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AlgebraQuestion and Answers: Page 295

Question Number 72291 Answers: 1 Comments: 0

Question Number 72289 Answers: 2 Comments: 0

Bonjour. Aidez moi a resoudre le systeme suivant dans R^2 x−y=2 xy=20

$${Bonjour}. \\ $$$${Aidez}\:{moi}\:{a}\:{resoudre}\:{le}\:{systeme}\: \\ $$$${suivant}\:\:\:\:{dans}\:\mathbb{R}^{\mathrm{2}} \:\:\:\:\: \\ $$$${x}−{y}=\mathrm{2} \\ $$$${xy}=\mathrm{20} \\ $$

Question Number 72190 Answers: 1 Comments: 2

3^x +4^x =5^x

$$\mathrm{3}^{\mathrm{x}} +\mathrm{4}^{\mathrm{x}} =\mathrm{5}^{\mathrm{x}} \\ $$

Question Number 72185 Answers: 0 Comments: 2

Question Number 72118 Answers: 0 Comments: 1

Question Number 72117 Answers: 0 Comments: 1

Please help with the proof of cauchy inequality.

$${Please}\:{help}\:{with}\:{the}\:{proof}\:{of}\:{cauchy}\:{inequality}. \\ $$

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Question Number 72175 Answers: 1 Comments: 3

(x^2 +y^2 −1)^3 =x^2 y^3 how large (area) is your heart ♥ ?

$$\left(\boldsymbol{{x}}^{\mathrm{2}} +\boldsymbol{{y}}^{\mathrm{2}} −\mathrm{1}\right)^{\mathrm{3}} =\boldsymbol{{x}}^{\mathrm{2}} \boldsymbol{{y}}^{\mathrm{3}} \\ $$$$ \\ $$$${how}\:{large}\:\left({area}\right)\:{is}\:{your}\:{heart}\:\heartsuit\:? \\ $$

Question Number 74587 Answers: 0 Comments: 0

If sum of n arithmetic means between two number is 20.if last mean is double of 1st mean and one is three times of another number. find the numbers.

$$\mathrm{If}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{n}\:\mathrm{arithmetic}\:\mathrm{means}\:\mathrm{between}\: \\ $$$$\mathrm{two}\:\mathrm{number}\:\mathrm{is}\:\mathrm{20}.\mathrm{if}\:\mathrm{last}\:\mathrm{mean}\:\mathrm{is}\:\mathrm{double} \\ $$$$\mathrm{of}\:\mathrm{1st}\:\mathrm{mean}\:\mathrm{and}\:\mathrm{one}\:\mathrm{is}\:\mathrm{three}\:\mathrm{times}\:\mathrm{of} \\ $$$$\mathrm{another}\:\mathrm{number}.\:\mathrm{find}\:\mathrm{the}\:\mathrm{numbers}. \\ $$$$ \\ $$

Question Number 71960 Answers: 1 Comments: 0

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Question Number 71824 Answers: 2 Comments: 1

solve x^x^x^(2019) =2019

$${solve}\: \\ $$$${x}^{{x}^{{x}^{\mathrm{2019}} } } =\mathrm{2019} \\ $$

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Question Number 71776 Answers: 1 Comments: 0

Question Number 71761 Answers: 0 Comments: 5

Find at least the first four non zero term in a power series expansion about x = 0 for a general solution to z′′ − x^2 z = 0

$$\mathrm{Find}\:\mathrm{at}\:\mathrm{least}\:\mathrm{the}\:\mathrm{first}\:\mathrm{four}\:\mathrm{non}\:\mathrm{zero}\:\mathrm{term}\:\mathrm{in}\:\mathrm{a}\:\mathrm{power} \\ $$$$\mathrm{series}\:\mathrm{expansion}\:\mathrm{about}\:\:\mathrm{x}\:\:=\:\:\mathrm{0}\:\:\mathrm{for}\:\mathrm{a}\:\mathrm{general}\:\mathrm{solution} \\ $$$$\mathrm{to}\:\:\:\:\mathrm{z}''\:\:−\:\:\mathrm{x}^{\mathrm{2}} \mathrm{z}\:\:\:=\:\:\mathrm{0} \\ $$

