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Question Number 62570 Answers: 0 Comments: 1

Question Number 62556 Answers: 1 Comments: 2

((1+3)/3) + ((1+3+5)/3^2 ) + ((1+3+5+7)/3^3 ) + ... = (a/b) , a, b ∈ Z^+

$$\frac{\mathrm{1}+\mathrm{3}}{\mathrm{3}}\:+\:\frac{\mathrm{1}+\mathrm{3}+\mathrm{5}}{\mathrm{3}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}+\mathrm{3}+\mathrm{5}+\mathrm{7}}{\mathrm{3}^{\mathrm{3}} }\:+\:...\:\:=\:\:\:\frac{{a}}{{b}}\:\:,\:\:{a},\:{b}\:\in\:\:\mathbb{Z}^{+} \: \\ $$

Question Number 62554 Answers: 0 Comments: 0

If a & b are two natural numbers then the following relation holds always. a×b=gcd(a,b)×lcm(a,b) ^• If a,b & c are three natural numbers what relation(anologous to the above) holds between numbers and their gcd & lcm?

$${If}\:{a}\:\&\:{b}\:{are}\:{two}\:{natural}\:{numbers} \\ $$$${then}\:{the}\:{following}\:{relation}\:{holds} \\ $$$${always}. \\ $$$$\:\:\:\:\:{a}×{b}=\mathrm{gcd}\left({a},{b}\right)×\mathrm{lcm}\left({a},{b}\right) \\ $$$$\:^{\bullet} {If}\:{a},{b}\:\&\:{c}\:\:{are}\:{three}\:{natural}\:{numbers} \\ $$$$\:\:\:{what}\:{relation}\left({anologous}\:{to}\:{the}\:{above}\right) \\ $$$$\:\:\:\:{holds}\:{between}\:{numbers}\:{and}\:{their} \\ $$$$\:\:\:\mathrm{gcd}\:\&\:\mathrm{lcm}? \\ $$

Question Number 62542 Answers: 1 Comments: 1

Question Number 62539 Answers: 1 Comments: 0

lim_(x→∞) ((x^3 +sin(2x)−2sin(x))/(arctan(x^3 )−(arctan(x))^3 ))

$$\mathrm{li}\underset{\mathrm{x}\rightarrow\infty} {\mathrm{m}}\frac{\mathrm{x}^{\mathrm{3}} +\mathrm{sin}\left(\mathrm{2x}\right)−\mathrm{2sin}\left(\mathrm{x}\right)}{\mathrm{arctan}\left(\mathrm{x}^{\mathrm{3}} \right)−\left(\mathrm{arctan}\left(\mathrm{x}\right)\right)^{\mathrm{3}} } \\ $$

Question Number 62538 Answers: 0 Comments: 0

Question Number 62587 Answers: 1 Comments: 1

three forces having equal magnitude s of 10N,20N and 30N make angles of 30°,120° and 210° respectively with the positive direction of the x axis. By scale drawing find the magnitude and the direction of the resultant force

$${three}\:{forces}\:{having}\:{equal}\:{magnitude} \\ $$$${s}\:{of}\:\mathrm{10}{N},\mathrm{20}{N}\:{and}\:\mathrm{30}{N}\:{make}\:{angles}\: \\ $$$${of}\:\mathrm{30}°,\mathrm{120}°\:{and}\:\mathrm{210}°\:{respectively}\:{with} \\ $$$${the}\:{positive}\:{direction}\:{of}\:{the}\:{x}\:{axis}. \\ $$$${By}\:{scale}\:{drawing}\:{find}\:{the}\:{magnitude} \\ $$$${and}\:{the}\:{direction}\:{of}\:{the}\:{resultant}\: \\ $$$${force} \\ $$

Question Number 62534 Answers: 1 Comments: 0

Question Number 62519 Answers: 1 Comments: 0

Question Number 62523 Answers: 1 Comments: 0

Question Number 62517 Answers: 4 Comments: 2

Question Number 62494 Answers: 0 Comments: 0

Question Number 62489 Answers: 3 Comments: 0

solve for x: (((√(2 − x)) + (√(2 + x)))/((√(2 − x)) − (√(2 + x)))) = 3

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x}:\:\:\:\:\:\:\:\frac{\sqrt{\mathrm{2}\:−\:\mathrm{x}}\:+\:\sqrt{\mathrm{2}\:+\:\mathrm{x}}}{\sqrt{\mathrm{2}\:−\:\mathrm{x}}\:−\:\sqrt{\mathrm{2}\:+\:\mathrm{x}}}\:\:=\:\:\mathrm{3} \\ $$

