∙181∙4+20∙27∙8+15∙9∙16+6∙3∙32+64)) is

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of} \\ $$$$\frac{\mathrm{18}^{\mathrm{3}} +\mathrm{7}^{\mathrm{3}} +\mathrm{3}\:\centerdot\:\mathrm{18}\:\centerdot\:\mathrm{7}\:\centerdot\:\mathrm{25}}{\mathrm{3}^{\mathrm{6}} +\mathrm{6}\centerdot\mathrm{243}\centerdot\mathrm{2}+\mathrm{15}\centerdot\mathrm{181}\centerdot\mathrm{4}+\mathrm{20}\centerdot\mathrm{27}\centerdot\mathrm{8}+\mathrm{15}\centerdot\mathrm{9}\centerdot\mathrm{16}+\mathrm{6}\centerdot\mathrm{3}\centerdot\mathrm{32}+\mathrm{64}} \\ $$$$\mathrm{is} \\ $$

Question Number 8035    Answers: 0   Comments: 2

prove >> a^n +b^n =c^n [n>2] it has no integer roots

$${prove}\:>>\:{a}^{{n}} +{b}^{{n}} ={c}^{{n}} \:\:\left[{n}>\mathrm{2}\right] \\ $$$${it}\:{has}\:{no}\:{integer}\:{roots} \\ $$$$ \\ $$

Question Number 8032    Answers: 1   Comments: 0

find the real root: 99x^3 +297x^2 +594x−7867=0

$${find}\:{the}\:{real}\:{root}: \\ $$$$\mathrm{99}{x}^{\mathrm{3}} +\mathrm{297}{x}^{\mathrm{2}} +\mathrm{594}{x}−\mathrm{7867}=\mathrm{0} \\ $$

Question Number 8031    Answers: 1   Comments: 0

(√2) ≈((19601)/(13860))

$$\:\:\:\:\:\:\:\:\:\:\:\:\:\sqrt{\mathrm{2}}\:\approx\frac{\mathrm{19601}}{\mathrm{13860}} \\ $$

Question Number 8043    Answers: 0   Comments: 4

solve (xz+y^2 )+(yz−zx^2 )q+2xy+z^2 =0

$${solve}\:\left({xz}+{y}^{\mathrm{2}} \right)+\left(\mathrm{yz}−\mathrm{zx}^{\mathrm{2}} \right)\mathrm{q}+\mathrm{2xy}+\mathrm{z}^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 8027    Answers: 1   Comments: 1

prove→ any prime number>2 can be written into( x^2 −y^(2 ) ) where (x,y)∈N

$${prove}\rightarrow\:{any}\:{prime}\:{number}>\mathrm{2}\: \\ $$$${can}\:{be}\:{written}\:{into}\left(\:{x}^{\mathrm{2}} −{y}^{\mathrm{2}\:} \right)\:{where} \\ $$$$\left({x},{y}\right)\in{N} \\ $$

Question Number 8026    Answers: 1   Comments: 0

Find the factor of (3^(200) +4)

$${Find}\:{the}\:{factor}\:{of}\:\left(\mathrm{3}^{\mathrm{200}} +\mathrm{4}\right) \\ $$

Question Number 8025    Answers: 1   Comments: 1

find factor of ≫ (2^(4n+2) +1) at the same way expand 2^(58) +1

$${find}\:{factor}\:{of}\:\gg \\ $$$$\:\:\:\:\:\:\:\:\:\left(\mathrm{2}^{\mathrm{4}{n}+\mathrm{2}} +\mathrm{1}\right) \\ $$$${at}\:{the}\:{same}\:{way}\:{expand}\:\mathrm{2}^{\mathrm{58}} +\mathrm{1} \\ $$$$ \\ $$

Question Number 8061    Answers: 1   Comments: 2

If 5 = a^x , then (5/a) =

$$\mathrm{If}\:\:\mathrm{5}\:=\:{a}^{{x}} \:,\:\mathrm{then}\:\frac{\mathrm{5}}{{a}}\:= \\ $$

Question Number 8022    Answers: 1   Comments: 1

prove that ∀x∈N (2x−1)^2 +(2x^2 −2x)^2 is a proper square number.

$$ \\ $$$${prove}\:{that}\:\forall{x}\in\boldsymbol{{N}}\: \\ $$$$\left(\mathrm{2}{x}−\mathrm{1}\right)^{\mathrm{2}} +\left(\mathrm{2}{x}^{\mathrm{2}} −\mathrm{2}{x}\right)^{\mathrm{2}} \:\:{is}\:{a}\:{proper} \\ $$$${square}\:{number}. \\ $$

Question Number 8016    Answers: 2   Comments: 2

if x≠0 then prove→ ((x^4 +x^(−4) +1)/(x^3 +x^(−3) ))=((x^2 +1)/x)−(x/(x^2 +1))

$$ \\ $$$$ \\ $$$$\:{if}\:{x}\neq\mathrm{0}\:{then} \\ $$$${prove}\rightarrow \\ $$$$\:\:\:\:\frac{{x}^{\mathrm{4}} +{x}^{−\mathrm{4}} +\mathrm{1}}{{x}^{\mathrm{3}} +{x}^{−\mathrm{3}} }=\frac{{x}^{\mathrm{2}} +\mathrm{1}}{{x}}−\frac{{x}}{{x}^{\mathrm{2}} +\mathrm{1}} \\ $$