Question Number 71750 Answers: 0 Comments: 2

∫ cos^3 θ (1 − sin^3 θ) Using beta function

$$\int\:\mathrm{cos}^{\mathrm{3}} \theta\:\left(\mathrm{1}\:−\:\mathrm{sin}^{\mathrm{3}} \theta\right) \\ $$$$\mathrm{Using}\:\mathrm{beta}\:\mathrm{function} \\ $$

Question Number 71729 Answers: 1 Comments: 2

find dU if U=x^2 e^(x/y)

$${find}\:{dU}\:\:\:{if}\:\:\:{U}={x}^{\mathrm{2}} {e}^{\frac{{x}}{{y}}} \\ $$$$ \\ $$

Question Number 71756 Answers: 1 Comments: 0

A=((8+3(√(21))))^(1/3) + ((8−3(√(21))))^(1/3) find A

$${A}=\sqrt[{\mathrm{3}}]{\mathrm{8}+\mathrm{3}\sqrt{\mathrm{21}}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{8}−\mathrm{3}\sqrt{\mathrm{21}}} \\ $$$$ \\ $$$${find}\:{A} \\ $$

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Question Number 71666 Answers: 1 Comments: 1

f:z→z f(x+y)=f(x)+f(y)+3(4xy−1) ,f(1)=0 ∀x,y ∈z evaluate f(19)

$${f}:{z}\rightarrow{z} \\ $$$$ \\ $$$${f}\left({x}+{y}\right)={f}\left({x}\right)+{f}\left({y}\right)+\mathrm{3}\left(\mathrm{4}{xy}−\mathrm{1}\right) \\ $$$$ \\ $$$$,{f}\left(\mathrm{1}\right)=\mathrm{0} \\ $$$$ \\ $$$$\forall{x},{y}\:\in{z} \\ $$$${evaluate}\:{f}\left(\mathrm{19}\right) \\ $$

Question Number 71633 Answers: 1 Comments: 0

let a,b,c ∈IR_+ show that (a+b)(a+c)≥2(√(abc(a+b+c)))

$$\mathrm{let}\:\mathrm{a},\mathrm{b},\mathrm{c}\:\in\mathrm{IR}_{+} \\ $$$$\mathrm{show}\:\mathrm{that}\:\left(\mathrm{a}+\mathrm{b}\right)\left(\mathrm{a}+\mathrm{c}\right)\geqslant\mathrm{2}\sqrt{\mathrm{abc}\left(\mathrm{a}+\mathrm{b}+\mathrm{c}\right)} \\ $$$$ \\ $$

Question Number 71534 Answers: 2 Comments: 0

a number consists of digits 1 and 2. the sum of its digits is 2018. if the number is multiplied with 5, the sum of the digits will be 10000. find how many digits this number has.

$${a}\:{number}\:{consists}\:{of}\:{digits}\:\mathrm{1}\:{and}\:\mathrm{2}. \\ $$$${the}\:{sum}\:{of}\:{its}\:{digits}\:{is}\:\mathrm{2018}. \\ $$$${if}\:{the}\:{number}\:{is}\:{multiplied}\:{with}\:\mathrm{5},\: \\ $$$${the}\:{sum}\:{of}\:{the}\:{digits}\:{will}\:{be}\:\mathrm{10000}. \\ $$$${find}\:{how}\:{many}\:{digits}\:{this}\:{number} \\ $$$${has}. \\ $$

Question Number 71533 Answers: 1 Comments: 0

Three interior angles of a nonagon are equal and the sum of the other six is 1050° Find the size of one of the equal angles.

$$\mathrm{Three}\:\mathrm{interior}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{nonagon}\:\mathrm{are} \\ $$$$\mathrm{equal}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{six}\:\mathrm{is}\:\mathrm{1050}° \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{size}\:\mathrm{of}\:\mathrm{one}\:\mathrm{of}\:\mathrm{the}\:\mathrm{equal}\:\mathrm{angles}. \\ $$

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