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AllQuestion and Answers: Page 8

Question Number 208814    Answers: 1   Comments: 2

Question Number 208809    Answers: 0   Comments: 1

Question Number 208812    Answers: 1   Comments: 0

Question Number 208805    Answers: 0   Comments: 3

Integrate: (xdz − zdx) − a^2 (2xzdz − z^2 dx) + 2x^3 = 0

$$\mathrm{Integrate}: \\ $$$$\left(\mathrm{xdz}\:−\:\mathrm{zdx}\right)\:−\:\mathrm{a}^{\mathrm{2}} \left(\mathrm{2xzdz}\:−\:\mathrm{z}^{\mathrm{2}} \mathrm{dx}\right)\:+\:\mathrm{2x}^{\mathrm{3}} \:=\:\mathrm{0} \\ $$

Question Number 208791    Answers: 0   Comments: 1

If ∫ (dx/(x^3 (1 + x^6 )^(2/3) )) = xf(x).(1 + x^6 )^(1/3) + C where C is constant of integration then find f(x).

$$\mathrm{If}\:\int\:\frac{{dx}}{{x}^{\mathrm{3}} \left(\mathrm{1}\:+\:{x}^{\mathrm{6}} \right)^{\frac{\mathrm{2}}{\mathrm{3}}} }\:=\:{xf}\left({x}\right).\left(\mathrm{1}\:+\:{x}^{\mathrm{6}} \right)^{\frac{\mathrm{1}}{\mathrm{3}}} \:+\:{C}\: \\ $$$$\mathrm{where}\:{C}\:\mathrm{is}\:\mathrm{constant}\:\mathrm{of}\:\mathrm{integration}\:\mathrm{then} \\ $$$$\mathrm{find}\:{f}\left({x}\right). \\ $$

Question Number 208789    Answers: 0   Comments: 3

Why is surface tension formula divided by 2L that is, surface tension = (F/(2L)) why divided by 2L. Where did the 2 come from? Example. Calculate the force required to lift a needle 4cm long off the surface of water, if surface tension of water is 7.3 × 10^(−4) Nm^(− 1) Why is the formula surface tension = (F/(2L)) why not surface tension = (F/L)

$$\mathrm{Why}\:\mathrm{is}\:\mathrm{surface}\:\mathrm{tension}\:\mathrm{formula}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{2L} \\ $$$$\mathrm{that}\:\mathrm{is},\:\:\:\:\mathrm{surface}\:\mathrm{tension}\:\:=\:\:\frac{\mathrm{F}}{\mathrm{2L}} \\ $$$$\mathrm{why}\:\mathrm{divided}\:\mathrm{by}\:\:\mathrm{2L}. \\ $$$$\mathrm{Where}\:\mathrm{did}\:\mathrm{the}\:\mathrm{2}\:\mathrm{come}\:\mathrm{from}? \\ $$$$ \\ $$$$\mathrm{Example}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{force}\:\mathrm{required}\:\mathrm{to}\:\mathrm{lift}\:\mathrm{a}\:\mathrm{needle} \\ $$$$\mathrm{4cm}\:\mathrm{long}\:\mathrm{off}\:\mathrm{the}\:\mathrm{surface}\:\mathrm{of}\:\mathrm{water},\:\mathrm{if}\:\mathrm{surface} \\ $$$$\mathrm{tension}\:\mathrm{of}\:\mathrm{water}\:\mathrm{is}\:\:\mathrm{7}.\mathrm{3}\:×\:\mathrm{10}^{−\mathrm{4}} \mathrm{Nm}^{−\:\mathrm{1}} \\ $$$$ \\ $$$$\mathrm{Why}\:\mathrm{is}\:\mathrm{the}\:\mathrm{formula}\:\:\:\mathrm{surface}\:\mathrm{tension}\:\:=\:\:\frac{\mathrm{F}}{\mathrm{2L}} \\ $$$$\mathrm{why}\:\mathrm{not}\:\:\:\:\:\:\mathrm{surface}\:\mathrm{tension}\:\:=\:\:\frac{\mathrm{F}}{\mathrm{L}} \\ $$

Question Number 208782    Answers: 1   Comments: 0

Question Number 208783    Answers: 0   Comments: 3

Solve for x and y. x^y − y^x = 17

$$\mathrm{Solve}\:\mathrm{for}\:\:\mathrm{x}\:\:\mathrm{and}\:\:\mathrm{y}. \\ $$$$\:\:\:\:\mathrm{x}^{\mathrm{y}} \:\:−\:\:\mathrm{y}^{\mathrm{x}} \:\:=\:\:\mathrm{17} \\ $$

