Question and Answers Forum

All Questions   Topic List

AlgebraQuestion and Answers: Page 229

Question Number 117828    Answers: 1   Comments: 0

1)((√3)−1)((√3)+1)=(√3)×(√3)−(√3)−1 =3−(√3)−1 =2−(√3) 2)(2x+(√3))(2x−(√3))=(2x)^2 −2x(√3)+2x(√3)−3 =4x^2 −3

$$\left.\mathrm{1}\right)\left(\sqrt{\mathrm{3}}−\mathrm{1}\right)\left(\sqrt{\mathrm{3}}+\mathrm{1}\right)=\sqrt{\mathrm{3}}×\sqrt{\mathrm{3}}−\sqrt{\mathrm{3}}−\mathrm{1} \\ $$$$=\mathrm{3}−\sqrt{\mathrm{3}}−\mathrm{1} \\ $$$$=\mathrm{2}−\sqrt{\mathrm{3}} \\ $$$$\left.\mathrm{2}\right)\left(\mathrm{2}{x}+\sqrt{\mathrm{3}}\right)\left(\mathrm{2}{x}−\sqrt{\mathrm{3}}\right)=\left(\mathrm{2}{x}\right)^{\mathrm{2}} −\mathrm{2}{x}\sqrt{\mathrm{3}}+\mathrm{2}{x}\sqrt{\mathrm{3}}−\mathrm{3} \\ $$$$=\mathrm{4}{x}^{\mathrm{2}} −\mathrm{3} \\ $$

Question Number 117827    Answers: 0   Comments: 5

Question Number 117781    Answers: 1   Comments: 0

Log (cosβ) = p ⇒ cos β = 10^p ∴ secβ = (1/(cosβ)) = (1/(10^p )) = 10^(−p) ∴ Log (secβ) = Log 10^(−p) = −p Log 10 = −p

$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{Log}\:\left(\mathrm{cos}\beta\right)\:=\:\mathrm{p}\:\:\:\:\:\Rightarrow\:\:\:\mathrm{cos}\:\beta\:=\:\mathrm{10}^{\mathrm{p}} \:\: \\ $$$$\:\:\:\:\:\:\:\therefore\:\:\:\mathrm{sec}\beta\:=\:\:\frac{\mathrm{1}}{\mathrm{cos}\beta}\:\:=\:\:\frac{\mathrm{1}}{\mathrm{10}^{\mathrm{p}} }\:\:=\:\mathrm{10}^{−\mathrm{p}} \\ $$$$\:\:\:\:\:\:\:\therefore\:\:\:\mathrm{Log}\:\left(\mathrm{sec}\beta\right)\:=\:\:\mathrm{Log}\:\mathrm{10}^{−\mathrm{p}} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:−\mathrm{p}\:\mathrm{Log}\:\mathrm{10} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\:−\mathrm{p} \\ $$

Question Number 117767    Answers: 1   Comments: 1

x^2 +y_ ^2 =a^2 (√(2 )) x^2 +y^2 =a^2 what is intersection Angle=?

$${x}^{\mathrm{2}} +{y}_{} ^{\mathrm{2}} ={a}^{\mathrm{2}} \sqrt{\mathrm{2}\:} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} ={a}^{\mathrm{2}} \:\:\:\:\:\: \\ $$$$ \\ $$$${what}\:{is}\:{intersection}\:\:{Angle}=?\: \\ $$

Question Number 117666    Answers: 0   Comments: 3

Question Number 117649    Answers: 1   Comments: 0

Let P(x) be a polynomial function of degree n such that P(k)=(k/(k+1)) for k=0,1,2,...,n. Then P(n+1) is equal to (A) −1 if n is even (B) 1 if n is odd (C) (n/(n+2)) if n is even (D) (n/(n+2)) if n is odd Which among the four proposals is/are correct ?

