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Question Number 104621 Answers: 1 Comments: 0

(1/((1−x)^2 ))−(4/((1+x)^2 ))=1

$$\frac{\mathrm{1}}{\left(\mathrm{1}−{x}\right)^{\mathrm{2}} }−\frac{\mathrm{4}}{\left(\mathrm{1}+{x}\right)^{\mathrm{2}} }=\mathrm{1} \\ $$

Question Number 104609 Answers: 1 Comments: 0

prove: ∫_0 ^1 ((x^4 (1−x)^4 )/(1+x^2 ))dx=((22)/7)−π

$${prove}: \\ $$$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{x}^{\mathrm{4}} \left(\mathrm{1}−{x}\right)^{\mathrm{4}} }{\mathrm{1}+{x}^{\mathrm{2}} }{dx}=\frac{\mathrm{22}}{\mathrm{7}}−\pi \\ $$

Question Number 104608 Answers: 1 Comments: 0

D^(1/2) (y)=1 ⇒ y(x)=(√(x/π))

$$\:\:{D}^{\frac{\mathrm{1}}{\mathrm{2}}} \left({y}\right)=\mathrm{1}\:\:\:\:\:\Rightarrow\:\:\:{y}\left({x}\right)=\sqrt{\frac{{x}}{\pi}} \\ $$

Question Number 104607 Answers: 0 Comments: 0

if a_0 =1 , ∀ n≥1 Σ_(p=0) ^n (a_(n−p) /((p+1)!))=0 explicit a_n in terms of n

$$\:{if}\:\:\:{a}_{\mathrm{0}} =\mathrm{1}\:\:\:,\:\forall\:{n}\geqslant\mathrm{1}\:\:\:\:\:\underset{{p}=\mathrm{0}} {\overset{{n}} {\sum}}\:\frac{{a}_{{n}−{p}} }{\left({p}+\mathrm{1}\right)!}=\mathrm{0}\: \\ $$$${explicit}\:\:{a}_{{n}} \:\:{in}\:{terms}\:{of}\:{n}\: \\ $$

Question Number 104606 Answers: 2 Comments: 0

lim_(x→0) {((x−1)/(∣x−1∣)) + ∣x∣}=?

$$\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\left\{\frac{{x}−\mathrm{1}}{\mid{x}−\mathrm{1}\mid}\:+\:\mid{x}\mid\right\}=? \\ $$

Question Number 104604 Answers: 1 Comments: 0

Σ_(n=1) ^∞ (1+(1/2)+...+(1/n))(1/2^n ) = ln4

$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+...+\frac{\mathrm{1}}{{n}}\right)\frac{\mathrm{1}}{\mathrm{2}^{{n}} }\:\:=\:{ln}\mathrm{4} \\ $$

Question Number 104603 Answers: 1 Comments: 0

lim_(x→−2) x∣x−2∣

$$\underset{{x}\rightarrow−\mathrm{2}} {\mathrm{lim}}\:{x}\mid{x}−\mathrm{2}\mid\: \\ $$

Question Number 104602 Answers: 0 Comments: 0

Question Number 104599 Answers: 0 Comments: 0

(1+t^3 )x′(t)+t^2 x(t)+2(x(t))^2 =0

$$\left(\mathrm{1}+\mathrm{t}^{\mathrm{3}} \right)\mathrm{x}'\left(\mathrm{t}\right)+\mathrm{t}^{\mathrm{2}} \mathrm{x}\left(\mathrm{t}\right)+\mathrm{2}\left(\mathrm{x}\left(\mathrm{t}\right)\right)^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 104595 Answers: 1 Comments: 0

Solve the DE x′′(t)+2x′(t)+x(t)=te^(−t)

$$\mathrm{Solve}\:\mathrm{the}\:\mathcal{DE} \\ $$$$\mathrm{x}''\left(\mathrm{t}\right)+\mathrm{2x}'\left(\mathrm{t}\right)+\mathrm{x}\left(\mathrm{t}\right)=\mathrm{te}^{−\mathrm{t}} \\ $$

Question Number 104592 Answers: 1 Comments: 0

(2xy−sec^2 x) dx + (x^2 +2y)dy = 0

$$\left(\mathrm{2}{xy}−\mathrm{sec}\:^{\mathrm{2}} {x}\right)\:{dx}\:+\:\left({x}^{\mathrm{2}} +\mathrm{2}{y}\right){dy}\:=\:\mathrm{0} \\ $$

Question Number 104588 Answers: 1 Comments: 1

solve in R ((96x−24)/(12x+5))=(√(−144x^2 +72x+7))

$${solve}\:{in}\:\mathbb{R} \\ $$$$\frac{\mathrm{96}{x}−\mathrm{24}}{\mathrm{12}{x}+\mathrm{5}}=\sqrt{−\mathrm{144}{x}^{\mathrm{2}} +\mathrm{72}{x}+\mathrm{7}} \\ $$

Question Number 104576 Answers: 4 Comments: 1

2sin 2x −4sin^2 x = 7cos 2x with (π/2)< x < π find sin 2x

$$\mathrm{2sin}\:\mathrm{2}{x}\:−\mathrm{4sin}\:^{\mathrm{2}} {x}\:=\:\mathrm{7cos}\:\mathrm{2}{x} \\ $$$${with}\:\frac{\pi}{\mathrm{2}}<\:{x}\:<\:\pi\: \\ $$$${find}\:\mathrm{sin}\:\mathrm{2}{x}\: \\ $$

