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Question Number 71790 Answers: 1 Comments: 0

Question Number 71756 Answers: 1 Comments: 0

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

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

Question Number 71717 Answers: 1 Comments: 3

Question Number 71698 Answers: 1 Comments: 2

Question Number 71695 Answers: 1 Comments: 0

Question Number 71693 Answers: 1 Comments: 0

Question Number 71680 Answers: 1 Comments: 0

Question Number 71674 Answers: 1 Comments: 0

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 71665 Answers: 1 Comments: 0

calculate ∫_0 ^∞ (dx/((x+1)^2 ((√(x^2 +4)))))

$${calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\frac{{dx}}{\left({x}+\mathrm{1}\right)^{\mathrm{2}} \left(\sqrt{{x}^{\mathrm{2}} +\mathrm{4}}\right)} \\ $$

Question Number 71664 Answers: 1 Comments: 1

find nature of the sequence U_n =(1/n)(Σ_(k=1) ^n (1/k))^2

$${find}\:{nature}\:{of}\:{the}\:{sequence}\:{U}_{{n}} =\frac{\mathrm{1}}{{n}}\left(\sum_{{k}=\mathrm{1}} ^{{n}} \:\frac{\mathrm{1}}{{k}}\right)^{\mathrm{2}} \\ $$

Question Number 71663 Answers: 1 Comments: 1

calculate A_n =∫_0 ^∞ (dx/((x^2 +1)(x^2 +2)....(x^2 +n))) with n integr and n≥1

$${calculate}\:{A}_{{n}} =\int_{\mathrm{0}} ^{\infty} \:\frac{{dx}}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} +\mathrm{2}\right)....\left({x}^{\mathrm{2}} \:+{n}\right)} \\ $$$${with}\:{n}\:{integr}\:{and}\:{n}\geqslant\mathrm{1} \\ $$

Question Number 71649 Answers: 0 Comments: 3

Question Number 71645 Answers: 1 Comments: 1

Question Number 71643 Answers: 0 Comments: 3

Question Number 71640 Answers: 0 Comments: 0

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 71617 Answers: 0 Comments: 0

One person drags a 10 kilogram sandbag at a distance of 8 meters employing a horizontal force of 90 N. Then lift the sandbag at a height of 1.5 meters, calculate the total work done by the person.

$${One}\:{person}\:{drags}\:{a}\:\mathrm{10}\:{kilogram} \\ $$$${sandbag}\:{at}\:{a}\:{distance}\:{of}\:\mathrm{8}\:{meters} \\ $$$${employing}\:{a}\:{horizontal}\:{force}\:{of} \\ $$$$\mathrm{90}\:{N}.\:{Then}\:{lift}\:{the}\:{sandbag}\:{at}\:{a} \\ $$$${height}\:{of}\:\mathrm{1}.\mathrm{5}\:{meters},\:{calculate}\:{the} \\ $$$${total}\:{work}\:{done}\:{by}\:{the}\:{person}. \\ $$

Question Number 71616 Answers: 0 Comments: 0

A boy leaves a 0.4 kilogram stone from the top of a 25 meter−high tower. Given g=10 m/s^2 , calvulate the total work done by the force of the weight until the stone hits the ground

$${A}\:{boy}\:{leaves}\:{a}\:\mathrm{0}.\mathrm{4}\:{kilogram}\:{stone}\: \\ $$$${from}\:{the}\:{top}\:{of}\:{a}\:\mathrm{25}\:{meter}−{high}\: \\ $$$${tower}.\:{Given}\:{g}=\mathrm{10}\:{m}/{s}^{\mathrm{2}} ,\:{calvulate} \\ $$$${the}\:{total}\:{work}\:{done}\:{by}\:{the}\:{force}\:{of}\:{the} \\ $$$${weight}\:{until}\:{the}\:{stone}\:{hits}\:{the}\:{ground} \\ $$

Question Number 71611 Answers: 2 Comments: 2