$$\mathrm{Let}\:\mathrm{P}\left({x}\right)\:\mathrm{be}\:\mathrm{a}\:\mathrm{polynomial}\:\mathrm{function}\:\mathrm{of}\:\mathrm{degree}\:\mathrm{n}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{P}\left({k}\right)=\frac{{k}}{{k}+\mathrm{1}}\:\:\mathrm{for}\:{k}=\mathrm{0},\mathrm{1},\mathrm{2},...,\mathrm{n}.\:\mathrm{Then}\:\mathrm{P}\left(\mathrm{n}+\mathrm{1}\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\: \\ $$$$\left(\mathrm{A}\right)\:−\mathrm{1}\:\mathrm{if}\:\mathrm{n}\:\mathrm{is}\:\mathrm{even}\:\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{B}\right)\:\mathrm{1}\:\mathrm{if}\:{n}\:\mathrm{is}\:\mathrm{odd} \\ $$$$\left(\mathrm{C}\right)\:\frac{{n}}{{n}+\mathrm{2}}\:\mathrm{if}\:{n}\:\mathrm{is}\:\mathrm{even}\:\:\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:\frac{{n}}{{n}+\mathrm{2}}\:\:\mathrm{if}\:{n}\:\mathrm{is}\:\mathrm{odd} \\ $$$$\mathrm{Which}\:\mathrm{among}\:\mathrm{the}\:\mathrm{four}\:\mathrm{proposals}\:\mathrm{is}/\mathrm{are}\:\mathrm{correct}\:? \\ $$

Question Number 117603    Answers: 0   Comments: 0

Let f : R→R be a function satisfying the following : (a) f(−x)=−f(x) (b) f(x+1)=f(x)+1 (c) f((1/x))=((f(x))/x^2 ) for all x≠0 Show that (i)f(x)=x for all x,y∈R (ii) f(x+y)=f(x)+f(y) for all x,y∈R (iii) f(xy)=f(x)f(y) for all x,y∈R (iv) f((x/y))=((f(x))/(f(y))) for all x,y∈R with y≠0

$$\mathrm{Let}\:\mathrm{f}\::\:\mathbb{R}\rightarrow\mathbb{R}\:\mathrm{be}\:\mathrm{a}\:\mathrm{function}\:\mathrm{satisfying}\:\mathrm{the}\:\mathrm{following}\:: \\ $$$$\left(\mathrm{a}\right)\:{f}\left(−{x}\right)=−{f}\left({x}\right) \\ $$$$\left(\mathrm{b}\right)\:{f}\left({x}+\mathrm{1}\right)={f}\left({x}\right)+\mathrm{1} \\ $$$$\left(\mathrm{c}\right)\:{f}\left(\frac{\mathrm{1}}{{x}}\right)=\frac{{f}\left({x}\right)}{{x}^{\mathrm{2}} }\:\mathrm{for}\:\mathrm{all}\:{x}\neq\mathrm{0} \\ $$$$\mathrm{Show}\:\mathrm{that} \\ $$$$\left(\mathrm{i}\right){f}\left({x}\right)={x}\:\mathrm{for}\:\mathrm{all}\:{x},\mathrm{y}\in\mathbb{R} \\ $$$$\left(\mathrm{ii}\right)\:{f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left(\mathrm{y}\right)\:\mathrm{for}\:\mathrm{all}\:{x},\mathrm{y}\in\mathbb{R} \\ $$$$\left(\mathrm{iii}\right)\:{f}\left({xy}\right)={f}\left({x}\right){f}\left(\mathrm{y}\right)\:\mathrm{for}\:\mathrm{all}\:{x},\mathrm{y}\in\mathbb{R} \\ $$$$\left(\mathrm{iv}\right)\:{f}\left(\frac{{x}}{\mathrm{y}}\right)=\frac{{f}\left({x}\right)}{{f}\left(\mathrm{y}\right)}\:\mathrm{for}\:\mathrm{all}\:{x},\mathrm{y}\in\mathbb{R}\:\mathrm{with}\:\mathrm{y}\neq\mathrm{0} \\ $$

Question Number 117555    Answers: 2   Comments: 0

Alternative forms { (((√x)+(√y)=((23)/(12)))),((9x+16y=29)) :}

$${Alternative}\:{forms} \\ $$$$\begin{cases}{\sqrt{{x}}+\sqrt{{y}}=\frac{\mathrm{23}}{\mathrm{12}}}\\{\mathrm{9}{x}+\mathrm{16}{y}=\mathrm{29}}\end{cases} \\ $$$$ \\ $$