Question Number 62486 Answers: 2 Comments: 1

Question Number 62468 Answers: 1 Comments: 1

Question Number 62462 Answers: 1 Comments: 0

Question Number 62609 Answers: 1 Comments: 0

If 5∣x∣ + 4∣y∣ = 4 and 2∣x∣ − 4∣y∣ = 10, then find x and y.

$$\mathrm{If}\:\:\mathrm{5}\mid{x}\mid\:+\:\mathrm{4}\mid{y}\mid\:=\:\mathrm{4}\:\mathrm{and}\:\mathrm{2}\mid{x}\mid\:−\:\mathrm{4}\mid{y}\mid\:=\:\mathrm{10}, \\ $$$$\mathrm{then}\:\mathrm{find}\:{x}\:\mathrm{and}\:{y}. \\ $$

Question Number 62456 Answers: 1 Comments: 1

Question Number 62455 Answers: 0 Comments: 3

Question Number 62611 Answers: 0 Comments: 2

If α and β are the roots of x^2 −(a+1)x+(1/2)(a^2 +a+1)=0 then α^2 +β^2 =_____.

$$\mathrm{If}\:\alpha\:\mathrm{and}\:\beta\:\mathrm{are}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of} \\ $$$${x}^{\mathrm{2}} −\left({a}+\mathrm{1}\right){x}+\frac{\mathrm{1}}{\mathrm{2}}\left({a}^{\mathrm{2}} +{a}+\mathrm{1}\right)=\mathrm{0}\:\mathrm{then} \\ $$$$\alpha^{\mathrm{2}} +\beta^{\mathrm{2}} =\_\_\_\_\_. \\ $$

Question Number 62610 Answers: 2 Comments: 2

Find the value of x in (1/(x−1)) + (1/(x−2)) = (3/(x−3)) .

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x}\:\mathrm{in} \\ $$$$\frac{\mathrm{1}}{{x}−\mathrm{1}}\:+\:\frac{\mathrm{1}}{{x}−\mathrm{2}}\:=\:\frac{\mathrm{3}}{{x}−\mathrm{3}}\:\:. \\ $$

Question Number 62453 Answers: 0 Comments: 3

∫ (x/(e^x − 1))dx, for x > 0

$$\int\:\frac{\mathrm{x}}{\mathrm{e}^{\mathrm{x}} \:−\:\mathrm{1}}\mathrm{dx},\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{for}\:\:\mathrm{x}\:>\:\mathrm{0} \\ $$

Question Number 62452 Answers: 1 Comments: 0

Find the remainder when 2014! is divisible by 2017

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{when}\:\:\:\mathrm{2014}!\:\:\mathrm{is}\:\mathrm{divisible}\:\mathrm{by}\:\:\mathrm{2017} \\ $$

Question Number 62449 Answers: 2 Comments: 1

Find the number of digit in 2^(50)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{digit}\:\mathrm{in}\:\:\:\:\mathrm{2}^{\mathrm{50}} \\ $$

Question Number 62448 Answers: 1 Comments: 1

Question Number 62440 Answers: 0 Comments: 2

let h(x)= arctan(x+(1/x)) 1)calculate h^((n)) (x) and h^((n)) (1) 2)developp f(x)at integr serie at x_0 =1

$${let}\:{h}\left({x}\right)=\:{arctan}\left({x}+\frac{\mathrm{1}}{{x}}\right) \\ $$$$\left.\mathrm{1}\right){calculate}\:{h}^{\left({n}\right)} \left({x}\right)\:{and}\:{h}^{\left({n}\right)} \left(\mathrm{1}\right) \\ $$$$\left.\mathrm{2}\right){developp}\:{f}\left({x}\right){at}\:{integr}\:{serie}\:{at}\:{x}_{\mathrm{0}} =\mathrm{1} \\ $$

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