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Question Number 156361 Answers: 1 Comments: 2

Solve in R (1/( (√(x^2 - 1)))) =1− (2/x)

$$\mathrm{Solve}\:\mathrm{in}\:\mathbb{R} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{1}}}\:=\mathrm{1}−\:\frac{\mathrm{2}}{\mathrm{x}} \\ $$

Question Number 156359 Answers: 0 Comments: 0

if a;b;c>0 and ab+bc+ca=3 then prove that: (((a^3 + 1)(b^3 + 1)(c^3 + 1)))^(1/3) ≥ 2

$$\mathrm{if}\:\:\mathrm{a};\mathrm{b};\mathrm{c}>\mathrm{0}\:\:\mathrm{and}\:\:\mathrm{ab}+\mathrm{bc}+\mathrm{ca}=\mathrm{3} \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}: \\ $$$$\sqrt[{\mathrm{3}}]{\left(\mathrm{a}^{\mathrm{3}} \:+\:\mathrm{1}\right)\left(\mathrm{b}^{\mathrm{3}} \:+\:\mathrm{1}\right)\left(\mathrm{c}^{\mathrm{3}} \:+\:\mathrm{1}\right)}\:\geqslant\:\mathrm{2} \\ $$

Question Number 156339 Answers: 1 Comments: 0

∫_0 ^1 (x^(2n) /(arcsinx))dx=...???

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{2}{n}} }{{arcsinx}}{dx}=...??? \\ $$

Question Number 156338 Answers: 1 Comments: 2

Solve in R (1/( (√(x^2 - 1)))) = (2/x) - 1

$$\mathrm{Solve}\:\mathrm{in}\:\mathbb{R} \\ $$$$\frac{\mathrm{1}}{\:\sqrt{\mathrm{x}^{\mathrm{2}} \:-\:\mathrm{1}}}\:=\:\frac{\mathrm{2}}{\mathrm{x}}\:-\:\mathrm{1} \\ $$$$ \\ $$

Question Number 156335 Answers: 1 Comments: 1

Question Number 156333 Answers: 1 Comments: 0

Question Number 156395 Answers: 0 Comments: 0

A car is moving along a straight road level when the driver see a boy crossing the road 1.5m when the driver immediately applies the brakes which produces constant retardation in the first second. After applying the brakes the car travels 25m and in the next second it traveles 15m. i) find the retardation in m/s^2 ii) show that the car comes to rest at the point where it started

$${A}\:{car}\:{is}\:{moving}\:{along}\:{a}\:{straight}\:{road}\:{level}\:{when}\: \\ $$$${the}\:{driver}\:{see}\:{a}\:{boy}\:{crossing}\:{the}\:{road}\:\mathrm{1}.\mathrm{5}{m}\:{when}\:{the}\:{driver} \\ $$$${immediately}\:{applies}\:{the}\:{brakes}\:{which}\:{produces} \\ $$$$\:{constant}\:{retardation}\:{in}\:{the}\:{first}\:{second}.\:{After}\:{applying}\:{the}\:{brakes} \\ $$$${the}\:{car}\:{travels}\:\mathrm{25}{m}\:{and}\:{in}\:{the}\:{next}\:{second}\:{it} \\ $$$${traveles}\:\mathrm{15}{m}.\: \\ $$$$\left.{i}\right)\:{find}\:{the}\:{retardation}\:{in}\:{m}/{s}^{\mathrm{2}} \\ $$$$\left.{ii}\right)\:{show}\:{that}\:{the}\:{car}\:{comes}\:{to}\:{rest}\:{at}\: \\ $$$${the}\:{point}\:{where}\:{it}\:{started} \\ $$

Question Number 156330 Answers: 0 Comments: 0

Question Number 156328 Answers: 1 Comments: 4

Question Number 156321 Answers: 0 Comments: 1

cos^4 ((π/9))+cos^4 (((2π)/9))+cos^4 (((3π)/9))+cos^4 (((4π)/9))=?

$$\:\:\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\pi}{\mathrm{9}}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\mathrm{2}\pi}{\mathrm{9}}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\mathrm{3}\pi}{\mathrm{9}}\right)+\mathrm{cos}\:^{\mathrm{4}} \left(\frac{\mathrm{4}\pi}{\mathrm{9}}\right)=? \\ $$

Question Number 156319 Answers: 1 Comments: 1

∫ ((36)/((12cos x+5sin x)^2 )) dx=?