Question Number 8015    Answers: 0   Comments: 0

∫((√(1 + x^2 ))/(1 + x)) dx

$$\int\frac{\sqrt{\mathrm{1}\:+\:{x}^{\mathrm{2}} }}{\mathrm{1}\:+\:{x}}\:{dx} \\ $$

Question Number 8013    Answers: 1   Comments: 4

Prove that, ∀m∈N, Σ_(r=1) ^m (((2m)),((2r−1)) ) (2r−1)^(2m−1) =Σ_(r=1) ^m (((2m)),((2r)) ) (2r)^(2m−1) .

$${Prove}\:{that},\:\forall{m}\in\mathbb{N}, \\ $$$$\underset{{r}=\mathrm{1}} {\overset{{m}} {\sum}}\begin{pmatrix}{\mathrm{2}{m}}\\{\mathrm{2}{r}−\mathrm{1}}\end{pmatrix}\:\left(\mathrm{2}{r}−\mathrm{1}\right)^{\mathrm{2}{m}−\mathrm{1}} =\underset{{r}=\mathrm{1}} {\overset{{m}} {\sum}}\begin{pmatrix}{\mathrm{2}{m}}\\{\mathrm{2}{r}}\end{pmatrix}\:\left(\mathrm{2}{r}\right)^{\mathrm{2}{m}−\mathrm{1}} . \\ $$

Question Number 8003    Answers: 1   Comments: 3

Σ_(m=1) ^∞ ((1/((Σ_(r=0) ^(m−1) (((2m)),((2r+1)) ) (−1)^(m−r) )^2 +(Σ_(r=0) ^m (((2m)),((2r)) ) (−1)^(m−r) )^2 )))=?

$$\underset{{m}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{1}}{\left(\underset{{r}=\mathrm{0}} {\overset{{m}−\mathrm{1}} {\sum}}\begin{pmatrix}{\mathrm{2}{m}}\\{\mathrm{2}{r}+\mathrm{1}}\end{pmatrix}\:\left(−\mathrm{1}\right)^{{m}−{r}} \right)^{\mathrm{2}} +\left(\underset{{r}=\mathrm{0}} {\overset{{m}} {\sum}}\begin{pmatrix}{\mathrm{2}{m}}\\{\mathrm{2}{r}}\end{pmatrix}\:\left(−\mathrm{1}\right)^{{m}−{r}} \right)^{\mathrm{2}} }\right)=? \\ $$

Question Number 7999    Answers: 1   Comments: 0

S=(1/n)+(1/(2n^2 ))+(1/(4n^4 ))+(1/(8n^8 ))+... S=(1/n)+Σ_(i=1) ^∞ (1/(2^i n^2^i )) Solvable?

$${S}=\frac{\mathrm{1}}{{n}}+\frac{\mathrm{1}}{\mathrm{2}{n}^{\mathrm{2}} }+\frac{\mathrm{1}}{\mathrm{4}{n}^{\mathrm{4}} }+\frac{\mathrm{1}}{\mathrm{8}{n}^{\mathrm{8}} }+... \\ $$$${S}=\frac{\mathrm{1}}{{n}}+\underset{{i}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}^{{i}} {n}^{\mathrm{2}^{{i}} } } \\ $$$$\mathrm{Solvable}? \\ $$

Question Number 7996    Answers: 1   Comments: 2

how to prove this (1/(cos^2 10^o ))+(1/(sin^2 20^o ))+(1/(cos^2 40))=12

$${how}\:{to}\:{prove}\:{this} \\ $$$$\frac{\mathrm{1}}{{cos}^{\mathrm{2}} \mathrm{10}^{{o}} }+\frac{\mathrm{1}}{{sin}^{\mathrm{2}} \mathrm{20}^{{o}} }+\frac{\mathrm{1}}{{cos}^{\mathrm{2}} \mathrm{40}}=\mathrm{12} \\ $$

Question Number 7988    Answers: 0   Comments: 16

Feedback request • Any symbols that needs to be added. We are aware of the following which will be added in next update: - vertical dots - contour integral - is congurant to Please let us know any symbols that you need to be added. Also let us know any other feedback or difficulties faced in using this app.