Question Number 208772    Answers: 2   Comments: 0

Question Number 208759    Answers: 0   Comments: 5

Question Number 208756    Answers: 0   Comments: 0

Question Number 208755    Answers: 1   Comments: 0

Question Number 208743    Answers: 1   Comments: 10

Question Number 208741    Answers: 1   Comments: 0

Question Number 208742    Answers: 0   Comments: 0

Question Number 208739    Answers: 0   Comments: 0

Question Number 208738    Answers: 1   Comments: 0

sum: (1/(1.4.7)) + (1/(4.7.10)) + (1/(7.10.13)) + (1/(10.13.16)) + (1/(13.16.19)) + ... + (1/(94.97.100))

$$\mathrm{sum}: \\ $$$$\:\:\:\frac{\mathrm{1}}{\mathrm{1}.\mathrm{4}.\mathrm{7}}\:\:\:+\:\:\frac{\mathrm{1}}{\mathrm{4}.\mathrm{7}.\mathrm{10}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{7}.\mathrm{10}.\mathrm{13}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{10}.\mathrm{13}.\mathrm{16}}\:\:+\:\:\frac{\mathrm{1}}{\mathrm{13}.\mathrm{16}.\mathrm{19}}\:\:+\:\:...\:\:+\:\:\frac{\mathrm{1}}{\mathrm{94}.\mathrm{97}.\mathrm{100}} \\ $$

Question Number 208733    Answers: 1   Comments: 0

2∫_(1/3) ^1 ((x(√(−3x^2 +4x−1)))/(7x^2 −4x+1))dx=? Exact solution needed.

$$\mathrm{2}\underset{\frac{\mathrm{1}}{\mathrm{3}}} {\overset{\mathrm{1}} {\int}}\frac{{x}\sqrt{−\mathrm{3}{x}^{\mathrm{2}} +\mathrm{4}{x}−\mathrm{1}}}{\mathrm{7}{x}^{\mathrm{2}} −\mathrm{4}{x}+\mathrm{1}}{dx}=? \\ $$$$\mathrm{Exact}\:\mathrm{solution}\:\mathrm{needed}. \\ $$

Question Number 208704    Answers: 1   Comments: 2

Find: arccos (arctg (5/(12)) + arcsin (4/5)) = ?

$$\mathrm{Find}: \\ $$$$\mathrm{arccos}\:\left(\mathrm{arctg}\:\frac{\mathrm{5}}{\mathrm{12}}\:\:+\:\:\mathrm{arcsin}\:\frac{\mathrm{4}}{\mathrm{5}}\right)\:=\:? \\ $$

Question Number 208692    Answers: 1   Comments: 0

∫_0 ^(π/2) xln sin x dx=?

$$\underset{\mathrm{0}} {\overset{\pi/\mathrm{2}} {\int}}{x}\mathrm{ln}\:\mathrm{sin}\:{x}\:{dx}=? \\ $$

Question Number 208690    Answers: 1   Comments: 0

Question Number 208686    Answers: 1   Comments: 0

cos^2 2x = sin^2 2x + ((√3)/2) x = ?

$$\mathrm{cos}^{\mathrm{2}} \:\mathrm{2x}\:=\:\mathrm{sin}^{\mathrm{2}} \:\mathrm{2x}\:+\:\frac{\sqrt{\mathrm{3}}}{\mathrm{2}} \\ $$$$\mathrm{x}\:=\:? \\ $$

Question Number 208685    Answers: 1   Comments: 0

25 tan x = 3 x = ?

$$\mathrm{25}\:\mathrm{tan}\:\mathrm{x}\:=\:\mathrm{3} \\ $$$$\mathrm{x}\:=\:? \\ $$

Question Number 208681    Answers: 2   Comments: 0

Question Number 208676    Answers: 1   Comments: 0

Question Number 208670    Answers: 2   Comments: 1

Find: ∫_0 ^( 5) (√((1/2) (x^2 − 2x + 1))) dx = ?

$$\mathrm{Find}:\:\:\:\int_{\mathrm{0}} ^{\:\mathrm{5}} \:\sqrt{\frac{\mathrm{1}}{\mathrm{2}}\:\left(\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{2x}\:+\:\mathrm{1}\right)}\:\mathrm{dx}\:\:=\:\:? \\ $$

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