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Question Number 94573    Answers: 1   Comments: 2

Given a, b, and c, 3 real numbers which satisfy the equation { ((a+b+c=312)),((c+a=192)) :} Find these real numbers such that they form 3 consecutive terms of a Geometric Progression.

$$\mathrm{Given}\:\mathrm{a},\:\mathrm{b},\:\mathrm{and}\:\mathrm{c},\:\mathrm{3}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{which}\:\mathrm{satisfy} \\ $$$$\mathrm{the}\:\mathrm{equation}\:\begin{cases}{\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{312}}\\{\mathrm{c}+\mathrm{a}=\mathrm{192}}\end{cases} \\ $$$$\mathrm{Find}\:\mathrm{these}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{such}\:\mathrm{that}\:\mathrm{they}\:\mathrm{form} \\ $$$$\mathrm{3}\:\mathrm{consecutive}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{a}\:\mathrm{Geometric}\:\mathrm{Progression}. \\ $$

Question Number 94572    Answers: 0   Comments: 0

Question Number 94579    Answers: 1   Comments: 0

A study indicates that x months from now the population of a certain town will be decreasing at the rate of 5+3x^(2/3) people per month. By how much will the population of the town increase per the next 8 months. I need help with the above question, please.

$$\mathrm{A}\:\mathrm{study}\:\mathrm{indicates}\:\mathrm{that}\:{x}\:\mathrm{months}\:\mathrm{from}\:\mathrm{now} \\ $$$$\mathrm{the}\:\mathrm{population}\:\mathrm{of}\:\mathrm{a}\:\mathrm{certain}\:\mathrm{town}\:\mathrm{will}\:\mathrm{be}\: \\ $$$$\mathrm{decreasing}\:\mathrm{at}\:\mathrm{the}\:\mathrm{rate}\:\mathrm{of}\:\mathrm{5}+\mathrm{3}{x}^{\frac{\mathrm{2}}{\mathrm{3}}} \:\mathrm{people} \\ $$$$\mathrm{per}\:\mathrm{month}.\:\mathrm{By}\:\mathrm{how}\:\mathrm{much}\:\mathrm{will}\:\mathrm{the}\:\mathrm{population} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{town}\:\mathrm{increase}\:\mathrm{per}\:\mathrm{the}\:\mathrm{next}\:\mathrm{8}\:\mathrm{months}. \\ $$$$\boldsymbol{{I}}\:\boldsymbol{{need}}\:\boldsymbol{{help}}\:\boldsymbol{{with}}\:\boldsymbol{{the}}\:\boldsymbol{{above}}\:\boldsymbol{{question}},\:\boldsymbol{{please}}. \\ $$

Question Number 94559    Answers: 0   Comments: 6

Question Number 94556    Answers: 2   Comments: 1

Question Number 94553    Answers: 1   Comments: 0

solve ((∣x+2∣−x)/x) < 2

$$\mathrm{solve}\:\frac{\mid{x}+\mathrm{2}\mid−{x}}{{x}}\:<\:\mathrm{2}\: \\ $$

Question Number 94544    Answers: 0   Comments: 0

1\Show that the function f(x)=[x] is of Riemann for all segments of R 2\Show that the function f(x) defined within x∈[0,1] f(x)= { ((1 if x∈Q∩[0,1])),((0 otherwise)) :} is not of Riemann on x∈[0,1]

$$\mathrm{1}\backslash\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)=\left[\mathrm{x}\right]\:\mathrm{is}\:\mathrm{of}\:\mathrm{Riemann} \\ $$$$\mathrm{for}\:\mathrm{all}\:\mathrm{segments}\:\mathrm{of}\:\mathbb{R} \\ $$$$\mathrm{2}\backslash\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{function}\:\mathrm{f}\left(\mathrm{x}\right)\:\mathrm{defined}\:\mathrm{within}\:\mathrm{x}\in\left[\mathrm{0},\mathrm{1}\right] \\ $$$$\mathrm{f}\left(\mathrm{x}\right)=\begin{cases}{\mathrm{1}\:\mathrm{if}\:\mathrm{x}\in\mathbb{Q}\cap\left[\mathrm{0},\mathrm{1}\right]}\\{\mathrm{0}\:\:\mathrm{otherwise}}\end{cases}\:\:\mathrm{is}\:\mathrm{not}\:\mathrm{of}\:\mathrm{Riemann}\:\mathrm{on}\:\mathrm{x}\in\left[\mathrm{0},\mathrm{1}\right] \\ $$

