Question and Answers Forum

All Questions   Topic List

AllQuestion and Answers: Page 1039

Question Number 103736    Answers: 0   Comments: 0

Solve: a^2 + c^2 = 196 ... (i) b^2 + (c − a)^2 = 169 ... (ii) c^2 + (b − c)^2 = 225 ... (iii)

$$\mathrm{Solve}:\:\:\:\:\:\:\mathrm{a}^{\mathrm{2}} \:\:+\:\:\mathrm{c}^{\mathrm{2}} \:\:=\:\:\:\mathrm{196}\:\:\:\:\:\:...\:\left(\mathrm{i}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{b}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{c}\:\:−\:\:\mathrm{a}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{169}\:\:\:\:\:...\:\left(\mathrm{ii}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{c}^{\mathrm{2}} \:\:+\:\:\left(\mathrm{b}\:\:−\:\:\mathrm{c}\right)^{\mathrm{2}} \:\:=\:\:\mathrm{225}\:\:\:\:\:...\:\left(\mathrm{iii}\right) \\ $$

Question Number 103723    Answers: 0   Comments: 0

Solve for n, such that; 1−(1/2)+∙∙∙+(((−1)^n )/(n+1))=∫_0 ^1 (x^(n+1) /(1+x))dx−ln2−(−1)^(n+1)

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{n},\:\mathrm{such}\:\mathrm{that}; \\ $$$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\centerdot\centerdot\centerdot+\frac{\left(−\mathrm{1}\right)^{\mathrm{n}} }{\mathrm{n}+\mathrm{1}}=\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{x}^{\mathrm{n}+\mathrm{1}} }{\mathrm{1}+\mathrm{x}}\mathrm{dx}−\mathrm{ln2}−\left(−\mathrm{1}\right)^{\mathrm{n}+\mathrm{1}} \\ $$

Question Number 103716    Answers: 1   Comments: 3

Question Number 103703    Answers: 1   Comments: 0

if an object moves along a straight line according to the relationship( x(t)=((1/2)t^2 −t+2)) find (1) the average speed between (x=(3/2) , x=(7/2)) (2) the pelvic velocity between (x=(7/2))

$${if}\:{an}\:{object}\:{moves}\:{along}\:{a}\:{straight}\:{line}\: \\ $$$${according}\:{to}\:{the}\:{relationship}\left(\:{x}\left({t}\right)=\left(\frac{\mathrm{1}}{\mathrm{2}}{t}^{\mathrm{2}} −{t}+\mathrm{2}\right)\right) \\ $$$${find}\: \\ $$$$\left(\mathrm{1}\right)\:{the}\:{average}\:{speed}\:{between}\:\left({x}=\frac{\mathrm{3}}{\mathrm{2}}\:,\:{x}=\frac{\mathrm{7}}{\mathrm{2}}\right) \\ $$$$\left(\mathrm{2}\right)\:{the}\:{pelvic}\:{velocity}\:{between}\:\left({x}=\frac{\mathrm{7}}{\mathrm{2}}\right) \\ $$

Question Number 103700    Answers: 1   Comments: 1

Question Number 103691    Answers: 1   Comments: 0

solve for x x^x =s

$${solve}\:{for}\:{x} \\ $$$${x}^{{x}} ={s} \\ $$

Question Number 103686    Answers: 1   Comments: 0

x^x^6 =(√2)^(√2) x=?

$${x}^{{x}^{\mathrm{6}} } =\sqrt{\mathrm{2}}\:^{\sqrt{\mathrm{2}}} \:{x}=? \\ $$

Question Number 103685    Answers: 1   Comments: 0

Question Number 103683    Answers: 1   Comments: 1

∫_0 ^1 tan^(−1) (((2x−1)/(1+x−x^2 )))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} {tan}^{−\mathrm{1}} \left(\frac{\mathrm{2}{x}−\mathrm{1}}{\mathrm{1}+{x}−{x}^{\mathrm{2}} }\right){dx} \\ $$

Question Number 103673    Answers: 1   Comments: 0

Σ_(k=1) ^(4095) (1/(((√k)+(√(k+1)))((k)^(1/4) +((k+1))^(1/4) ))) ?

