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AlgebraQuestion and Answers: Page 263

Question Number 97694 Answers: 1 Comments: 7

Question Number 97675 Answers: 1 Comments: 0

Question Number 97637 Answers: 0 Comments: 1

Given p,q∈R_+ ^∗ −{−1}/(1/p)+(1/q)=1 show that; ∀a,b ∈R ab≤(a^p /p)+(b^q /q)

$$\mathrm{Given}\:\mathrm{p},\mathrm{q}\in\mathbb{R}_{+} ^{\ast} −\left\{−\mathrm{1}\right\}/\frac{\mathrm{1}}{\mathrm{p}}+\frac{\mathrm{1}}{\mathrm{q}}=\mathrm{1}\:\mathrm{show}\:\mathrm{that}; \\ $$$$\forall\mathrm{a},\mathrm{b}\:\in\mathbb{R}\:\mathrm{ab}\leqslant\frac{\mathrm{a}^{\mathrm{p}} }{\mathrm{p}}+\frac{\mathrm{b}^{\mathrm{q}} }{\mathrm{q}} \\ $$

Question Number 97564 Answers: 1 Comments: 0

Question Number 97512 Answers: 0 Comments: 2

The value of k for which the quadratic equation (1−2k)x^2 −6kx−1=0 and kx^2 −x+1=0 have atleast one roots in common are ___

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{k}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the} \\ $$$$\mathrm{quadratic}\:\mathrm{equation}\:\left(\mathrm{1}−\mathrm{2k}\right)\mathrm{x}^{\mathrm{2}} −\mathrm{6kx}−\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{and}\:\mathrm{kx}^{\mathrm{2}} −\mathrm{x}+\mathrm{1}=\mathrm{0}\:\mathrm{have}\:\mathrm{atleast} \\ $$$$\mathrm{one}\:\mathrm{roots}\:\mathrm{in}\:\mathrm{common}\:\mathrm{are}\:\_\_\_ \\ $$

Question Number 97501 Answers: 0 Comments: 2

The natural number n for which the expression y = 5log^2 _3 (n) − log _3 (n^(12) )+9 , has the minimum value is ___

$$\mathrm{The}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{n}\:\mathrm{for}\:\mathrm{which}\: \\ $$$$\mathrm{the}\:\mathrm{expression}\:\mathrm{y}\:=\:\mathrm{5log}^{\mathrm{2}} \:_{\mathrm{3}} \left(\mathrm{n}\right)\:− \\ $$$$\mathrm{log}\:_{\mathrm{3}} \left(\mathrm{n}^{\mathrm{12}} \right)+\mathrm{9}\:,\:\mathrm{has}\:\mathrm{the}\:\mathrm{minimum} \\ $$$$\mathrm{value}\:\mathrm{is}\:\_\_\_ \\ $$

Question Number 97496 Answers: 1 Comments: 0

if f(((2x+5)/(x−3)))=3x+5 find f(x) please solve it

$${if}\:\:\:\:\:\:{f}\left(\frac{\mathrm{2}{x}+\mathrm{5}}{{x}−\mathrm{3}}\right)=\mathrm{3}{x}+\mathrm{5}\:\:\:{find}\:\:\:{f}\left({x}\right) \\ $$$$ \\ $$$${please}\:{solve}\:{it} \\ $$

Question Number 97485 Answers: 1 Comments: 3

Question Number 97428 Answers: 2 Comments: 5

Question Number 97386 Answers: 0 Comments: 2

Question Number 97306 Answers: 0 Comments: 2

if sin14=x then cos^2 22−cos^2 8=?

$$\mathrm{if}\:\:\:\:\:\:\:\:\:\mathrm{sin14}=\mathrm{x} \\ $$$$\mathrm{then} \\ $$$$\mathrm{cos}^{\mathrm{2}} \mathrm{22}−\mathrm{cos}^{\mathrm{2}} \mathrm{8}=? \\ $$

Question Number 97303 Answers: 0 Comments: 0

Given x_1 +x_2 +x_3 = 0 , y_1 + y_2 +y_3 = 0 and x_1 y_1 + x_2 y_2 + x_3 y_3 = 0 . The value of (x_1 ^2 /(x_1 ^2 +x_2 ^2 +x_3 ^2 )) + (y_1 ^2 /(y_1 ^2 +y_2 ^2 +y_3 ^2 )) = ?