Question Number 104572 Answers: 1 Comments: 1

Question Number 104571 Answers: 2 Comments: 0

(1/8) ÷ (1/8) ÷ (1/8) ÷ (1/8) = ?

$$\frac{\mathrm{1}}{\mathrm{8}}\:\boldsymbol{\div}\:\frac{\mathrm{1}}{\mathrm{8}}\:\boldsymbol{\div}\:\frac{\mathrm{1}}{\mathrm{8}}\:\boldsymbol{\div}\:\frac{\mathrm{1}}{\mathrm{8}}\:=\:? \\ $$

Question Number 104544 Answers: 2 Comments: 0

Given a_(n+1) = 5a_n −6a_(n−1) .If a_1 = 10 and a_2 = 26, find a_n ?

$$\mathcal{G}{iven}\:{a}_{{n}+\mathrm{1}} \:=\:\mathrm{5}{a}_{{n}} −\mathrm{6}{a}_{{n}−\mathrm{1}} \\ $$$$.\mathcal{I}{f}\:{a}_{\mathrm{1}} =\:\mathrm{10}\:{and}\:{a}_{\mathrm{2}} =\:\mathrm{26},\:{find}\:{a}_{{n}} ? \\ $$

Question Number 104542 Answers: 2 Comments: 0

Question Number 104539 Answers: 1 Comments: 0

1−(1/(1−(1/(1+(1/(1−(1/2)))))))

$$ \\ $$$$\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{1}+\frac{\mathrm{1}}{\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}}}}} \\ $$

Question Number 104536 Answers: 1 Comments: 1

The sum of two numbers is 384 and their GCD is 48. What is the LCM of the numbers ?

$$\boldsymbol{\mathrm{The}}\:\boldsymbol{\mathrm{sum}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{two}}\:\boldsymbol{\mathrm{numbers}}\:\boldsymbol{\mathrm{is}}\:\mathrm{384}\:\boldsymbol{\mathrm{and}} \\ $$$$\mathrm{t}\boldsymbol{\mathrm{heir}}\:\boldsymbol{\mathrm{GCD}}\:\boldsymbol{\mathrm{is}}\:\mathrm{48}.\:\boldsymbol{\mathrm{What}}\:\boldsymbol{\mathrm{is}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{LCM}}\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{numbers}}\:? \\ $$

Question Number 104533 Answers: 3 Comments: 0

find : lim_(x→1) (((x+2)^2 +(x+1)^3 −17)/((√(x+3))−((x+7))^(1/3) ))

$${find}\:: \\ $$$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{\left({x}+\mathrm{2}\right)^{\mathrm{2}} +\left({x}+\mathrm{1}\right)^{\mathrm{3}} −\mathrm{17}}{\sqrt{{x}+\mathrm{3}}−\sqrt[{\mathrm{3}}]{{x}+\mathrm{7}}} \\ $$

Question Number 105006 Answers: 2 Comments: 0

Miranda did market in 3 day. The monday, she bought 3kg of fish^ ,2kg of meat ,1kg of rice at 10000 $. The wednesday she bought 1kg of fish, 3kg of meat, 2kg of rice at 10000$. And the thursday she bought 4kg of fish, 2kg of meat,3 kg of rice at 12500$. 1) Which price(sum) will spend Miranda if she she go to the market at saturday to buy at the same price 3kg of fish, 1kg of meat and 1.5kg of rice?

$$ \\ $$$${Miranda}\:{did}\:{market}\:{in}\:\mathrm{3}\:{day}. \\ $$$${The}\:{monday},\:{she}\:{bought}\:\mathrm{3}{kg}\:{of}\:{fis}\bar {{h}} \\ $$$$,\mathrm{2}{kg}\:{of}\:{meat}\:,\mathrm{1}{kg}\:{of}\:{rice}\:{at}\:\mathrm{10000}\:\$. \\ $$$${The}\:{wednesday}\:{she}\:{bought}\:\mathrm{1}{kg}\:{of} \\ $$$${fish},\:\mathrm{3}{kg}\:{of}\:{meat},\:\mathrm{2}{kg}\:{of}\:{rice}\:{at} \\ $$$$\mathrm{10000\$}. \\ $$$${And}\:{the}\:{thursday}\:{she}\:{bought}\:\mathrm{4}{kg}\:{of} \\ $$$${fish},\:\mathrm{2}{kg}\:{of}\:{meat},\mathrm{3}\:{kg}\:{of}\:{rice}\:{at} \\ $$$$\mathrm{12500\$}. \\ $$$$\left.\mathrm{1}\right)\:{Which}\:{price}\left({sum}\right)\:{will}\:{spend}\:{Miranda} \\ $$$${if}\:{she}\:{she}\:{go}\:{to}\:{the}\:{market}\:{at} \\ $$$${saturday}\:{to}\:{buy}\:{at}\:{the}\:{same}\:{price} \\ $$$$\mathrm{3}{kg}\:{of}\:{fish},\:\mathrm{1}{kg}\:{of}\:{meat}\:{and}\:\mathrm{1}.\mathrm{5}{kg}\:{of} \\ $$$${rice}? \\ $$

Question Number 105001 Answers: 1 Comments: 1

Question Number 104998 Answers: 2 Comments: 2

Question Number 104997 Answers: 0 Comments: 0

Question Number 104523 Answers: 0 Comments: 0

∫((xdx)/((x^3 +x+1)^2 ))

$$\int\frac{\mathrm{xdx}}{\left(\mathrm{x}^{\mathrm{3}} +\mathrm{x}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 104517 Answers: 2 Comments: 0

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