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AlgebraQuestion and Answers: Page 222

Question Number 134763 Answers: 1 Comments: 0

Given a= (3)^(1/3) + (1/( (√3))) Find the value of 3a^3 −9a+1.

$$\mathrm{Given}\:{a}=\:\sqrt[{\mathrm{3}}]{\mathrm{3}}\:+\:\frac{\mathrm{1}}{\:\sqrt{\mathrm{3}}} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{3}{a}^{\mathrm{3}} −\mathrm{9}{a}+\mathrm{1}. \\ $$

Question Number 134733 Answers: 0 Comments: 0

Question Number 134854 Answers: 0 Comments: 0

(√x) why the root is so thing? How can i make it bold?

$$ \\ $$$$\sqrt{\boldsymbol{{x}}}\:\:\mathrm{why}\:\mathrm{the}\:\mathrm{root}\:\mathrm{is}\:\mathrm{so}\:\mathrm{thing}?\:\mathrm{How}\:\mathrm{can}\:\mathrm{i}\:\mathrm{make}\:\mathrm{it}\:\mathrm{bold}? \\ $$

Question Number 134668 Answers: 1 Comments: 0

1+1+4−6−8−10+12+14+16−18−20−22+... S_(900) = ?

$$\mathrm{1}+\mathrm{1}+\mathrm{4}−\mathrm{6}−\mathrm{8}−\mathrm{10}+\mathrm{12}+\mathrm{14}+\mathrm{16}−\mathrm{18}−\mathrm{20}−\mathrm{22}+... \\ $$$$\mathrm{S}_{\mathrm{900}} \:=\:? \\ $$

Question Number 134627 Answers: 1 Comments: 0

ALGEBRA If Bobby walks to school at 50m/min. He will be late for 3 minutes. If he walks 60 m/min, he arrives at school early by 2 mins. What is the distance between Bobby's home and school?

$$\mathcal{ALGEBRA} \\ $$If Bobby walks to school at 50m/min. He will be late for 3 minutes. If he walks 60 m/min, he arrives at school early by 2 mins. What is the distance between Bobby's home and school?

Question Number 134571 Answers: 1 Comments: 0

Prove the sequence Σ_(n=2) ^∞ (1/((ln n)^(100) )) divergent or convergent

$$\mathrm{Prove}\:\mathrm{the}\:\mathrm{sequence}\:\underset{\mathrm{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\left(\mathrm{ln}\:\mathrm{n}\right)^{\mathrm{100}} } \\ $$$$\mathrm{divergent}\:\mathrm{or}\:\mathrm{convergent}\: \\ $$

Question Number 135771 Answers: 0 Comments: 1

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Question Number 134467 Answers: 1 Comments: 0

determinant (((If x^2 =2y+5 and y^2 =2x+5 )),((what the value of x^3 −2x^2 y^2 +y^2 .)))

$$\begin{array}{|c|c|}{\mathrm{If}\:\mathrm{x}^{\mathrm{2}} =\mathrm{2y}+\mathrm{5}\:\mathrm{and}\:\mathrm{y}^{\mathrm{2}} =\mathrm{2x}+\mathrm{5}\:}\\{\mathrm{what}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}^{\mathrm{3}} −\mathrm{2x}^{\mathrm{2}} \mathrm{y}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} .}\\\hline\end{array} \\ $$

Question Number 134410 Answers: 1 Comments: 2

{ ((x^2 +y^2 +xy=2)),((x^2 +z^2 +zx=1)),((y^2 +z^2 +yz=1)) :} ⇒ (x+y+z)^2 =?

$$\:\begin{cases}{{x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{xy}=\mathrm{2}}\\{{x}^{\mathrm{2}} +{z}^{\mathrm{2}} +{zx}=\mathrm{1}}\\{{y}^{\mathrm{2}} +{z}^{\mathrm{2}} +{yz}=\mathrm{1}}\end{cases}\:\Rightarrow\:\left({x}+{y}+{z}\right)^{\mathrm{2}} \:=? \\ $$

Question Number 134335 Answers: 1 Comments: 0

Two Team A&B of workers at a bridge site. Each team consist of W workers. On a particular day, a worker was shifted from team A to team B . Now if the ratio of the amount of workdone by teamA in (W+1) he & by teamB in (W+2) hr is 10:12 rsp. Find W?

$$ \\ $$Two Team A&B of workers at a bridge site. Each team consist of W workers. On a particular day, a worker was shifted from team A to team B . Now if the ratio of the amount of workdone by teamA in (W+1) he & by teamB in (W+2) hr is 10:12 rsp. Find W?

Question Number 134331 Answers: 1 Comments: 0

cos^2 (((3π)/2)−x)=cos^2 (x+π) 0≤x≤π x=?

$$\mathrm{cos}^{\mathrm{2}} \left(\frac{\mathrm{3}\pi}{\mathrm{2}}−\mathrm{x}\right)=\mathrm{cos}^{\mathrm{2}} \left(\mathrm{x}+\pi\right) \\ $$$$\mathrm{0}\leqslant\mathrm{x}\leqslant\pi \\ $$$$\mathrm{x}=? \\ $$

Question Number 134297 Answers: 1 Comments: 0

Question Number 134278 Answers: 0 Comments: 0

Question Number 134277 Answers: 0 Comments: 0

Question Number 134269 Answers: 1 Comments: 0

Σ_(k = 2) ^(99) ((k^2 + 1)/(k^2 − 1))

$$\underset{\mathrm{k}\:\:\:=\:\:\:\:\mathrm{2}} {\overset{\mathrm{99}} {\sum}}\:\:\:\frac{\mathrm{k}^{\mathrm{2}} \:\:+\:\:\mathrm{1}}{\mathrm{k}^{\mathrm{2}} \:\:−\:\:\mathrm{1}} \\ $$

