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Question Number 32832    Answers: 0   Comments: 0

Determine n such that 1001n+1 is perfect cube.

$$\mathrm{Determine}\:\mathrm{n}\:\mathrm{such}\:\mathrm{that}\:\mathrm{1001n}+\mathrm{1}\:\mathrm{is} \\ $$$$\mathrm{perfect}\:\mathrm{cube}. \\ $$

Question Number 32830    Answers: 0   Comments: 0

Thank you

$$\mathrm{Thank}\:\mathrm{you} \\ $$

Question Number 32810    Answers: 1   Comments: 2

Question Number 33004    Answers: 0   Comments: 3

how do i solve for x a) 2^(3−x) +2^x = 6 b) (log_3 x)^2 − 6(log_3 x) + 9=0

$${how}\:{do}\:{i}\:{solve}\: \\ $$$$\:\:\:\:{for}\:{x}\: \\ $$$$\left.{a}\right)\:\mathrm{2}^{\mathrm{3}−{x}} +\mathrm{2}^{{x}} =\:\mathrm{6} \\ $$$$\left.{b}\right)\:\left({log}_{\mathrm{3}} {x}\right)^{\mathrm{2}} \:−\:\mathrm{6}\left({log}_{\mathrm{3}} {x}\right)\:+\:\mathrm{9}=\mathrm{0} \\ $$

Question Number 32965    Answers: 0   Comments: 2

Question Number 32960    Answers: 1   Comments: 0

log_2 x+log_4 x+log_(16) x=7

$$\:\boldsymbol{\mathrm{log}}_{\mathrm{2}} \boldsymbol{{x}}+\boldsymbol{\mathrm{log}}_{\mathrm{4}} \boldsymbol{{x}}+\boldsymbol{\mathrm{log}}_{\mathrm{16}} \boldsymbol{{x}}=\mathrm{7} \\ $$

Question Number 32789    Answers: 0   Comments: 0

∣∫_a ^b f(x)dx≤∣∫_a ^b ∣f(x)∣dx∣

$$\mid\underset{{a}} {\overset{{b}} {\int}}{f}\left({x}\right){dx}\leqslant\mid\underset{{a}} {\overset{{b}} {\int}}\mid{f}\left({x}\right)\mid{dx}\mid \\ $$

Question Number 32788    Answers: 0   Comments: 1

The least positive integral value of ′x′ satisfying : (e^x −2)(sin (x+(π/4)))(x−log_e 2_ )(sinx − cosx)<0

$$\boldsymbol{{T}}{he}\:{least}\:{positive}\:{integral}\:{value}\:{of} \\ $$$$'{x}'\:{satisfying}\:: \\ $$$$\left({e}^{{x}} −\mathrm{2}\right)\left(\mathrm{sin}\:\left({x}+\frac{\pi}{\mathrm{4}}\right)\right)\left({x}−\mathrm{log}_{{e}} \:\underset{} {\mathrm{2}}\right)\left({sinx}\:−\:{cosx}\right)<\mathrm{0} \\ $$

Question Number 32785    Answers: 1   Comments: 0

∫((3x^2 +2x−4)/(7x^2 −9x+2))dx

$$\int\frac{\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{4}}{\mathrm{7}{x}^{\mathrm{2}} −\mathrm{9}{x}+\mathrm{2}}{dx} \\ $$

Question Number 32780    Answers: 2   Comments: 0

10−8=(p/9)

$$\mathrm{10}−\mathrm{8}=\frac{{p}}{\mathrm{9}} \\ $$

Question Number 32776    Answers: 1   Comments: 0

Find the optimum points of the function y=f(x) f(x)=2x^3 −3x^2 −36x+34

$${Find}\:{the}\:{optimum}\:{points}\:{of} \\ $$$${the}\:{function}\:{y}={f}\left({x}\right) \\ $$$$\:\:{f}\left({x}\right)=\mathrm{2}{x}^{\mathrm{3}} −\mathrm{3}{x}^{\mathrm{2}} −\mathrm{36}{x}+\mathrm{34} \\ $$

Question Number 32775    Answers: 1   Comments: 0

Find the area bounded by the curve y=3x^2 +2x−3,the x axis and the line x=5 and x=2

$${Find}\:{the}\:{area}\:{bounded}\:{by}\:{the} \\ $$$${curve}\:{y}=\mathrm{3}{x}^{\mathrm{2}} +\mathrm{2}{x}−\mathrm{3},{the}\:{x}\:{axis} \\ $$$${and}\:{the}\:{line}\:{x}=\mathrm{5}\:{and}\:{x}=\mathrm{2} \\ $$

Question Number 32768    Answers: 1   Comments: 0

Prove that a^2 +b^2 +c^2 ≥ab+bc+ca ∀ a,b,c∈R

$$\mathrm{Prove}\:\mathrm{that}\:{a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} \geqslant{ab}+{bc}+{ca} \\ $$$$\forall\:{a},{b},{c}\in\mathbb{R} \\ $$

Question Number 32767    Answers: 0   Comments: 2

For a,b,c≥0 if a+b+c=n, determine minimum and maximum values of a^2 +b^2 +c^2 −ab−bc−ca.