$$\underset{{k}=\mathrm{1}} {\overset{\mathrm{4095}} {\sum}}\frac{\mathrm{1}}{\left(\sqrt{{k}}+\sqrt{{k}+\mathrm{1}}\right)\left(\sqrt[{\mathrm{4}}]{{k}}+\sqrt[{\mathrm{4}}]{{k}+\mathrm{1}}\right)}\:? \\ $$

Question Number 103672    Answers: 1   Comments: 3

Question Number 103670    Answers: 4   Comments: 0

Given b_n = 3.2^n is a GP . find the value of (1/b_1 )+(1/b_2 )+(1/b_3 )+...+(1/b_(10) ) ?

$${Given}\:{b}_{{n}} \:=\:\mathrm{3}.\mathrm{2}^{{n}} \:{is}\:{a}\:{GP}\:.\:{find}\:{the}\:{value} \\ $$$${of}\:\frac{\mathrm{1}}{{b}_{\mathrm{1}} }+\frac{\mathrm{1}}{{b}_{\mathrm{2}} }+\frac{\mathrm{1}}{{b}_{\mathrm{3}} }+...+\frac{\mathrm{1}}{{b}_{\mathrm{10}} }\:?\: \\ $$

Question Number 103669    Answers: 2   Comments: 0

prove that : a) ∫_(−3) ^(−1) x^2 dx ≥∫_1 ^3 (2x−1)dx b)∫_(−2) ^0 xdx ≤∫_0 ^2 (x^2 + x )dx c)∫_1 ^4 (x^2 + 2)dx ≥∫_2 ^5 (2x −5)dx d)∫_(−π) ^(−((3π)/4)) cos 2x dx ≥∫_((3π)/4) ^π sin 2x dx

$${prove}\:{that}\:: \\ $$$$\left.{a}\right)\:\int_{−\mathrm{3}} ^{−\mathrm{1}} {x}^{\mathrm{2}} {dx}\:\geqslant\int_{\mathrm{1}} ^{\mathrm{3}} \left(\mathrm{2}{x}−\mathrm{1}\right){dx} \\ $$$$\left.{b}\right)\int_{−\mathrm{2}} ^{\mathrm{0}} {xdx}\:\leqslant\int_{\mathrm{0}} ^{\mathrm{2}} \left({x}^{\mathrm{2}} \:+\:{x}\:\right){dx} \\ $$$$\left.{c}\right)\int_{\mathrm{1}} ^{\mathrm{4}} \left({x}^{\mathrm{2}} \:+\:\mathrm{2}\right){dx}\:\:\geqslant\int_{\mathrm{2}} ^{\mathrm{5}} \left(\mathrm{2}{x}\:−\mathrm{5}\right){dx} \\ $$$$\left.{d}\right)\int_{−\pi} ^{−\frac{\mathrm{3}\pi}{\mathrm{4}}} \mathrm{cos}\:\mathrm{2}{x}\:{dx}\:\geqslant\int_{\frac{\mathrm{3}\pi}{\mathrm{4}}} ^{\pi} \mathrm{sin}\:\mathrm{2}{x}\:{dx} \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 103665    Answers: 0   Comments: 0

Question Number 103664    Answers: 1   Comments: 0

Question Number 103659    Answers: 2   Comments: 1

When y=ax+b is a tangent line to the curve f(x)=x^3 passing through (0; −2), find a+b?

$$\mathrm{When}\:\mathrm{y}=\mathrm{ax}+\mathrm{b}\:\mathrm{is}\:\mathrm{a}\:\mathrm{tangent}\:\mathrm{line}\:\mathrm{to}\:\mathrm{the} \\ $$$$\mathrm{curve}\:\mathrm{f}\left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{3}} \:\mathrm{passing}\:\mathrm{through}\:\left(\mathrm{0};\:−\mathrm{2}\right), \\ $$$$\mathrm{find}\:\mathrm{a}+\mathrm{b}? \\ $$

