Question and Answers Forum

AlgebraQuestion and Answers: Page 222

Question Number 136824 Answers: 0 Comments: 0

Question Number 136793 Answers: 1 Comments: 0

Question Number 136749 Answers: 2 Comments: 0

Given system equation { ((x^2 +3xy+y^2 +1=0)),((x^3 +y^3 −7=0)) :} has solution (x_1 ,y_1 ) &(x_2 ,y_2 ) for x,y∈R. Find the value of x_1 ^2 .y_2 +x_2 ^2 .y_1 .

$$\mathrm{Given}\:\mathrm{system}\:\mathrm{equation}\: \\ $$$$\:\begin{cases}{\mathrm{x}^{\mathrm{2}} +\mathrm{3xy}+\mathrm{y}^{\mathrm{2}} +\mathrm{1}=\mathrm{0}}\\{\mathrm{x}^{\mathrm{3}} +\mathrm{y}^{\mathrm{3}} −\mathrm{7}=\mathrm{0}}\end{cases}\:\mathrm{has}\:\mathrm{solution}\: \\ $$$$\left(\mathrm{x}_{\mathrm{1}} ,\mathrm{y}_{\mathrm{1}} \right)\:\&\left(\mathrm{x}_{\mathrm{2}} ,\mathrm{y}_{\mathrm{2}} \right)\:\mathrm{for}\:\mathrm{x},\mathrm{y}\in\mathbb{R}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{value} \\ $$$$\mathrm{of}\:\mathrm{x}_{\mathrm{1}} ^{\mathrm{2}} .\mathrm{y}_{\mathrm{2}} \:+\mathrm{x}_{\mathrm{2}} ^{\mathrm{2}} .\mathrm{y}_{\mathrm{1}} .\: \\ $$

Question Number 136741 Answers: 1 Comments: 0

Question Number 136703 Answers: 2 Comments: 2

(√((√x)^(log x) ))=x faind x

$$\sqrt{\sqrt{{x}}\:^{\mathrm{log}\:{x}} }={x}\:\:\:\:\:\:\:{faind}\:\:{x} \\ $$

Question Number 136667 Answers: 2 Comments: 0

if f(x)=ax^2 +bx+c and f(5)=−3f(2) an intersiction point (−4,0) an the X-axis faind another point the X-axis

$${if}\:\:\:\:\:\:{f}\left({x}\right)={ax}^{\mathrm{2}} +{bx}+{c}\:\:\:\:\:\:{and}\:\:\:{f}\left(\mathrm{5}\right)=−\mathrm{3}{f}\left(\mathrm{2}\right) \\ $$$${an}\:{intersiction}\:\:{point}\:\:\left(−\mathrm{4},\mathrm{0}\right) \\ $$$${an}\:{the}\:\:{X}-{axis}\:\:\:\:\:{faind}\:{another}\:{point}\: \\ $$$${the}\:{X}-{axis} \\ $$$$ \\ $$

Question Number 136649 Answers: 0 Comments: 2

What the value of series (4/2) + (4.7/2.6) + (4.7.10/2.6.10) + (4.7.10.13/2.6.10.14) +…?

$$ \\ $$What the value of series (4/2) + (4.7/2.6) + (4.7.10/2.6.10) + (4.7.10.13/2.6.10.14) +…?

Question Number 136614 Answers: 1 Comments: 0

If a+(1/a) = 23 then (a)^(1/4) + (1/( (a)^(1/4) )) =?

$${If}\:{a}+\frac{\mathrm{1}}{{a}}\:=\:\mathrm{23}\:{then}\:\sqrt[{\mathrm{4}}]{{a}}\:+\:\frac{\mathrm{1}}{\:\sqrt[{\mathrm{4}}]{{a}}}\:=? \\ $$

Question Number 136607 Answers: 2 Comments: 0

What is the value of a^2 +b^2 if ax+by=3 bx−ay = 4 and x^2 +y^2 = 4

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \:\mathrm{if}\:\mathrm{ax}+\mathrm{by}=\mathrm{3} \\ $$$$\mathrm{bx}−\mathrm{ay}\:=\:\mathrm{4}\:\mathrm{and}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} \:=\:\mathrm{4} \\ $$

Question Number 136636 Answers: 0 Comments: 1

b=a+c y=x+c x=a+z y=b+z x=?,y=?,z=?