Question Number 134255 Answers: 2 Comments: 2

Question Number 134237 Answers: 1 Comments: 0

f(x)=((2x^(100!) )/((100!)!))+x^(100) +1 faind ((d^(100!) f(x))/dx^(100!) )=?

$${f}\left({x}\right)=\frac{\mathrm{2}{x}^{\mathrm{100}!} }{\left(\mathrm{100}!\right)!}+{x}^{\mathrm{100}} +\mathrm{1} \\ $$$${faind}\:\:\:\:\:\frac{{d}^{\mathrm{100}!} {f}\left({x}\right)}{{dx}^{\mathrm{100}!} }=? \\ $$

Question Number 134134 Answers: 1 Comments: 0

If cos^(−1) x_1 +cos^(−1) x_2 +...+cos^(−1) x_n =nπ, then x_1 + x_2 ^2 + x_3 ^3 + ...+ x_n ^n =?

$$\mathrm{If}\:\mathrm{cos}^{−\mathrm{1}} {x}_{\mathrm{1}} +\mathrm{cos}^{−\mathrm{1}} {x}_{\mathrm{2}} +...+\mathrm{cos}^{−\mathrm{1}} {x}_{{n}} ={n}\pi, \\ $$$$\mathrm{then}\:\:{x}_{\mathrm{1}} \:+\:{x}_{\mathrm{2}} ^{\mathrm{2}} \:+\:{x}_{\mathrm{3}} ^{\mathrm{3}} \:+\:...+\:{x}_{{n}} ^{{n}} \:=? \\ $$

Question Number 134067 Answers: 1 Comments: 0

Calculate lim_(n→∞) Π_(k=2) ^n ((k^3 −1)/(k^3 +1)) = ?

$$\:\mathrm{Calculate}\:\underset{\mathrm{n}\rightarrow\infty} {\mathrm{lim}}\:\underset{\mathrm{k}=\mathrm{2}} {\overset{\mathrm{n}} {\prod}}\:\frac{\mathrm{k}^{\mathrm{3}} −\mathrm{1}}{\mathrm{k}^{\mathrm{3}} +\mathrm{1}}\:=\:? \\ $$

Question Number 134061 Answers: 1 Comments: 0

If Σ a_n is a convergent series of nonnegative terms,what can be said about Σ a_n .a_(n+1) ? (a) always converges (b) always diverges (c) may converges or diverge

$$\mathrm{If}\:\Sigma\:\mathrm{a}_{\mathrm{n}} \:\mathrm{is}\:\mathrm{a}\:\mathrm{convergent}\:\mathrm{series}\:\mathrm{of} \\ $$$$\mathrm{nonnegative}\:\mathrm{terms},\mathrm{what}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{said}\:\mathrm{about}\:\Sigma\:\mathrm{a}_{\mathrm{n}} .\mathrm{a}_{\mathrm{n}+\mathrm{1}} \:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{always}\:\mathrm{converges} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{always}\:\mathrm{diverges} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{may}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverge} \\ $$

Question Number 134060 Answers: 2 Comments: 0

If p>1 and q>1 what can be said about the convergence of Σ_(n=2) ^∞ (1/(n^p .(ln n)^q )) ? (a) always converges (b) always diverges (c) may converges or diverges

$$\mathrm{If}\:\mathrm{p}>\mathrm{1}\:\mathrm{and}\:\mathrm{q}>\mathrm{1}\:\mathrm{what}\:\mathrm{can}\:\mathrm{be} \\ $$$$\mathrm{said}\:\mathrm{about}\:\mathrm{the}\:\mathrm{convergence}\: \\ $$$$\mathrm{of}\:\underset{\mathrm{n}=\mathrm{2}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{\mathrm{n}^{\mathrm{p}} .\left(\mathrm{ln}\:\mathrm{n}\right)^{\mathrm{q}} }\:? \\ $$$$\left(\mathrm{a}\right)\:\mathrm{always}\:\mathrm{converges} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{always}\:\mathrm{diverges} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{may}\:\mathrm{converges}\:\mathrm{or}\:\mathrm{diverges} \\ $$

Question Number 134052 Answers: 1 Comments: 0

Question Number 134034 Answers: 1 Comments: 0

how many zeros has the number 1000! at the end? and what is the last digit before these zeros?

$${how}\:{many}\:{zeros}\:{has}\:{the}\:{number} \\ $$$$\mathrm{1000}!\:{at}\:{the}\:{end}?\:{and}\:{what}\:{is}\:{the} \\ $$$${last}\:{digit}\:{before}\:{these}\:{zeros}? \\ $$

Question Number 134005 Answers: 1 Comments: 0

solve x^3 −2⌊x⌋=5

$${solve}\:{x}^{\mathrm{3}} −\mathrm{2}\lfloor{x}\rfloor=\mathrm{5} \\ $$

Question Number 133996 Answers: 2 Comments: 0

show that (√2)<log_2 3<(√3)

$${show}\:{that}\:\sqrt{\mathrm{2}}<\mathrm{log}_{\mathrm{2}} \:\mathrm{3}<\sqrt{\mathrm{3}} \\ $$

Question Number 133991 Answers: 1 Comments: 0

∣ 3x−∣ 4x+2 ∣∣ ≥ 4 > ∣ 5x+8 ∣

$$\:\mid\:\mathrm{3x}−\mid\:\mathrm{4x}+\mathrm{2}\:\mid\mid\:\geqslant\:\mathrm{4}\:>\:\mid\:\mathrm{5x}+\mathrm{8}\:\mid\: \\ $$

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