Question Number 97272 Answers: 0 Comments: 0

Question Number 97227 Answers: 2 Comments: 1

Question Number 97206 Answers: 2 Comments: 0

Question Number 97136 Answers: 0 Comments: 3

Evaluate (3/(1! + 2! + 3!)) + (4/(2! + 3! + 4!)) + ... + ((2001)/(1999! + 2000! + 2001!))

$$\mathrm{Evaluate} \\ $$$$\:\:\frac{\mathrm{3}}{\mathrm{1}!\:+\:\mathrm{2}!\:+\:\mathrm{3}!}\:\:+\:\:\frac{\mathrm{4}}{\mathrm{2}!\:+\:\mathrm{3}!\:+\:\mathrm{4}!}\:\:+\:\:...\:+\:\:\frac{\mathrm{2001}}{\mathrm{1999}!\:\:+\:\:\mathrm{2000}!\:\:+\:\:\mathrm{2001}!} \\ $$

Question Number 97135 Answers: 0 Comments: 1

prove that: sin(16x) cot(x)=1+2cos(2x)+2cos(4x)+2cos(6x)+...+2cos(16x)

$${prove}\:{that}: \\ $$$${sin}\left(\mathrm{16}{x}\right)\:{cot}\left({x}\right)=\mathrm{1}+\mathrm{2}{cos}\left(\mathrm{2}{x}\right)+\mathrm{2}{cos}\left(\mathrm{4}{x}\right)+\mathrm{2}{cos}\left(\mathrm{6}{x}\right)+...+\mathrm{2}{cos}\left(\mathrm{16}{x}\right) \\ $$

Question Number 97134 Answers: 0 Comments: 0

find the laplace transform of t^(3/2) erf(t)

$${find}\:{the}\:{laplace}\:{transform}\:{of}\:{t}^{\frac{\mathrm{3}}{\mathrm{2}}} {erf}\left({t}\right) \\ $$

Question Number 97114 Answers: 0 Comments: 0

pls find x x^x^x +ln(2x)−1=0

$${pls}\:{find}\:{x} \\ $$$$ \\ $$$${x}^{{x}^{{x}} } +{ln}\left(\mathrm{2}{x}\right)−\mathrm{1}=\mathrm{0} \\ $$

Question Number 97067 Answers: 2 Comments: 1

if p is the natural number then what is the degree of x^(6p+1) +3x^(4p−3) +4x^(8p−10) +8 polynomial?

$$\mathrm{if}\:\mathrm{p}\:\mathrm{is}\:\mathrm{the}\:\mathrm{natural}\:\mathrm{number}\:\mathrm{then}\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{degree}\:\mathrm{of} \\ $$$$\mathrm{x}^{\mathrm{6p}+\mathrm{1}} +\mathrm{3x}^{\mathrm{4p}−\mathrm{3}} +\mathrm{4x}^{\mathrm{8p}−\mathrm{10}} +\mathrm{8}\:\:\mathrm{polynomial}? \\ $$

Question Number 97064 Answers: 0 Comments: 1

find the value of (an) in this utility (3xy^2 )^3

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{an}\right)\:\mathrm{in}\:\mathrm{this}\:\mathrm{utility}\:\:\left(\mathrm{3xy}^{\mathrm{2}} \right)^{\mathrm{3}} \\ $$

Question Number 97051 Answers: 2 Comments: 2

what is the perimeter of a regular dodecagon (12 sides) whose area is 24+12(√3) ?

$$\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{perimeter}\:\mathrm{of}\:\mathrm{a}\:\mathrm{regular}\: \\ $$$$\mathrm{dodecagon}\:\left(\mathrm{12}\:\mathrm{sides}\right)\:\mathrm{whose}\: \\ $$$$\mathrm{area}\:\mathrm{is}\:\mathrm{24}+\mathrm{12}\sqrt{\mathrm{3}}\:?\: \\ $$

Question Number 97019 Answers: 0 Comments: 1

Question Number 96951 Answers: 1 Comments: 5

prove that 1−(1/2)+(1/3)−(1/4)+(1/5)+...+((−1^(n−1) )/n) is always positive

$${prove}\:{that}\:\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}−\frac{\mathrm{1}}{\mathrm{4}}+\frac{\mathrm{1}}{\mathrm{5}}+...+\frac{−\mathrm{1}^{{n}−\mathrm{1}} }{{n}}\:\:{is}\:{always}\:{positive} \\ $$$$ \\ $$

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Question Number 96839 Answers: 0 Comments: 0

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