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Question Number 32845    Answers: 1   Comments: 0

how many moles are there in 3g of Na_2_ CO_3

$${how}\:{many}\:{moles}\:{are}\:{there}\:{in}\:\mathrm{3}{g}\:{of} \\ $$$${Na}_{\mathrm{2}_{} } {CO}_{\mathrm{3}} \\ $$

Question Number 32844    Answers: 0   Comments: 1

sketch on the x−y plain the locus of a point,P which moves such that its x and y coordinates are same. state the locus.

$${sketch}\:{on}\:{the}\:{x}−{y}\:{plain}\:{the}\:{locus} \\ $$$${of}\:{a}\:{point},{P}\:{which}\:{moves}\:{such}\:{that} \\ $$$${its}\:{x}\:{and}\:\:{y}\:{coordinates}\:{are}\:{same}. \\ $$$${state}\:{the}\:{locus}. \\ $$

Question Number 32841    Answers: 1   Comments: 0

A+B+C=180^0 3sin A +4cosB =6 3cosA + 4sin B =(√(13)) sin C=....

$${A}+{B}+{C}=\mathrm{180}^{\mathrm{0}} \\ $$$$\mathrm{3}{sin}\:{A}\:+\mathrm{4}{cosB}\:=\mathrm{6} \\ $$$$\mathrm{3}{cosA}\:+\:\mathrm{4}{sin}\:{B}\:=\sqrt{\mathrm{13}} \\ $$$${sin}\:{C}=.... \\ $$

Question Number 32837    Answers: 0   Comments: 1

the length of the line segment joining A and B is (√(10)) .Given that its double the line segment joining the points (7,n) and (6,2) find the possible values of n.

$${the}\:{length}\:{of}\:{the}\:{line}\:{segment}\:{joining} \\ $$$${A}\:{and}\:{B}\:{is}\:\sqrt{\mathrm{10}}\:.{Given}\:{that}\:{its}\:{double} \\ $$$${the}\:{line}\:{segment}\:{joining}\:{the}\:{points} \\ $$$$\left(\mathrm{7},{n}\right)\:{and}\:\left(\mathrm{6},\mathrm{2}\right)\:{find}\:{the}\:{possible}\:{values}\:{of}\:{n}. \\ $$$$ \\ $$

Question Number 32838    Answers: 2   Comments: 2

the points M(1,1),N(2,4) andR (3 ,q) lie on theresame straight line. find the coordinates of R

$${the}\:{points}\:{M}\left(\mathrm{1},\mathrm{1}\right),{N}\left(\mathrm{2},\mathrm{4}\right)\:{andR}\:\left(\mathrm{3}\:,{q}\right) \\ $$$${lie}\:{on}\:{theresame}\:{straight}\:{line}. \\ $$$${find}\:{the}\:{coordinates}\:{of}\:{R} \\ $$

Question Number 32834    Answers: 1   Comments: 0

find the value of k for which the length of the line segment joining (k^ ,2) and (−1,4) is 2(√2) units. show full working...

$${find}\:\:{the}\:{value}\:{of}\:{k}\:{for}\:{which}\:{the}\: \\ $$$${length}\:{of}\:{the}\:{line}\:{segment}\:{joining} \\ $$$$\left(\bar {{k}},\mathrm{2}\right)\:{and}\:\left(−\mathrm{1},\mathrm{4}\right)\:{is}\:\mathrm{2}\sqrt{\mathrm{2}}\:{units}. \\ $$$$\:\:\:\:{show}\:{full}\:{working}... \\ $$

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 ) = ....???

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

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