Question Number 94530    Answers: 2   Comments: 1

Question Number 94528    Answers: 1   Comments: 1

Question Number 94523    Answers: 0   Comments: 1

Question Number 94522    Answers: 3   Comments: 0

if sinA+sinB=n and cosA+cosB=m then sin(A+B)=? a: ((3mn)/(m^2 +n^2 )) b:((2mn)/(m^2 +n^2 )) c:((mn)/(m^2 +n^2 )) d:((2mn)/(m+n)) with steps?

$$\mathrm{if}\:\:\mathrm{sinA}+\mathrm{sinB}=\mathrm{n}\:\mathrm{and}\:\mathrm{cosA}+\mathrm{cosB}=\mathrm{m} \\ $$$$\mathrm{then}\:\:\mathrm{sin}\left(\mathrm{A}+\mathrm{B}\right)=? \\ $$$$\mathrm{a}:\:\frac{\mathrm{3mn}}{\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} }\:\:\:\:\mathrm{b}:\frac{\mathrm{2mn}}{\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} }\:\:\mathrm{c}:\frac{\mathrm{mn}}{\mathrm{m}^{\mathrm{2}} +\mathrm{n}^{\mathrm{2}} }\:\:\mathrm{d}:\frac{\mathrm{2mn}}{\mathrm{m}+\mathrm{n}} \\ $$$$\mathrm{with}\:\mathrm{steps}? \\ $$

Question Number 94521    Answers: 3   Comments: 3

if a^(10) +a^5 +1=0 then a^(2005) +(1/a^(2005) )=? a: a^(10) +a^(11) b:a^(10) +a^5 c:3(a^(10) +a^5 ) d:0 with steps?

$$\mathrm{if}\:\mathrm{a}^{\mathrm{10}} +\mathrm{a}^{\mathrm{5}} +\mathrm{1}=\mathrm{0} \\ $$$$\mathrm{then}\:\mathrm{a}^{\mathrm{2005}} +\frac{\mathrm{1}}{\mathrm{a}^{\mathrm{2005}} }=? \\ $$$$\mathrm{a}:\:\mathrm{a}^{\mathrm{10}} +\mathrm{a}^{\mathrm{11}} \:\:\:\:\mathrm{b}:\mathrm{a}^{\mathrm{10}} +\mathrm{a}^{\mathrm{5}} \:\:\:\mathrm{c}:\mathrm{3}\left(\mathrm{a}^{\mathrm{10}} +\mathrm{a}^{\mathrm{5}} \right)\:\:\mathrm{d}:\mathrm{0} \\ $$$$\mathrm{with}\:\mathrm{steps}? \\ $$

Question Number 94520    Answers: 4   Comments: 0

∫ (√(e^(4x) +1)) dx

$$\int\:\sqrt{{e}^{\mathrm{4}{x}} +\mathrm{1}}\:{dx}\: \\ $$

Question Number 94510    Answers: 0   Comments: 3

∫ ((√(tan x))/(sin x.cos x))dx

$$\int\:\frac{\sqrt{\mathrm{tan}\:{x}}}{\mathrm{sin}\:{x}.\mathrm{cos}\:{x}}{dx}\: \\ $$

Question Number 94508    Answers: 2   Comments: 0

Question Number 94500    Answers: 1   Comments: 0

what is E(X) if the joint density function of X and Y is given f(x,y) = { ((24xy , 0<x<1,0<y<1−x)),((0 , elsewhere)) :}

$$\mathrm{what}\:\mathrm{is}\:\mathrm{E}\left(\mathrm{X}\right)\:\mathrm{if}\:\mathrm{the}\:\mathrm{joint} \\ $$$$\mathrm{density}\:\mathrm{function}\:\mathrm{of}\:\mathrm{X}\:\mathrm{and}\:\mathrm{Y}\: \\ $$$$\mathrm{is}\:\mathrm{given}\:\mathrm{f}\left(\mathrm{x},\mathrm{y}\right)\:=\:\begin{cases}{\mathrm{24xy}\:,\:\mathrm{0}<\mathrm{x}<\mathrm{1},\mathrm{0}<\mathrm{y}<\mathrm{1}−\mathrm{x}}\\{\mathrm{0}\:,\:\mathrm{elsewhere}}\end{cases} \\ $$

