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AllQuestion and Answers: Page 125

Question Number 206881 Answers: 3 Comments: 0

$$\:\:\cancel{\underline{\underbrace{\boldsymbol{{x}}}}} \\ $$

Question Number 206879 Answers: 0 Comments: 5

solve for positive integers (x/(y+z))+(y/(z+x))+(z/(x+y))=4

$${solve}\:{for}\:{positive}\:{integers} \\ $$$$\frac{{x}}{{y}+{z}}+\frac{{y}}{{z}+{x}}+\frac{{z}}{{x}+{y}}=\mathrm{4} \\ $$

Question Number 206958 Answers: 2 Comments: 0

If (1/3^(−x) ) = 5 find: 9^(x+1) = ?

$$\mathrm{If}\:\:\:\frac{\mathrm{1}}{\mathrm{3}^{−\boldsymbol{\mathrm{x}}} }\:=\:\mathrm{5}\:\:\:\mathrm{find}:\:\:\mathrm{9}^{\boldsymbol{\mathrm{x}}+\mathrm{1}} \:=\:? \\ $$

Question Number 206869 Answers: 0 Comments: 2

Question Number 206868 Answers: 1 Comments: 0

If A, B and A+B are non−singular square matrices, prove that A^(−1) +B^(−1) is also non−singular.

$$\mathrm{If}\:{A},\:{B}\:\mathrm{and}\:{A}+{B}\:\mathrm{are}\:\mathrm{non}−\mathrm{singular} \\ $$$$\mathrm{square}\:\mathrm{matrices},\:\mathrm{prove}\:\mathrm{that}\:{A}^{−\mathrm{1}} +{B}^{−\mathrm{1}} \\ $$$$\mathrm{is}\:\mathrm{also}\:\mathrm{non}−\mathrm{singular}. \\ $$

Question Number 206862 Answers: 0 Comments: 1

Question Number 206861 Answers: 0 Comments: 0

𝚺_(k=1) ^∞ (1/k^2 )𝚺_(n=0) ^∞ (1/2^(1+n) )(((𝚪(n+1)𝚪(k+1)H_(n+k+1) )/(𝚪(n+k+2))))=???

$$\underset{\boldsymbol{\mathrm{k}}=\mathrm{1}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\mathrm{1}}{\boldsymbol{\mathrm{k}}^{\mathrm{2}} }\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\boldsymbol{\sum}}}\frac{\mathrm{1}}{\mathrm{2}^{\mathrm{1}+\boldsymbol{\mathrm{n}}} }\left(\frac{\boldsymbol{\Gamma}\left(\boldsymbol{\mathrm{n}}+\mathrm{1}\right)\boldsymbol{\Gamma}\left(\boldsymbol{\mathrm{k}}+\mathrm{1}\right)\boldsymbol{\mathrm{H}}_{\boldsymbol{\mathrm{n}}+\boldsymbol{\mathrm{k}}+\mathrm{1}} }{\boldsymbol{\Gamma}\left(\boldsymbol{\mathrm{n}}+\boldsymbol{\mathrm{k}}+\mathrm{2}\right)}\right)=??? \\ $$

Question Number 206858 Answers: 2 Comments: 0

prove that H_n =∫_0 ^1 ((t^n −1)/(t−1))dt

$$\mathrm{prove}\:\mathrm{that} \\ $$$${H}_{{n}} =\underset{\mathrm{0}} {\overset{\mathrm{1}} {\int}}\:\frac{{t}^{{n}} −\mathrm{1}}{{t}−\mathrm{1}}{dt} \\ $$

Question Number 206848 Answers: 1 Comments: 1

Question Number 206845 Answers: 1 Comments: 3

Find: ((∞!)/∞^∞ ) = ?

$$\mathrm{Find}:\:\:\:\frac{\infty!}{\infty^{\infty} }\:=\:? \\ $$

Question Number 206839 Answers: 1 Comments: 0

Question Number 206838 Answers: 0 Comments: 0

Question Number 206837 Answers: 0 Comments: 0

Question Number 206833 Answers: 3 Comments: 0

Question Number 206830 Answers: 0 Comments: 0

c = (√((∫_a_0 ^a_1 (√(1+[f′(x)]^2 ))dx)^2 +(∫_b_0 ^b_1 (√(1+[f′(x)]^2 ))dx)^2 )) c = (√(L_1 ^2 +L_2 ^2 ))

$${c}\:=\:\sqrt{\left(\int_{{a}_{\mathrm{0}} } ^{{a}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} +\left(\int_{{b}_{\mathrm{0}} } ^{{b}_{\mathrm{1}} } \sqrt{\mathrm{1}+\left[{f}'\left({x}\right)\right]^{\mathrm{2}} }{dx}\right)^{\mathrm{2}} } \\ $$$${c}\:=\:\sqrt{{L}_{\mathrm{1}} ^{\mathrm{2}} +{L}_{\mathrm{2}} ^{\mathrm{2}} } \\ $$

