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AlgebraQuestion and Answers: Page 66

Question Number 195592 Answers: 0 Comments: 2

f(x)=((1376)/((x−1)^(ln((2/(4689)))) )) dom f(x)=? answer this

$${f}\left({x}\right)=\frac{\mathrm{1376}}{\left({x}−\mathrm{1}\right)^{{ln}\left(\frac{\mathrm{2}}{\mathrm{4689}}\right)} } \\ $$$${dom}\:{f}\left({x}\right)=? \\ $$$${answer}\:{this} \\ $$

Question Number 199608 Answers: 2 Comments: 0

1) 3<∣2x−1∣<7 find Σx ;x∈Z 2) 4≤∣x−2∣<5 find Σx ;x∈Z

$$\left.\mathrm{1}\right)\:\:\:\mathrm{3}<\mid\mathrm{2}{x}−\mathrm{1}\mid<\mathrm{7}\:\:{find}\:\Sigma{x}\:\:\:\:;{x}\in{Z} \\ $$$$\left.\mathrm{2}\right)\:\:\:\mathrm{4}\leqslant\mid{x}−\mathrm{2}\mid<\mathrm{5}\:\:{find}\:\Sigma{x}\:\:\:\:;{x}\in{Z} \\ $$$$ \\ $$

Question Number 195511 Answers: 1 Comments: 0

Question Number 195435 Answers: 2 Comments: 0

(√(5+1(√(6+2(√(7+3(√(8+4(√(...)))))))))) = ?

$$\sqrt{\mathrm{5}+\mathrm{1}\sqrt{\mathrm{6}+\mathrm{2}\sqrt{\mathrm{7}+\mathrm{3}\sqrt{\mathrm{8}+\mathrm{4}\sqrt{...}}}}}\:\:=\:\:\:? \\ $$

Question Number 195428 Answers: 2 Comments: 0

3^a =7^b =441 ((ab)/(a+b))=?

$$\mathrm{3}^{{a}} =\mathrm{7}^{{b}} =\mathrm{441} \\ $$$$\frac{{ab}}{{a}+{b}}=? \\ $$

Question Number 195419 Answers: 1 Comments: 0

x≠0. Σ_(i=1) ^n ix^(i−1) =?

$${x}\neq\mathrm{0}.\:\underset{{i}=\mathrm{1}} {\overset{{n}} {\sum}}{ix}^{{i}−\mathrm{1}} =? \\ $$

Question Number 195413 Answers: 0 Comments: 5

Question Number 195407 Answers: 2 Comments: 0

f′(2)=g′(2)=g(2)=2 then find the (fog)′(2)=?

$$\mathrm{f}'\left(\mathrm{2}\right)=\mathrm{g}'\left(\mathrm{2}\right)=\mathrm{g}\left(\mathrm{2}\right)=\mathrm{2} \\ $$$$\mathrm{then}\:\mathrm{find}\:\mathrm{the}\:\left(\mathrm{fog}\right)'\left(\mathrm{2}\right)=? \\ $$

Question Number 195404 Answers: 1 Comments: 0

Question Number 195377 Answers: 0 Comments: 0

Question Number 195370 Answers: 0 Comments: 0

Question Number 195369 Answers: 1 Comments: 0

Question Number 195368 Answers: 0 Comments: 0

Question Number 195361 Answers: 0 Comments: 0

Question Number 195357 Answers: 2 Comments: 0

Question Number 195356 Answers: 2 Comments: 0

remark to question 195301 and similar ones x^2 +y=a x+y^2 =b a, b >0 how many solutions depending on a, b?

$$\mathrm{remark}\:\mathrm{to}\:\mathrm{question}\:\mathrm{195301}\:\mathrm{and}\:\mathrm{similar}\:\mathrm{ones} \\ $$$${x}^{\mathrm{2}} +{y}={a} \\ $$$${x}+{y}^{\mathrm{2}} ={b} \\ $$$${a},\:{b}\:>\mathrm{0} \\ $$$$\mathrm{how}\:\mathrm{many}\:\mathrm{solutions}\:\mathrm{depending}\:\mathrm{on}\:{a},\:{b}? \\ $$

Question Number 195349 Answers: 0 Comments: 0

Question Number 195331 Answers: 1 Comments: 0

Question Number 195330 Answers: 0 Comments: 1

Question Number 200302 Answers: 1 Comments: 0

Question Number 195292 Answers: 1 Comments: 0

Question Number 195291 Answers: 1 Comments: 0

it is given a,b,c ∈ N^∗ and ab<c . Prove that a+b≤c.

$$\:\:{it}\:{is}\:{given}\:{a},{b},{c}\:\in\:\mathbb{N}^{\ast} \:\:{and}\:\:{ab}<{c}\:.\:{Prove}\:{that}\:{a}+{b}\leqslant{c}. \\ $$

Question Number 195288 Answers: 0 Comments: 1

x, y, z∈R_+ , P = (x/(x + y)) + (y/(y + z)) + (z/(z + x)), Q = (y/(x + y)) + (z/(y + z)) + (x/(z + x)), Q = (z/(x + y)) + (x/(y + z)) + (y/(z + x)). f(x, y, z)=max{P, Q, R}, find f_(min) .

$${x},\:{y},\:{z}\in\mathbb{R}_{+} , \\ $$$${P}\:=\:\frac{{x}}{{x}\:+\:{y}}\:+\:\frac{{y}}{{y}\:+\:{z}}\:+\:\frac{{z}}{{z}\:+\:{x}}, \\ $$$${Q}\:=\:\frac{{y}}{{x}\:+\:{y}}\:+\:\frac{{z}}{{y}\:+\:{z}}\:+\:\frac{{x}}{{z}\:+\:{x}}, \\ $$$${Q}\:=\:\frac{{z}}{{x}\:+\:{y}}\:+\:\frac{{x}}{{y}\:+\:{z}}\:+\:\frac{{y}}{{z}\:+\:{x}}. \\ $$$${f}\left({x},\:{y},\:{z}\right)=\mathrm{max}\left\{{P},\:{Q},\:{R}\right\},\:\mathrm{find}\:{f}_{\mathrm{min}} . \\ $$

Question Number 195454 Answers: 4 Comments: 1

Question Number 195255 Answers: 2 Comments: 0

∫(dx/(cos^3 x(√(4sin xcos x))))

$$\int\frac{{dx}}{\mathrm{cos}\:^{\mathrm{3}} {x}\sqrt{\mathrm{4sin}\:{x}\mathrm{cos}\:{x}}} \\ $$

Question Number 195254 Answers: 1 Comments: 0

∫^(spillover) ((sin^2 xcos^2 x)/((sin^5 x+cos^3 xsin^2 x+sin^3 xcos^2 x+cos^5 x)^2 ))dx

$$\int^{\boldsymbol{{spillover}}} \frac{\mathrm{sin}\:^{\mathrm{2}} {x}\mathrm{cos}\:^{\mathrm{2}} {x}}{\left(\mathrm{sin}\:^{\mathrm{5}} {x}+\mathrm{cos}\:^{\mathrm{3}} {x}\mathrm{sin}\:^{\mathrm{2}} {x}+\mathrm{sin}\:^{\mathrm{3}} {x}\mathrm{cos}\:^{\mathrm{2}} {x}+\mathrm{cos}\:^{\mathrm{5}} {x}\right)^{\mathrm{2}} }{dx} \\ $$

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