Question Number 94479    Answers: 1   Comments: 0

find solution in C x^4 +x^3 +x^2 +x+1 = 0

$$\mathrm{find}\:\mathrm{solution}\:\mathrm{in}\:\mathbb{C}\: \\ $$$$\mathrm{x}^{\mathrm{4}} +\mathrm{x}^{\mathrm{3}} +\mathrm{x}^{\mathrm{2}} +\mathrm{x}+\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 94463    Answers: 0   Comments: 2

lim_(x→∞) ((6x^(k−2) +3x^2 +10)/(3x^5 +x+20)) then k^2 +1=?

$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\frac{\mathrm{6x}^{\mathrm{k}−\mathrm{2}} +\mathrm{3x}^{\mathrm{2}} +\mathrm{10}}{\mathrm{3x}^{\mathrm{5}} +\mathrm{x}+\mathrm{20}} \\ $$$$\mathrm{then}\:\mathrm{k}^{\mathrm{2}} +\mathrm{1}=? \\ $$

Question Number 94457    Answers: 1   Comments: 0

a practical example 1 construction worker can excavate a pit in 3 hours. how long will it take 3 workers to do this job?

$${a}\:{practical}\:{example} \\ $$$$\mathrm{1}\:\mathrm{construction}\:\mathrm{worker}\:\mathrm{can}\:\mathrm{excavate}\:\mathrm{a} \\ $$$$\mathrm{pit}\:\mathrm{in}\:\mathrm{3}\:\mathrm{hours}.\:\mathrm{how}\:\mathrm{long}\:\mathrm{will}\:\mathrm{it}\:\mathrm{take}\:\mathrm{3} \\ $$$$\mathrm{workers}\:\mathrm{to}\:\mathrm{do}\:\mathrm{this}\:\mathrm{job}? \\ $$

Question Number 94456    Answers: 1   Comments: 0

log_x 16+log_(16) x=log_(512) x+log_x 512 x=?

$$\mathrm{log}_{\mathrm{x}} \mathrm{16}+\mathrm{log}_{\mathrm{16}} \mathrm{x}=\mathrm{log}_{\mathrm{512}} \mathrm{x}+\mathrm{log}_{\mathrm{x}} \mathrm{512} \\ $$$$\mathrm{x}=? \\ $$

Question Number 94455    Answers: 1   Comments: 3

Solve (D^2 −2D+1)y=xe^x sinx pleas help me sir

$${Solve}\:\left({D}^{\mathrm{2}} −\mathrm{2}{D}+\mathrm{1}\right){y}={xe}^{{x}} {sinx}\: \\ $$$${pleas}\:{help}\:{me}\:{sir}\: \\ $$

Question Number 94448    Answers: 3   Comments: 2

Question Number 94434    Answers: 0   Comments: 0

what is super-erf(y)−hyper ?

$${what}\:{is}\:{super}-{erf}\left({y}\right)−{hyper}\:? \\ $$

Question Number 94432    Answers: 0   Comments: 3

∫ ((x^n −x^(n−2) )/(Σ_(r=0) ^(2n) C_r ^(2n) x^r ))dx=? The result is a little pretty

$$\int\:\frac{{x}^{{n}} −{x}^{{n}−\mathrm{2}} }{\underset{{r}=\mathrm{0}} {\overset{\mathrm{2}{n}} {\sum}}{C}_{{r}} ^{\mathrm{2}{n}} {x}^{{r}} }{dx}=? \\ $$$${The}\:{result}\:{is}\:{a}\:{little}\:{pretty} \\ $$

Question Number 95190    Answers: 1   Comments: 1

Question Number 94424    Answers: 1   Comments: 4

y=x^x y^′ =?

$$\mathrm{y}=\mathrm{x}^{\mathrm{x}} \\ $$$$\mathrm{y}^{'} =? \\ $$

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