Question Number 206829 Answers: 0 Comments: 1

∮(x/(x+2))dx^2 is wrong?

$$\:\:\:\:\:\oint\frac{{x}}{{x}+\mathrm{2}}{dx}^{\mathrm{2}} \:\:\:\:{is}\:{wrong}? \\ $$

Question Number 206827 Answers: 0 Comments: 1

log (x) = sin (x) x = ?

$$\mathrm{log}\:\left({x}\right)\:=\:\mathrm{sin}\:\left({x}\right) \\ $$$${x}\:=\:? \\ $$

Question Number 211180 Answers: 1 Comments: 0

Question Number 206808 Answers: 2 Comments: 0

lim_(x→0) ((10^x −1)/x^(10) )

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\mathrm{10}^{\mathrm{x}} −\mathrm{1}}{\mathrm{x}^{\mathrm{10}} } \\ $$

Question Number 206806 Answers: 0 Comments: 0

Given is a square with side length 15. We need to find exactly 17 smaller squares to fill the big one. How many solutions are possible? (Note: it′s not enough to find squares with the sum of their areas being 225, they must fit into the 15×15 square. Example with 3 squares: 2×2+5×5+14×14=225 but you cannot fit these in a 15×15 square)

$$\mathrm{Given}\:\mathrm{is}\:\mathrm{a}\:\mathrm{square}\:\mathrm{with}\:\mathrm{side}\:\mathrm{length}\:\mathrm{15}. \\ $$$$\mathrm{We}\:\mathrm{need}\:\mathrm{to}\:\mathrm{find}\:\mathrm{exactly}\:\mathrm{17}\:\mathrm{smaller}\:\mathrm{squares} \\ $$$$\mathrm{to}\:\mathrm{fill}\:\mathrm{the}\:\mathrm{big}\:\mathrm{one}.\:\mathrm{How}\:\mathrm{many}\:\mathrm{solutions}\:\mathrm{are} \\ $$$$\mathrm{possible}? \\ $$$$\left(\mathrm{Note}:\:\mathrm{it}'\mathrm{s}\:\mathrm{not}\:\mathrm{enough}\:\mathrm{to}\:\mathrm{find}\:\mathrm{squares}\:\mathrm{with}\right. \\ $$$$\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{their}\:\mathrm{areas}\:\mathrm{being}\:\mathrm{225},\:\mathrm{they}\:\mathrm{must} \\ $$$$\mathrm{fit}\:\mathrm{into}\:\mathrm{the}\:\mathrm{15}×\mathrm{15}\:\mathrm{square}.\:\mathrm{Example}\:\mathrm{with} \\ $$$$\mathrm{3}\:\mathrm{squares}:\:\mathrm{2}×\mathrm{2}+\mathrm{5}×\mathrm{5}+\mathrm{14}×\mathrm{14}=\mathrm{225}\:\mathrm{but} \\ $$$$\left.\mathrm{you}\:\mathrm{cannot}\:\mathrm{fit}\:\mathrm{these}\:\mathrm{in}\:\mathrm{a}\:\mathrm{15}×\mathrm{15}\:\mathrm{square}\right) \\ $$

Question Number 206805 Answers: 2 Comments: 0

Question Number 206804 Answers: 2 Comments: 0

Question Number 206795 Answers: 0 Comments: 3

Question Number 206794 Answers: 1 Comments: 0

help me... ∫_0 ^∞ ((sin(t)ln(t))/t)e^(−t) dt

$${help}\:{me}... \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\:\frac{\mathrm{sin}\left({t}\right)\mathrm{ln}\left({t}\right)}{{t}}{e}^{−{t}} \:{dt} \\ $$

Question Number 206787 Answers: 0 Comments: 1

Question Number 206789 Answers: 1 Comments: 0

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