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AllQuestion and Answers: Page 29

Question Number 211276 Answers: 2 Comments: 0

Prove , in AB^Δ C : ((cosA)/(sin^2 A)) + ((cosB)/(sin^2 B)) +((cosC)/(sin^2 C)) ≥ (r/R) r : incircle radius R: circumcircle radius

$$ \\ $$$$\:\:{Prove}\:,\:{in}\:{A}\overset{\Delta} {{B}C}\:\::\: \\ $$$$ \\ $$$$\:\:\:\:\:\frac{{cosA}}{{sin}^{\mathrm{2}} {A}}\:+\:\frac{{cosB}}{{sin}^{\mathrm{2}} {B}}\:\:+\frac{{cosC}}{{sin}^{\mathrm{2}} {C}}\:\geqslant\:\frac{{r}}{{R}} \\ $$$$\:\:\:\:\: \\ $$$$\:\:\:\:\:\:\:{r}\::\:{incircle}\:\:{radius} \\ $$$$\:\:\:\:\:{R}:\:{circumcircle}\:\:{radius} \\ $$$$ \\ $$

Question Number 211279 Answers: 1 Comments: 1

Question Number 211265 Answers: 0 Comments: 0

Question Number 211262 Answers: 1 Comments: 0

Question Number 211258 Answers: 1 Comments: 0

Question Number 211255 Answers: 1 Comments: 3

(√(a+(√(b−x))+(√(b−(√(a+x))))))=2x solve for x.

$$\sqrt{{a}+\sqrt{{b}−{x}}+\sqrt{{b}−\sqrt{{a}+{x}}}}=\mathrm{2}{x} \\ $$$${solve}\:{for}\:{x}.\:\:\:\: \\ $$

Question Number 211252 Answers: 1 Comments: 0

Question Number 211251 Answers: 0 Comments: 2

Question Number 211250 Answers: 1 Comments: 0

Find the number of 4 digit numbers so that when decomposed into prime factors, have the sum of prime factors equal to the sum of the exponents?

$${Find}\:{the}\:{number}\:{of}\:\mathrm{4}\:{digit}\:{numbers} \\ $$$$\:{so}\:{that}\:{when}\:{decomposed}\:{into}\:{prime} \\ $$$$\:{factors},\:{have}\:{the}\:{sum}\:{of}\:{prime}\:{factors} \\ $$$$\:{equal}\:{to}\:{the}\:{sum}\:{of}\:{the}\:{exponents}? \\ $$

Question Number 211245 Answers: 1 Comments: 0

prove: ∫_0 ^∞ (t^(α−1) /(t^π +1))dt=(1/(sin α))

$$\mathrm{prove}: \\ $$$$\underset{\mathrm{0}} {\overset{\infty} {\int}}\frac{{t}^{\alpha−\mathrm{1}} }{{t}^{\pi} +\mathrm{1}}{dt}=\frac{\mathrm{1}}{\mathrm{sin}\:\alpha} \\ $$

Question Number 211241 Answers: 1 Comments: 4

lim_(x→0) ((cos x^2 −cos (sin^2 x ))/x^6 ) =?

$$\:\:\:\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\mathrm{cos}\:\mathrm{x}^{\mathrm{2}} −\mathrm{cos}\:\left(\mathrm{sin}\:^{\mathrm{2}} \mathrm{x}\:\right)}{\mathrm{x}^{\mathrm{6}} }\:=? \\ $$

Question Number 211235 Answers: 2 Comments: 1

Question Number 211232 Answers: 1 Comments: 0

Question Number 211231 Answers: 0 Comments: 0

Question Number 211230 Answers: 0 Comments: 0

Question Number 211277 Answers: 0 Comments: 4

Question Number 211222 Answers: 1 Comments: 0

How many integers are there such that, 0≤n≤720 and n^2 ≡1(mod)720?

$${How}\:{many}\:{integers}\:{are}\:{there} \\ $$$$\:\:\:{such}\:{that},\:\:\mathrm{0}\leqslant{n}\leqslant\mathrm{720}\:{and}\: \\ $$$$\:\:\:{n}^{\mathrm{2}} \equiv\mathrm{1}\left({mod}\right)\mathrm{720}? \\ $$

Question Number 211216 Answers: 2 Comments: 0

Question Number 211207 Answers: 2 Comments: 0

Question Number 211201 Answers: 5 Comments: 0

((x−1))^(1/3) + ((x−2))^(1/3) −((2x−3))^(1/3) = 0 x=?

$$\:\:\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{1}}\:+\:\sqrt[{\mathrm{3}}]{\mathrm{x}−\mathrm{2}}\:−\sqrt[{\mathrm{3}}]{\mathrm{2x}−\mathrm{3}}\:=\:\mathrm{0} \\ $$$$\:\:\:\mathrm{x}=? \\ $$

Question Number 211191 Answers: 2 Comments: 0

Question Number 211188 Answers: 1 Comments: 0

Question Number 211184 Answers: 3 Comments: 0

Question Number 211190 Answers: 3 Comments: 0

Question Number 211157 Answers: 1 Comments: 1

Question Number 211155 Answers: 1 Comments: 0

∫(((sin^n (θ)−sin (θ))^(1/n) cos (θ))/(sin^(n+1) (θ)))dθ

$$\int\frac{\left(\mathrm{sin}\:^{{n}} \left(\theta\right)−\mathrm{sin}\:\left(\theta\right)\right)^{\frac{\mathrm{1}}{{n}}} \mathrm{cos}\:\left(\theta\right)}{\mathrm{sin}\:^{{n}+\mathrm{1}} \left(\theta\right)}{d}\theta \\ $$$$ \\ $$

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