$${b}={a}+{c} \\ $$$${y}={x}+{c} \\ $$$${x}={a}+{z} \\ $$$${y}={b}+{z} \\ $$$${x}=?,{y}=?,{z}=? \\ $$

Question Number 136505 Answers: 1 Comments: 0

Question Number 136494 Answers: 3 Comments: 0

5((√(1−x)) +(√(1+x)) )= 6x + 8(√(1−x^2 ))

$$\mathrm{5}\left(\sqrt{\mathrm{1}−{x}}\:+\sqrt{\mathrm{1}+{x}}\:\right)=\:\mathrm{6}{x}\:+\:\mathrm{8}\sqrt{\mathrm{1}−{x}^{\mathrm{2}} }\: \\ $$

Question Number 136489 Answers: 1 Comments: 0

(1/2)+(2/4)+(3/8)+(6/(16))+((11)/(32))+((20)/(64))+((37)/(128))+... =?

$$\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{2}}{\mathrm{4}}+\frac{\mathrm{3}}{\mathrm{8}}+\frac{\mathrm{6}}{\mathrm{16}}+\frac{\mathrm{11}}{\mathrm{32}}+\frac{\mathrm{20}}{\mathrm{64}}+\frac{\mathrm{37}}{\mathrm{128}}+...\:=? \\ $$

Question Number 136475 Answers: 0 Comments: 1

Question Number 136433 Answers: 1 Comments: 0

Σ_(k=0) ^n C_(2n+1) ^(2k+1) 8^k =...???

$$\underset{{k}=\mathrm{0}} {\overset{{n}} {\sum}}{C}_{\mathrm{2}{n}+\mathrm{1}} ^{\mathrm{2}{k}+\mathrm{1}} \mathrm{8}^{{k}} =...??? \\ $$

Question Number 136408 Answers: 2 Comments: 0

S=Σ_(k=0) ^∞ ((3k^2 )/(2k^3 +2)) =? =Σ_(k=0) ^∞ (1/2)(((3k^2 )/(k^3 +1)))=Σ_(k=0) ^∞ (1/2)[(1/(k+1))+((2k−1)/(k^2 −k+1))] I dont know how to continue...Please Help.

$$\:\:\:\:\:\:{S}=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\:\:\frac{\mathrm{3}{k}^{\mathrm{2}} }{\mathrm{2}{k}^{\mathrm{3}} +\mathrm{2}}\:\:=? \\ $$$$\:\:\:\:\:\:\:\:\:=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}}\left(\frac{\mathrm{3}{k}^{\mathrm{2}} }{{k}^{\mathrm{3}} +\mathrm{1}}\right)=\underset{{k}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\mathrm{2}}\left[\frac{\mathrm{1}}{{k}+\mathrm{1}}+\frac{\mathrm{2}{k}−\mathrm{1}}{{k}^{\mathrm{2}} −{k}+\mathrm{1}}\right] \\ $$$$\:\:\:\:\:\:\:\:\:{I}\:{dont}\:{know}\:{how}\:{to}\:{continue}...{Please}\:{Help}. \\ $$$$ \\ $$

Question Number 136340 Answers: 1 Comments: 0

If (√(3+(√2))) = (√((a+(√b))/c)) + (√((a−(√b))/c)) then a+bc = ?

$${If}\:\sqrt{\mathrm{3}+\sqrt{\mathrm{2}}}\:=\:\sqrt{\frac{{a}+\sqrt{{b}}}{{c}}}\:+\:\sqrt{\frac{{a}−\sqrt{{b}}}{{c}}} \\ $$$${then}\:{a}+{bc}\:=\:? \\ $$

Question Number 136283 Answers: 1 Comments: 0

Question Number 136161 Answers: 1 Comments: 0

How do I find the sum of 1+3x+6x^2 +10x^3 +15x^4 +.......∞, where −1<x<1 ? Please Help..

$${How}\:{do}\:{I}\:{find}\:{the}\:{sum}\:{of} \\ $$$$\:\:\mathrm{1}+\mathrm{3}{x}+\mathrm{6}{x}^{\mathrm{2}} +\mathrm{10}{x}^{\mathrm{3}} +\mathrm{15}{x}^{\mathrm{4}} +.......\infty,\:\:{where}\:−\mathrm{1}<{x}<\mathrm{1}\:? \\ $$$$\:\:{Please}\:{Help}.. \\ $$