Question Number 103652    Answers: 0   Comments: 1

Question Number 103649    Answers: 0   Comments: 0

Question Number 103648    Answers: 2   Comments: 0

Evaluate (1/(1∙2∙3))+(3/(2∙3∙4))+(5/(3∙4∙5))+...+((2n−1)/(n(n+1)(n+2))

$$\boldsymbol{\mathrm{Evaluate}}\:\frac{\mathrm{1}}{\mathrm{1}\centerdot\mathrm{2}\centerdot\mathrm{3}}+\frac{\mathrm{3}}{\mathrm{2}\centerdot\mathrm{3}\centerdot\mathrm{4}}+\frac{\mathrm{5}}{\mathrm{3}\centerdot\mathrm{4}\centerdot\mathrm{5}}+...+\frac{\mathrm{2}\boldsymbol{\mathrm{n}}−\mathrm{1}}{\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{n}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{n}}+\mathrm{2}\right.} \\ $$

Question Number 103647    Answers: 0   Comments: 0

Question Number 103644    Answers: 1   Comments: 1

Question Number 103643    Answers: 4   Comments: 0

if sin x+cos x = (5/6) then (1/(sin x)) + (1/(cos x)) ?

$${if}\:\mathrm{sin}\:{x}+\mathrm{cos}\:{x}\:=\:\frac{\mathrm{5}}{\mathrm{6}} \\ $$$${then}\:\frac{\mathrm{1}}{\mathrm{sin}\:{x}}\:+\:\frac{\mathrm{1}}{\mathrm{cos}\:{x}}\:?\: \\ $$

Question Number 103633    Answers: 2   Comments: 1

The question is Σ_(n=1) ^∞ (((2n−1)/(n(n+1)(n+2)))=...

$$ \\ $$$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{question}}\:\boldsymbol{\mathrm{is}} \\ $$$$\underset{\boldsymbol{\mathrm{n}}=\mathrm{1}} {\overset{\infty} {\sum}}\left(\frac{\mathrm{2}\boldsymbol{\mathrm{n}}−\mathrm{1}}{\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{n}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{n}}+\mathrm{2}\right.}\right)=... \\ $$

Question Number 103624    Answers: 0   Comments: 0

Question Number 103623    Answers: 2   Comments: 0

find the sum of the series whose nth term is ((2n−1)/(n(n+1)(n+2)). i have a problem with this and i need help please

$$\boldsymbol{\mathrm{find}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{series}}\:\boldsymbol{\mathrm{whose}}\:\boldsymbol{\mathrm{nth}} \\ $$$$\boldsymbol{\mathrm{term}}\:\boldsymbol{\mathrm{is}}\:\frac{\mathrm{2}\boldsymbol{\mathrm{n}}−\mathrm{1}}{\boldsymbol{\mathrm{n}}\left(\boldsymbol{\mathrm{n}}+\mathrm{1}\right)\left(\boldsymbol{\mathrm{n}}+\mathrm{2}\right.}. \\ $$$$\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{have}}\:\boldsymbol{\mathrm{a}}\:\boldsymbol{\mathrm{problem}}\:\boldsymbol{\mathrm{with}}\:\boldsymbol{\mathrm{this}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{need}} \\ $$$$\boldsymbol{\mathrm{help}}\:\boldsymbol{\mathrm{please}} \\ $$

Question Number 103622    Answers: 2   Comments: 0

Given a = Σ_(n=1) ^(24) (1/((√(n+1))+(√n))) then the value of a + (1/(log _a (bc)+1)) + (1/(log _b (ac)+1)) + (1/(log _c (ab)+1)) = ?

$${Given}\:{a}\:=\:\underset{{n}=\mathrm{1}} {\overset{\mathrm{24}} {\sum}}\frac{\mathrm{1}}{\sqrt{{n}+\mathrm{1}}+\sqrt{{n}}}\:{then}\:{the}\:{value}\:{of} \\ $$$${a}\:+\:\frac{\mathrm{1}}{\mathrm{log}\:_{{a}} \left({bc}\right)+\mathrm{1}}\:+\:\frac{\mathrm{1}}{\mathrm{log}\:_{{b}} \left({ac}\right)+\mathrm{1}}\:+ \\ $$$$\frac{\mathrm{1}}{\mathrm{log}\:_{{c}} \left({ab}\right)+\mathrm{1}}\:=\:? \\ $$

  Pg 1034      Pg 1035      Pg 1036      Pg 1037      Pg 1038      Pg 1039      Pg 1040      Pg 1041      Pg 1042      Pg 1043   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com