$$\boldsymbol{\mathrm{Feedback}}\:\boldsymbol{\mathrm{request}} \\ $$$$\bullet\:\mathrm{Any}\:\mathrm{symbols}\:\mathrm{that}\:\mathrm{needs}\:\mathrm{to}\:\mathrm{be} \\ $$$$\:\:\:\:\mathrm{added}.\:\mathrm{We}\:\mathrm{are}\:\mathrm{aware}\:\mathrm{of}\:\mathrm{the}\:\mathrm{following} \\ $$$$\:\:\:\:\mathrm{which}\:\mathrm{will}\:\mathrm{be}\:\mathrm{added}\:\mathrm{in}\:\mathrm{next}\:\mathrm{update}: \\ $$$$\:\:\:\:-\:\mathrm{vertical}\:\mathrm{dots}\: \\ $$$$\:\:\:\:-\:\mathrm{contour}\:\mathrm{integral} \\ $$$$\:\:\:\:-\:\mathrm{is}\:\mathrm{congurant}\:\mathrm{to} \\ $$$$\mathrm{Please}\:\mathrm{let}\:\mathrm{us}\:\mathrm{know}\:\mathrm{any}\:\mathrm{symbols} \\ $$$$\mathrm{that}\:\mathrm{you}\:\mathrm{need}\:\mathrm{to}\:\mathrm{be}\:\mathrm{added}. \\ $$$$ \\ $$$$\mathrm{Also}\:\mathrm{let}\:\mathrm{us}\:\mathrm{know}\:\mathrm{any}\:\mathrm{other}\:\mathrm{feedback} \\ $$$$\mathrm{or}\:\mathrm{difficulties}\:\mathrm{faced}\:\mathrm{in}\:\mathrm{using}\:\mathrm{this} \\ $$$$\mathrm{app}. \\ $$

Question Number 7962    Answers: 0   Comments: 0

prove that tanx<((4x)/π) for 0<x<(π/4)

$${prove}\:{that}\:\:\:{tanx}<\frac{\mathrm{4}{x}}{\pi}\:{for}\:\mathrm{0}<{x}<\frac{\pi}{\mathrm{4}} \\ $$

Question Number 7961    Answers: 1   Comments: 0

∫((5 − x)/(1 + (√(x − 4)))) dx

$$\int\frac{\mathrm{5}\:−\:{x}}{\mathrm{1}\:+\:\sqrt{{x}\:−\:\mathrm{4}}}\:{dx} \\ $$

Question Number 7960    Answers: 1   Comments: 2

∫((4 − x)/(4 + x)) dx

$$\int\frac{\mathrm{4}\:−\:{x}}{\mathrm{4}\:+\:{x}}\:{dx} \\ $$

Question Number 7969    Answers: 2   Comments: 0

During one year in a school, (5/8) of the students had measiles. (1/2) had chickenpox, and (1/8) had Neither. What fraction of the school had both measiles and chickenpox.

$${During}\:{one}\:{year}\:{in}\:{a}\:{school},\:\frac{\mathrm{5}}{\mathrm{8}}\:{of}\:{the}\:{students} \\ $$$${had}\:{measiles}.\:\frac{\mathrm{1}}{\mathrm{2}}\:{had}\:{chickenpox},\:{and}\:\frac{\mathrm{1}}{\mathrm{8}}\:{had} \\ $$$${Neither}.\:{What}\:{fraction}\:{of}\:{the}\:{school}\:{had}\:{both} \\ $$$${measiles}\:{and}\:{chickenpox}. \\ $$

Question Number 7959    Answers: 1   Comments: 2

∫((sin^(−1) (x))/(1 − x^2 )) dx

$$\int\frac{{sin}^{−\mathrm{1}} \left({x}\right)}{\mathrm{1}\:−\:{x}^{\mathrm{2}} }\:{dx} \\ $$

Question Number 7958    Answers: 1   Comments: 2

∫cos^4 x sin^3 x dx

$$\int{cos}^{\mathrm{4}} {x}\:{sin}^{\mathrm{3}} {x}\:\:{dx}\: \\ $$

Question Number 7945    Answers: 1   Comments: 4

Question Number 7939    Answers: 1   Comments: 3

f(x, y) = xy^3 + 5xy^2 + 2x + 1 find: f_x , f_y , f_(xx) , f_(yy) , f_(xy) , f_(yx)

$${f}\left({x},\:{y}\right)\:=\:{xy}^{\mathrm{3}} \:+\:\mathrm{5}{xy}^{\mathrm{2}} \:+\:\mathrm{2}{x}\:+\:\mathrm{1} \\ $$$${find}:\:\:{f}_{{x}} \:,\:{f}_{{y}} \:,\:{f}_{{xx}} \:,\:{f}_{{yy}} \:,\:{f}_{{xy}} \:,\:{f}_{{yx}} \\ $$

Question Number 7938    Answers: 0   Comments: 0

if f(x) = xlog(x + r) − r and r^2 = x^2 + y^2 prove that: f_(xx) + f_(yy) = (1/(x + r))

$${if}\:\:{f}\left({x}\right)\:=\:{xlog}\left({x}\:+\:{r}\right)\:−\:{r}\:\:{and}\:\:{r}^{\mathrm{2}} \:=\:{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} \\ $$$${prove}\:{that}:\:\:{f}_{{xx}} \:+\:{f}_{{yy}} \:\:=\:\:\frac{\mathrm{1}}{{x}\:+\:{r}} \\ $$

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