Question Number 117172    Answers: 1   Comments: 0

Question Number 117142    Answers: 0   Comments: 0

Question Number 117122    Answers: 0   Comments: 4

Given a,b,c ∈R^3 such that abc=1. Show that: (a−1+(1/b))(b−1+(1/c))(c−1+(1/a))≤1

$$\mathrm{Given}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\in\mathbb{R}^{\mathrm{3}} \:\mathrm{such}\:\mathrm{that}\:\mathrm{abc}=\mathrm{1}.\:\mathrm{Show}\:\mathrm{that}: \\ $$$$\:\:\:\:\:\left(\mathrm{a}−\mathrm{1}+\frac{\mathrm{1}}{\mathrm{b}}\right)\left(\mathrm{b}−\mathrm{1}+\frac{\mathrm{1}}{\mathrm{c}}\right)\left(\mathrm{c}−\mathrm{1}+\frac{\mathrm{1}}{\mathrm{a}}\right)\leqslant\mathrm{1} \\ $$

Question Number 117101    Answers: 2   Comments: 0

If sin^2 θ and cos^2 θ are the roots of quadratic equation, find the equation.

$$\mathrm{If}\:\mathrm{sin}^{\mathrm{2}} \theta\:\mathrm{and}\:\mathrm{cos}^{\mathrm{2}} \theta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\: \\ $$$$\mathrm{of}\:\mathrm{quadratic}\:\mathrm{equation},\:\mathrm{find}\:\mathrm{the}\:\mathrm{equation}. \\ $$

Question Number 117095    Answers: 1   Comments: 0

Question Number 117082    Answers: 1   Comments: 0

If 6−3x is the geometric mean between the integer x^2 +2 and 2^ what are the values of x ?

$$\mathrm{If}\:\mathrm{6}−\mathrm{3x}\:\mathrm{is}\:\mathrm{the}\:\mathrm{geometric}\:\mathrm{mean}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{integer}\:\mathrm{x}^{\mathrm{2}} +\mathrm{2}\:\mathrm{and}\:\bar {\mathrm{2}}\:\mathrm{what}\:\mathrm{are}\:\mathrm{the}\: \\ $$$$\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:? \\ $$

Question Number 117027    Answers: 2   Comments: 0

solve: ((x − 4)/(x − 3)) < ((2x − 1)/2)

$$\mathrm{solve}:\:\:\:\:\frac{\mathrm{x}\:\:−\:\:\mathrm{4}}{\mathrm{x}\:\:−\:\:\mathrm{3}}\:\:\:<\:\:\:\frac{\mathrm{2x}\:\:−\:\:\mathrm{1}}{\mathrm{2}} \\ $$

Question Number 117026    Answers: 2   Comments: 0

((√(1−x))/( (√x))) + ((√x)/( (√(1−x)))) = ((13)/6)

$$\:\frac{\sqrt{\mathrm{1}−\mathrm{x}}}{\:\sqrt{\mathrm{x}}}\:+\:\frac{\sqrt{\mathrm{x}}}{\:\sqrt{\mathrm{1}−\mathrm{x}}}\:=\:\frac{\mathrm{13}}{\mathrm{6}} \\ $$

Question Number 116921    Answers: 1   Comments: 0

Question Number 116917    Answers: 1   Comments: 0

Find the greatest coefficient and greatest term in (3x − 2)^(− 7) . Sir is it: (− 1)^(− 7) .(2 − 3x)^(− 7) = − (2 − 3x)^(− 7) = − ((8008 × 2^(10) )/3^(17) )