$$\mathrm{For}\:{a},{b},{c}\geqslant\mathrm{0}\:\mathrm{if}\:{a}+{b}+{c}={n},\:\mathrm{determine} \\ $$$$\mathrm{minimum}\:\mathrm{and}\:\mathrm{maximum}\:\mathrm{values}\:\mathrm{of} \\ $$$${a}^{\mathrm{2}} +{b}^{\mathrm{2}} +{c}^{\mathrm{2}} −{ab}−{bc}−{ca}. \\ $$

Question Number 32765    Answers: 0   Comments: 0

Question Number 32763    Answers: 1   Comments: 1

Question Number 32760    Answers: 1   Comments: 0

if y=3x^(4 ) .find the approximate percentage increase in y when x increase by 2(1/2)%.

$$\mathrm{if}\:{y}=\mathrm{3}{x}^{\mathrm{4}\:} .{find}\:{the}\:{approximate}\:{percentage} \\ $$$${increase}\:{in}\:{y}\:{when}\:{x}\:{increase}\:{by}\:\:\:\mathrm{2}\frac{\mathrm{1}}{\mathrm{2}}\%. \\ $$

Question Number 32757    Answers: 1   Comments: 5

A mass oscillating on a spring has amplitude of 1.2m and a period of 2s.Deduce the equation for the displacement x if the timing starts at the instant when the masd has its maximum displacement. b)calculate the time interval from t=0 before the displacement is 0.08m

$${A}\:{mass}\:{oscillating}\:{on}\:{a}\:{spring} \\ $$$${has}\:{amplitude}\:{of}\:\mathrm{1}.\mathrm{2}{m}\:{and}\:{a}\:{period} \\ $$$${of}\:\mathrm{2}{s}.{Deduce}\:{the}\:{equation}\:{for} \\ $$$${the}\:{displacement}\:{x}\:{if}\:{the}\:{timing} \\ $$$${starts}\:{at}\:{the}\:{instant}\:{when}\:{the}\:{masd} \\ $$$${has}\:{its}\:{maximum}\:{displacement}. \\ $$$$\left.{b}\right){calculate}\:{the}\:{time}\:{interval}\:{from} \\ $$$${t}=\mathrm{0}\:{before}\:{the}\:{displacement}\:{is} \\ $$$$\mathrm{0}.\mathrm{08}{m} \\ $$$$ \\ $$

Question Number 32756    Answers: 1   Comments: 0

Please help Find the area bounded by y(x+2)=x^4 ,x=0,y=0,and x=3

$${Please}\:{help} \\ $$$$ \\ $$$${Find}\:{the}\:{area}\:{bounded}\:{by} \\ $$$${y}\left({x}+\mathrm{2}\right)={x}^{\mathrm{4}} ,{x}=\mathrm{0},{y}=\mathrm{0},{and}\:{x}=\mathrm{3} \\ $$

Question Number 32755    Answers: 0   Comments: 5

Σ_(n=1) ^∞ (1/n^2 ) = ....???

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\frac{\mathrm{1}}{{n}^{\mathrm{2}} }\:=\:....??? \\ $$

Question Number 32745    Answers: 1   Comments: 0

The first, second and middle terms of an AP are a, b, c respectively. Their sum is

$$\mathrm{The}\:\mathrm{first},\:\mathrm{second}\:\mathrm{and}\:\mathrm{middle}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an} \\ $$$$\mathrm{AP}\:\mathrm{are}\:{a},\:{b},\:{c}\:\mathrm{respectively}.\:\mathrm{Their}\:\mathrm{sum}\:\mathrm{is} \\ $$

Question Number 32743    Answers: 2   Comments: 1

f (f (n)) = 2n f (n) = ?

$${f}\:\left({f}\:\left({n}\right)\right)\:\:=\:\:\mathrm{2}{n} \\ $$$${f}\:\left({n}\right)\:\:=\:\:? \\ $$

Question Number 32741    Answers: 0   Comments: 0

find ∫_0 ^1 ((ln(t^2 +2t cosx +1))/t)dt .

$${find}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\frac{{ln}\left({t}^{\mathrm{2}} \:+\mathrm{2}{t}\:{cosx}\:+\mathrm{1}\right)}{{t}}{dt}\:. \\ $$

Question Number 32740    Answers: 0   Comments: 2

find∫_0 ^∞ ((ln(x^2 +t^2 ))/(1+t^2 ))dt

$${find}\int_{\mathrm{0}} ^{\infty} \:\frac{{ln}\left({x}^{\mathrm{2}} \:+{t}^{\mathrm{2}} \right)}{\mathrm{1}+{t}^{\mathrm{2}} }{dt} \\ $$

Question Number 32739    Answers: 0   Comments: 1

let f(x)=∫_0 ^∞ (e^(−t) /(1+xt))dt calculate f^((n)) (0).

$${let}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\infty} \:\:\:\frac{{e}^{−{t}} }{\mathrm{1}+{xt}}{dt} \\ $$$${calculate}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right). \\ $$

Question Number 32737    Answers: 1   Comments: 0

let give 0≤x≤1 calculate ∫_0 ^∞ ((arctan((x/t)))/(1+t^2 )) dt

$${let}\:{give}\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:\:{calculate}\:\:\int_{\mathrm{0}} ^{\infty} \frac{{arctan}\left(\frac{{x}}{{t}}\right)}{\mathrm{1}+{t}^{\mathrm{2}} }\:{dt} \\ $$

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