$$\:\int\:\frac{\mathrm{36}}{\left(\mathrm{12cos}\:\mathrm{x}+\mathrm{5sin}\:\mathrm{x}\right)^{\mathrm{2}} }\:\mathrm{dx}=? \\ $$

Question Number 156316 Answers: 3 Comments: 1

Question Number 156313 Answers: 0 Comments: 0

rationalize (2/( (2)^(1/3) −(6)^(1/3) −(9)^(1/3) ))

$$\:\mathrm{rationalize}\:\frac{\mathrm{2}}{\:\sqrt[{\mathrm{3}}]{\mathrm{2}}−\sqrt[{\mathrm{3}}]{\mathrm{6}}−\sqrt[{\mathrm{3}}]{\mathrm{9}}}\: \\ $$

Question Number 156308 Answers: 0 Comments: 0

Find exact form sin 1°

$$\mathrm{Find}\:\mathrm{exact}\:\mathrm{form}\:\mathrm{sin}\:\mathrm{1}° \\ $$

Question Number 156305 Answers: 1 Comments: 0

∫ ((sec^2 (x))/(3sin^2 (x)−1)) dx

$$\:\:\int\:\frac{\mathrm{sec}\:^{\mathrm{2}} \left(\mathrm{x}\right)}{\mathrm{3sin}\:^{\mathrm{2}} \left(\mathrm{x}\right)−\mathrm{1}}\:\mathrm{dx} \\ $$

Question Number 156296 Answers: 0 Comments: 4

Question Number 156295 Answers: 2 Comments: 0

Question Number 156292 Answers: 0 Comments: 0

(1/3)+(3/(3×7))+(5/(3×7×11))+(7/(3×7×11×15))+…

$$\frac{\mathrm{1}}{\mathrm{3}}+\frac{\mathrm{3}}{\mathrm{3}×\mathrm{7}}+\frac{\mathrm{5}}{\mathrm{3}×\mathrm{7}×\mathrm{11}}+\frac{\mathrm{7}}{\mathrm{3}×\mathrm{7}×\mathrm{11}×\mathrm{15}}+\ldots \\ $$

Question Number 156290 Answers: 0 Comments: 0

Question Number 156281 Answers: 2 Comments: 0

∫_(−3) ^5 (√(∣x∣^3 ))dx

$$\int_{−\mathrm{3}} ^{\mathrm{5}} \:\sqrt{\mid{x}\mid^{\mathrm{3}} }{dx} \\ $$

Question Number 156275 Answers: 1 Comments: 0

Helllo to All Good (morning night) we are her too shar our knowelegdes we must respect evrey one we need that positiv energy sorry for my English

$${Helllo}\:{to}\:{All}\:{Good}\:\left({morning}\:{night}\right) \\ $$$${we}\:{are}\:{her}\:{too}\:{shar}\:{our}\:{knowelegdes} \\ $$$${we}\:{must}\:{respect}\:{evrey}\:{one}\:{we}\:{need}\:{that} \\ $$$${positiv}\:{energy}\:{sorry}\:{for}\:{my}\:{English} \\ $$$$ \\ $$

Question Number 156270 Answers: 1 Comments: 1

Show that i = sin^(− 1) (((√2)/2))^2 in air, if the refractive index n = ((sin^2 (60))/(sin^2 (45)))

$$\mathrm{Show}\:\mathrm{that}\:\:\:\:\:\:\mathrm{i}\:\:\:\:=\:\:\:\mathrm{sin}^{−\:\mathrm{1}} \left(\frac{\sqrt{\mathrm{2}}}{\mathrm{2}}\right)^{\mathrm{2}} \:\:\:\:\mathrm{in}\:\mathrm{air},\:\mathrm{if}\:\mathrm{the}\:\mathrm{refractive} \\ $$$$\mathrm{index}\:\:\:\:\:\:\:\:\mathrm{n}\:\:\:=\:\:\:\frac{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{60}\right)}{\mathrm{sin}^{\mathrm{2}} \left(\mathrm{45}\right)} \\ $$

Question Number 156259 Answers: 0 Comments: 0

Question Number 156257 Answers: 0 Comments: 0

∫ ((xsin^(−1) (x^2 ))/(1−x^4 )) dx=?

$$\:\int\:\frac{{x}\mathrm{sin}^{−\mathrm{1}} \left({x}^{\mathrm{2}} \right)}{\mathrm{1}−{x}^{\mathrm{4}} }\:{dx}=? \\ $$

Question Number 156253 Answers: 1 Comments: 0

Question Number 156252 Answers: 1 Comments: 1

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