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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

Question Number 71593 Answers: 1 Comments: 0

Question Number 71578 Answers: 0 Comments: 0

Question Number 71572 Answers: 2 Comments: 1

Question Number 71570 Answers: 1 Comments: 0

Solve: (2x + x^2 )y′′ − 2(1 + x)y′ + 2y = 0 Given y = x^2 is a solution.

$$\mathrm{Solve}:\:\:\:\:\:\left(\mathrm{2x}\:+\:\mathrm{x}^{\mathrm{2}} \right)\mathrm{y}''\:−\:\mathrm{2}\left(\mathrm{1}\:+\:\mathrm{x}\right)\mathrm{y}'\:+\:\mathrm{2y}\:\:=\:\:\mathrm{0} \\ $$$$\mathrm{Given}\:\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{2}} \:\:\mathrm{is}\:\mathrm{a}\:\mathrm{solution}. \\ $$

Question Number 71564 Answers: 1 Comments: 2

(z−i)^4 =−7+24i

$$\left(\mathrm{z}−\mathrm{i}\right)^{\mathrm{4}} =−\mathrm{7}+\mathrm{24i} \\ $$

Question Number 71563 Answers: 2 Comments: 0

find maximum and minimum cos x+(√3) sin x for (π/6)≤x≤π

$$\mathrm{find}\:\mathrm{maximum}\:\mathrm{and}\:\mathrm{minimum} \\ $$$$\mathrm{cos}\:{x}+\sqrt{\mathrm{3}}\:\mathrm{sin}\:{x} \\ $$$${for} \\ $$$$\frac{\pi}{\mathrm{6}}\leqslant{x}\leqslant\pi \\ $$

Question Number 71560 Answers: 0 Comments: 0

Question Number 71551 Answers: 1 Comments: 0

whats the mean R^(++) ?and R^(−−) ?

$${whats}\:{the}\:{mean}\:{R}^{++} \:?{and}\:{R}^{−−} ? \\ $$

Question Number 71550 Answers: 1 Comments: 0

Question Number 71548 Answers: 1 Comments: 0

let f:U⊂R^n →R^p be an application where U is an open set prove that ∀x∈U,∃h∈R^n such as x+h∈U

$$\mathrm{let}\:\mathrm{f}:\boldsymbol{\mathrm{U}}\subset\mathbb{R}^{\mathrm{n}} \rightarrow\mathbb{R}^{\mathrm{p}} \:\mathrm{be}\:\mathrm{an}\:\mathrm{application} \\ $$$$\mathrm{where}\:\boldsymbol{\mathrm{U}}\:\mathrm{is}\:\mathrm{an}\:\mathrm{open}\:\mathrm{set} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\forall\mathrm{x}\in\boldsymbol{{U}},\exists\mathrm{h}\in\mathbb{R}^{\mathrm{n}} \mathrm{such}\:\mathrm{as} \\ $$$$\mathrm{x}+\mathrm{h}\in\boldsymbol{{U}} \\ $$

Question Number 71538 Answers: 2 Comments: 1

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.

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

Question Number 71518 Answers: 1 Comments: 8

Express (√(28)) as continued fraction

$$\mathrm{Express}\:\:\sqrt{\mathrm{28}}\:\:\mathrm{as}\:\mathrm{continued}\:\mathrm{fraction} \\ $$

Question Number 71517 Answers: 1 Comments: 0

Question Number 71516 Answers: 1 Comments: 0

5y′′=(1+y′^2 )^(3/2) please solve the differtial equation

$$\mathrm{5y}''=\left(\mathrm{1}+\mathrm{y}'^{\mathrm{2}} \right)^{\frac{\mathrm{3}}{\mathrm{2}}} \\ $$$$\mathrm{please}\:\mathrm{solve}\:\mathrm{the}\:\mathrm{differtial}\:\mathrm{equation} \\ $$

Question Number 71508 Answers: 1 Comments: 2

montrer que:∀a,b∈R ona 2∣ab∣≤a^2 +b^2 Endeduire que ∀x_1 ,...,x_n ∈R on a: (Σ_(i=1) ^n ∣x_i ∣)^2 ≤nΣ_(i=1) ^n x_i ^2 please i need help

$$\mathrm{montrer}\:\mathrm{que}:\forall\mathrm{a},\mathrm{b}\in\mathbb{R}\:\mathrm{ona} \\ $$$$\mathrm{2}\mid\mathrm{ab}\mid\leqslant\mathrm{a}^{\mathrm{2}} +\mathrm{b}^{\mathrm{2}} \\ $$$$\mathrm{Endeduire}\:\mathrm{que}\:\forall\mathrm{x}_{\mathrm{1}} ,...,\mathrm{x}_{\mathrm{n}} \in\mathbb{R}\:\mathrm{on}\:\mathrm{a}: \\ $$$$\left(\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mid\mathrm{x}_{\mathrm{i}} \mid\right)^{\mathrm{2}} \leqslant\mathrm{n}\underset{\mathrm{i}=\mathrm{1}} {\overset{\mathrm{n}} {\sum}}\mathrm{x}_{\mathrm{i}} ^{\mathrm{2}} \\ $$$$\:\:\:\:\:\boldsymbol{\mathrm{please}}\:\boldsymbol{\mathrm{i}}\:\boldsymbol{\mathrm{need}}\:\boldsymbol{\mathrm{help}} \\ $$

Question Number 71499 Answers: 1 Comments: 1

Question Number 71490 Answers: 2 Comments: 2

Question Number 71506 Answers: 1 Comments: 1

Question Number 71513 Answers: 0 Comments: 2

Question Number 71448 Answers: 0 Comments: 1

find the domain f(x)=(1/(sin(sin(x))))

$${find}\:{the}\:{domain} \\ $$$$ \\ $$$${f}\left({x}\right)=\frac{\mathrm{1}}{{sin}\left({sin}\left({x}\right)\right)} \\ $$

Question Number 71673 Answers: 1 Comments: 1

Question Number 71439 Answers: 1 Comments: 1

If a seller could purchase goods at an 8% lower price by keeping the selling price fixed, his profit over the cost price would increase from the current x% to (x+10)%. So, what is the value of x?

$${If}\:{a}\:{seller}\:{could}\:{purchase}\:{goods}\:{at}\:{an} \\ $$$$\mathrm{8\%}\:{lower}\:{price}\:{by}\:{keeping}\:{the}\:{selling} \\ $$$${price}\:{fixed},\:{his}\:{profit}\:{over}\:{the}\:{cost} \\ $$$${price}\:{would}\:{increase}\:{from}\:{the}\: \\ $$$${current}\:{x\%}\:{to}\:\left({x}+\mathrm{10}\right)\%.\:{So},\:{what}\:{is} \\ $$$${the}\:{value}\:{of}\:{x}? \\ $$

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