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AlgebraQuestion and Answers: Page 222

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.

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

Question Number 136000 Answers: 1 Comments: 0

A room has 5 doors, if a person enters through a dooor, that person cannot leave through that same door. Find the number of ways that person can enter and leave that room.

$$\mathrm{A}\:\mathrm{room}\:\mathrm{has}\:\mathrm{5}\:\mathrm{doors},\:\mathrm{if}\:\mathrm{a}\:\mathrm{person}\:\mathrm{enters}\:\mathrm{through}\:\mathrm{a}\:\mathrm{dooor}, \\ $$$$\mathrm{that}\:\mathrm{person}\:\mathrm{cannot}\:\mathrm{leave}\:\mathrm{through}\:\mathrm{that}\:\mathrm{same}\:\mathrm{door}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\: \\ $$$$\mathrm{of}\:\mathrm{ways}\:\mathrm{that}\:\mathrm{person}\:\mathrm{can}\:\mathrm{enter}\:\mathrm{and}\:\mathrm{leave}\:\mathrm{that}\:\mathrm{room}. \\ $$

Question Number 135928 Answers: 1 Comments: 0

When the expression x³+ax²+bx+c is divided by x²-4, the remainder is 18-x, and when it is divided by X+3 the remainder is 21. What is the remainder when the expression is divided by X+1?

$$ \\ $$When the expression x³+ax²+bx+c is divided by x²-4, the remainder is 18-x, and when it is divided by X+3 the remainder is 21. What is the remainder when the expression is divided by X+1?

Question Number 135910 Answers: 1 Comments: 0

Algebra (√(23−6(√(6−4(√2))))) = p+q(√2) then (q^2 /(p(√2))) + p^2 q =?

$${Algebra}\: \\ $$$$\:\:\sqrt{\mathrm{23}−\mathrm{6}\sqrt{\mathrm{6}−\mathrm{4}\sqrt{\mathrm{2}}}}\:=\:{p}+{q}\sqrt{\mathrm{2}} \\ $$$${then}\:\frac{{q}^{\mathrm{2}} }{{p}\sqrt{\mathrm{2}}}\:+\:{p}^{\mathrm{2}} {q}\:=? \\ $$

Question Number 135786 Answers: 1 Comments: 1

Question Number 135756 Answers: 0 Comments: 1

Question Number 135682 Answers: 2 Comments: 0

Σ_(k=1) ^∞ ((k^3 +2k)/(k^2 +6k+9)) =?

$$\underset{{k}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{{k}^{\mathrm{3}} +\mathrm{2}{k}}{{k}^{\mathrm{2}} +\mathrm{6}{k}+\mathrm{9}}\:=? \\ $$

Question Number 135536 Answers: 1 Comments: 0

(u^v )′=? u ,v tow fonctions

$$\left(\boldsymbol{{u}}^{\boldsymbol{{v}}} \right)'=? \\ $$$${u}\:,{v}\:\:\:{tow}\:{fonctions} \\ $$

Question Number 135532 Answers: 2 Comments: 1

Question Number 135493 Answers: 1 Comments: 0

(√(2x^2 −5x+2)) −(√(x^2 −x−2)) = (√(x^2 −3x+2))

$$\:\sqrt{\mathrm{2}{x}^{\mathrm{2}} −\mathrm{5}{x}+\mathrm{2}}\:−\sqrt{{x}^{\mathrm{2}} −{x}−\mathrm{2}}\:=\:\sqrt{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}} \\ $$

Question Number 135486 Answers: 4 Comments: 3

(((√(2x+1))+(√(x−1)))/( (√(2x+1))−(√(x−1)))) = (3/( (√(x+2))))

$$\frac{\sqrt{\mathrm{2x}+\mathrm{1}}+\sqrt{\mathrm{x}−\mathrm{1}}}{\:\sqrt{\mathrm{2x}+\mathrm{1}}−\sqrt{\mathrm{x}−\mathrm{1}}}\:=\:\frac{\mathrm{3}}{\:\sqrt{\mathrm{x}+\mathrm{2}}}\: \\ $$

Question Number 135472 Answers: 1 Comments: 0

for x+y+z=10 with x,y,z∈N find Σ((10!)/(x!y!z!))

$${for}\:{x}+{y}+{z}=\mathrm{10}\:{with}\:{x},{y},{z}\in\mathbb{N} \\ $$$${find}\:\Sigma\frac{\mathrm{10}!}{{x}!{y}!{z}!} \\ $$

Question Number 135424 Answers: 1 Comments: 0

Find solution set the inequality (√(2x−5)) + (√(25−3x)) > x

$${Find}\:{solution}\:{set}\:{the}\:{inequality} \\ $$$$\sqrt{\mathrm{2}{x}−\mathrm{5}}\:+\:\sqrt{\mathrm{25}−\mathrm{3}{x}}\:>\:{x} \\ $$

Question Number 135420 Answers: 1 Comments: 0

Algebra Pipe A can fill a tank in two hours and pipe B can fill it in half the time it takes pipe C to empty it. When all 3 are opened, it takes 1.5 hours to fill the pool how much time is required for pipe 'C to empty the tank?

$${Algebra} \\ $$Pipe A can fill a tank in two hours and pipe B can fill it in half the time it takes pipe C to empty it. When all 3 are opened, it takes 1.5 hours to fill the pool how much time is required for pipe 'C to empty the tank?

Question Number 135418 Answers: 2 Comments: 0

Given x+(1/x) = 5 then ((x^4 +(1/x^4 ))/(x^2 −3x+1)) ?

$${Given}\:{x}+\frac{\mathrm{1}}{{x}}\:=\:\mathrm{5}\:{then}\:\frac{{x}^{\mathrm{4}} +\frac{\mathrm{1}}{{x}^{\mathrm{4}} }}{{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{1}}\:? \\ $$

Question Number 135415 Answers: 3 Comments: 1

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