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{coefficient}\:\mathrm{and}\:\mathrm{greatest}\:\mathrm{term}\:\mathrm{in} \\ $$$$\left(\mathrm{3x}\:\:−\:\:\mathrm{2}\right)^{−\:\mathrm{7}} . \\ $$$$ \\ $$$$\mathrm{Sir}\:\mathrm{is}\:\mathrm{it}:\:\:\:\:\:\left(−\:\mathrm{1}\right)^{−\:\mathrm{7}} .\left(\mathrm{2}\:\:−\:\:\mathrm{3x}\right)^{−\:\mathrm{7}} \:\:\:\:=\:\:\:−\:\left(\mathrm{2}\:\:−\:\:\mathrm{3x}\right)^{−\:\mathrm{7}} \\ $$$$=\:\:\:−\:\:\frac{\mathrm{8008}\:\:×\:\:\mathrm{2}^{\mathrm{10}} }{\mathrm{3}^{\mathrm{17}} } \\ $$

Question Number 116913    Answers: 1   Comments: 0

Question Number 116854    Answers: 4   Comments: 0

... calculus elementary algebra ... please solve :: ((6x+9))^(1/3) +((7−7x))^(1/3) +((x−8))^(1/3) =2 ...m.n.july.1970...

$$\:\:\:...\:\:\:{calculus}\:\:\:{elementary}\:\:{algebra}\:...\:\: \\ $$$$ \\ $$$$ \\ $$$$\:{please}\:{solve}\::: \\ $$$$ \\ $$$$\sqrt[{\mathrm{3}}]{\mathrm{6}{x}+\mathrm{9}}\:+\sqrt[{\mathrm{3}}]{\mathrm{7}−\mathrm{7}{x}}\:+\sqrt[{\mathrm{3}}]{{x}−\mathrm{8}}\:=\mathrm{2} \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:...{m}.{n}.{july}.\mathrm{1970}... \\ $$$$\: \\ $$

Question Number 116824    Answers: 2   Comments: 0

Given a>b>0 , a&b real number such that a^2 −ab+b^2 =7 and a−ab+b=−1. find the value of a^2 −b^2

$$\mathrm{Given}\:\mathrm{a}>\mathrm{b}>\mathrm{0}\:,\:\mathrm{a\&b}\:\mathrm{real}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{a}^{\mathrm{2}} −\mathrm{ab}+\mathrm{b}^{\mathrm{2}} =\mathrm{7}\:\mathrm{and}\:\mathrm{a}−\mathrm{ab}+\mathrm{b}=−\mathrm{1}. \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}^{\mathrm{2}} −\mathrm{b}^{\mathrm{2}} \\ $$

Question Number 116780    Answers: 2   Comments: 1

Question Number 116683    Answers: 2   Comments: 0

Given 1+3+5+7=16 we know that 16=4^2 and 4 is the half of 8 which is the successor of 7. conjecture the result of this sum: 1+3+5+7+...+25

$$\mathrm{Given}\:\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}=\mathrm{16}\:\:\:\mathrm{we}\:\mathrm{know}\:\mathrm{that} \\ $$$$\mathrm{16}=\mathrm{4}^{\mathrm{2}} \:\:\mathrm{and}\:\mathrm{4}\:\mathrm{is}\:\mathrm{the}\:\mathrm{half}\:\mathrm{of}\:\mathrm{8}\:\mathrm{which}\:\mathrm{is}\:\mathrm{the}\: \\ $$$$\mathrm{successor}\:\mathrm{of}\:\mathrm{7}. \\ $$$$ \\ $$$$\mathrm{conjecture}\:\mathrm{the}\:\mathrm{result}\:\mathrm{of}\:\mathrm{this}\:\mathrm{sum}: \\ $$$$\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}+...+\mathrm{25} \\ $$

Question Number 116759    Answers: 2   Comments: 0

Question Number 116722    Answers: 1   Comments: 0

find the range of values of k for which the equation e^x −5=k has no solution

$${find}\:{the}\:{range}\:{of}\:{values}\:{of}\:{k}\:{for} \\ $$$${which}\:{the}\:{equation}\:{e}^{{x}} −\mathrm{5}={k}\:{has}\:{no} \\ $$$${solution} \\ $$

Question Number 116633    Answers: 1   Comments: 0

  Pg 224      Pg 225      Pg 226      Pg 227      Pg 228      Pg 229      Pg 230      Pg 231      Pg 232      Pg 233   

Terms of Service

Privacy Policy

Contact: info@tinkutara.com