Question and Answers Forum

AllQuestion and Answers: Page 158

Question Number 206934 Answers: 0 Comments: 3

Question Number 206922 Answers: 1 Comments: 0

solve for x, y, z ∈R^+ x^2 +y^2 −2xy cos γ=c^2 y^2 +z^2 −2yz cos α=a^2 z^2 +x^2 −2zx cos β=b^2 with α+β+γ=360° example: a=12, b=8, c=10 α=120°, β=90°, γ=150°

$${solve}\:{for}\:{x},\:{y},\:{z}\:\in{R}^{+} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} −\mathrm{2}{xy}\:\mathrm{cos}\:\gamma={c}^{\mathrm{2}} \\ $$$${y}^{\mathrm{2}} +{z}^{\mathrm{2}} −\mathrm{2}{yz}\:\mathrm{cos}\:\alpha={a}^{\mathrm{2}} \\ $$$${z}^{\mathrm{2}} +{x}^{\mathrm{2}} −\mathrm{2}{zx}\:\mathrm{cos}\:\beta={b}^{\mathrm{2}} \\ $$$${with}\:\alpha+\beta+\gamma=\mathrm{360}° \\ $$$$ \\ $$$${example}:\: \\ $$$${a}=\mathrm{12},\:{b}=\mathrm{8},\:{c}=\mathrm{10} \\ $$$$\alpha=\mathrm{120}°,\:\beta=\mathrm{90}°,\:\gamma=\mathrm{150}° \\ $$

Question Number 206919 Answers: 2 Comments: 0

Question Number 206912 Answers: 3 Comments: 0

Question Number 206899 Answers: 3 Comments: 0

If tanθ = ((2x(x + 1))/(2x + 1)) then find sinθ and cosθ.

$$\mathrm{If}\:\mathrm{tan}\theta\:=\:\frac{\mathrm{2}{x}\left({x}\:+\:\mathrm{1}\right)}{\mathrm{2}{x}\:+\:\mathrm{1}}\:\mathrm{then}\:\mathrm{find}\:\mathrm{sin}\theta\:\mathrm{and} \\ $$$$\mathrm{cos}\theta. \\ $$

Question Number 206892 Answers: 1 Comments: 0

find ∫_0 ^1 (√(1+(√(1+x^2 ))))dx

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \sqrt{\mathrm{1}+\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 206890 Answers: 0 Comments: 1

can some one find the exact value of Σ_(n=0) ^∞ (1/((n!)^2 ))

$${can}\:{some}\:{one}\:{find}\:{the}\:{exact}\:{value}\:{of} \\ $$$$\sum_{{n}=\mathrm{0}} ^{\infty} \:\frac{\mathrm{1}}{\left({n}!\right)^{\mathrm{2}} } \\ $$

Question Number 206888 Answers: 0 Comments: 0

Question Number 206885 Answers: 4 Comments: 0

Question Number 206924 Answers: 2 Comments: 1

Question Number 206882 Answers: 1 Comments: 0

f(x)=tan^2 x (√(tan x((tan x((tan x((tan x(√(...))))^(1/5) ))^(1/4) ))^(1/3) )) f ′((π/4))=?

$$\:\:{f}\left({x}\right)=\mathrm{tan}\:^{\mathrm{2}} {x}\:\sqrt{\mathrm{tan}\:{x}\sqrt[{\mathrm{3}}]{\mathrm{tan}\:{x}\sqrt[{\mathrm{4}}]{\mathrm{tan}\:{x}\sqrt[{\mathrm{5}}]{\mathrm{tan}\:{x}\sqrt{...}}}}} \\ $$$$\:{f}\:'\left(\frac{\pi}{\mathrm{4}}\right)=? \\ $$

Question Number 206881 Answers: 3 Comments: 0

2+(1/(2!))+(1/(3!))+(1/(4!))+(1/(5!))+(1/(6!))+...

$$\: \mathrm{2}+\frac{\mathrm{1}}{\mathrm{2}!}+\frac{\mathrm{1}}{\mathrm{3}!}+\frac{\mathrm{1}}{\mathrm{4}!}+\frac{\mathrm{1}}{\mathrm{5}!}+\frac{\mathrm{1}}{\mathrm{6}!}+... \\ $$

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 ))

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

Pg 153 Pg 154 Pg 155 Pg 156 Pg 157 Pg 158 Pg 159 Pg 160 Pg 161 Pg 162

Contact: info@tinkutara.com