Question Number 136123 Answers: 3 Comments: 0

(({ (((12−x)^2 ))^(1/3) +(((12−x)(x−3)))^(1/3) +(√((x−3)^2 )) }^2 )/( ((12−x))^(1/3) +((x−3))^(1/3) )) = ((49)/3)

$$\frac{\left\{\:\sqrt[{\mathrm{3}}]{\left(\mathrm{12}−{x}\right)^{\mathrm{2}} }\:+\sqrt[{\mathrm{3}}]{\left(\mathrm{12}−{x}\right)\left({x}−\mathrm{3}\right)}\:+\sqrt{\left({x}−\mathrm{3}\right)^{\mathrm{2}} }\:\right\}^{\mathrm{2}} }{\:\sqrt[{\mathrm{3}}]{\mathrm{12}−{x}}\:+\sqrt[{\mathrm{3}}]{{x}−\mathrm{3}}}\:=\:\frac{\mathrm{49}}{\mathrm{3}} \\ $$

Question Number 139505 Answers: 1 Comments: 1

Find the greatest value of x^2 y^3 when 3x+4y=5

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} \mathrm{y}^{\mathrm{3}} \: \\ $$$$\mathrm{when}\:\mathrm{3x}+\mathrm{4y}=\mathrm{5} \\ $$

Question Number 136063 Answers: 2 Comments: 0

A and B can do a job in 10 days and 5 days, respectively. They worked together for two days, after which B was replaced by C and the work was finished in the next three days. How long will C alone take to finish 40% of the job?

$$ \\ $$A and B can do a job in 10 days and 5 days, respectively. They worked together for two days, after which B was replaced by C and the work was finished in the next three days. How long will C alone take to finish 40% of the job?

Question Number 136054 Answers: 0 Comments: 2

Question Number 136039 Answers: 4 Comments: 2

Find the value of a^2 +b^2 for a,b real number such that a = b+(1/(a+(1/(b+(1/(a+...)))))) and b = a−(1/(b+(1/(a−(1/(b+...))))))

$${Find}\:{the}\:{value}\:{of}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} \: \\ $$$${for}\:{a},{b}\:{real}\:{number}\:{such}\:{that} \\ $$$$\:{a}\:=\:{b}+\frac{\mathrm{1}}{{a}+\frac{\mathrm{1}}{{b}+\frac{\mathrm{1}}{{a}+...}}} \\ $$$${and}\:{b}\:=\:{a}−\frac{\mathrm{1}}{{b}+\frac{\mathrm{1}}{{a}−\frac{\mathrm{1}}{{b}+...}}} \\ $$

Question Number 136003 Answers: 0 Comments: 0

let′s define a relation R such that _a R_b ⇔ a ≤ b is this relation reflexive, symmetic and transitive? (equivalence relation)

$$\mathrm{let}'\mathrm{s}\:\mathrm{define}\:\mathrm{a}\:\mathrm{relation}\:\boldsymbol{{R}}\:\mathrm{such}\:\mathrm{that} \\ $$$$\:\:_{{a}} {R}_{{b}} \:\Leftrightarrow\:{a}\:\leqslant\:{b} \\ $$$$\mathrm{is}\:\mathrm{this}\:\mathrm{relation}\:\mathrm{reflexive},\:\mathrm{symmetic}\:\mathrm{and}\:\mathrm{transitive}?\:\left(\mathrm{equivalence}\:\mathrm{relation}\right) \\ $$

Question Number 136002 Answers: 1 Comments: 0

A man has a set of 5 balls, in which 3 are red and 2 are blue what are the number of ways these 5 balls can be arranged in a line.

$$\mathrm{A}\:\mathrm{man}\:\mathrm{has}\:\mathrm{a}\:\mathrm{set}\:\mathrm{of}\:\mathrm{5}\:\mathrm{balls},\:\mathrm{in}\:\mathrm{which}\:\mathrm{3}\:\mathrm{are}\:\mathrm{red}\:\mathrm{and}\:\mathrm{2}\:\mathrm{are}\:\mathrm{blue} \\ $$$$\mathrm{what}\:\mathrm{are}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{these}\:\mathrm{5}\:\mathrm{balls}\:\mathrm{can}\:\mathrm{be}\:\mathrm{arranged}\:\mathrm{in}\:\mathrm{a}\: \\ $$$$\mathrm{line}. \\ $$

Pg 217 Pg 218 Pg 219 Pg 220 Pg 221 Pg 222 Pg 223 Pg 224 Pg 225 Pg 226

Contact: info@tinkutara.com