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AllQuestion and Answers: Page 354

Question Number 177826 Answers: 0 Comments: 0

Question Number 177822 Answers: 1 Comments: 2

what is coefficient of x^2 in (1−x)(1+2x)(1−3x)(1+4x)(1−5x) ... (1+14x)(1−15x) ?

$$\:\:\:\mathrm{what}\:\mathrm{is}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{x}^{\mathrm{2}} \:\mathrm{in}\: \\ $$$$\:\:\:\left(\mathrm{1}−\mathrm{x}\right)\left(\mathrm{1}+\mathrm{2x}\right)\left(\mathrm{1}−\mathrm{3x}\right)\left(\mathrm{1}+\mathrm{4x}\right)\left(\mathrm{1}−\mathrm{5x}\right) \\ $$$$\:\:\:\:...\:\left(\mathrm{1}+\mathrm{14x}\right)\left(\mathrm{1}−\mathrm{15x}\right)\:? \\ $$

Question Number 177820 Answers: 2 Comments: 0

∫_(π/2) ^π (dx/((sin x−2cos x)^2 )) =?

$$\:\:\:\:\underset{\pi/\mathrm{2}} {\overset{\pi} {\int}}\:\frac{\mathrm{dx}}{\left(\mathrm{sin}\:\mathrm{x}−\mathrm{2cos}\:\mathrm{x}\right)^{\mathrm{2}} }\:=? \\ $$

Question Number 177815 Answers: 2 Comments: 0

Question Number 177814 Answers: 1 Comments: 3

The probability that you give the right answer to this question is... A) 0% B) 25% C) 50% D)100%

$${The}\:{probability}\:{that}\:{you}\:{give}\:{the}\:{right} \\ $$$${answer}\:{to}\:{this}\:{question}\:{is}... \\ $$$$ \\ $$$$\left.{A}\left.\right)\left.\:\left.\mathrm{0\%}\:\:\:\:{B}\right)\:\mathrm{25\%}\:\:\:\:{C}\right)\:\mathrm{50\%}\:\:\:\:{D}\right)\mathrm{100\%} \\ $$

Question Number 177812 Answers: 1 Comments: 0

Question Number 177811 Answers: 1 Comments: 0

Question Number 177810 Answers: 1 Comments: 0

Question Number 177802 Answers: 0 Comments: 0

Question Number 177796 Answers: 3 Comments: 4

Question Number 177793 Answers: 1 Comments: 0

Determine the minimum value ((sec^4 α)/(tan^2 β)) + ((sec^4 β)/(tan^2 α)) over all α,β ≠ ((kπ)/2) , k ε Z

$$\:\:\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{minimum}\:\mathrm{value} \\ $$$$\:\:\frac{\mathrm{sec}\:^{\mathrm{4}} \alpha}{\mathrm{tan}\:^{\mathrm{2}} \beta}\:+\:\frac{\mathrm{sec}\:^{\mathrm{4}} \beta}{\mathrm{tan}\:^{\mathrm{2}} \alpha}\: \\ $$$$\:\:\mathrm{over}\:\mathrm{all}\:\alpha,\beta\:\neq\:\frac{\mathrm{k}\pi}{\mathrm{2}}\:,\:\mathrm{k}\:\varepsilon\:\mathbb{Z}\: \\ $$

Question Number 177792 Answers: 1 Comments: 0

Let f_k (x)= (1/k)(sin^k (x)+cos^k (x)) for k=1,2,3,... . Prove that f_4 (x)−f_6 (x)= (1/(12)) for all real numbers x

$$\:\:\mathrm{Let}\:\mathrm{f}_{\mathrm{k}} \left(\mathrm{x}\right)=\:\frac{\mathrm{1}}{\mathrm{k}}\left(\mathrm{sin}\:^{\mathrm{k}} \left(\mathrm{x}\right)+\mathrm{cos}\:^{\mathrm{k}} \left(\mathrm{x}\right)\right) \\ $$$$\:\:\mathrm{for}\:\mathrm{k}=\mathrm{1},\mathrm{2},\mathrm{3},...\:.\: \\ $$$$\:\:\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\mathrm{f}_{\mathrm{4}} \left(\mathrm{x}\right)−\mathrm{f}_{\mathrm{6}} \left(\mathrm{x}\right)=\:\frac{\mathrm{1}}{\mathrm{12}}\:\mathrm{for}\:\mathrm{all}\:\mathrm{real}\:\mathrm{numbers}\:\mathrm{x} \\ $$

Question Number 177791 Answers: 2 Comments: 0

Prove that 1−cot 23° = (2/(1−cot 22°))

$$\mathrm{Prove}\:\mathrm{that}\: \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\mathrm{1}−\mathrm{cot}\:\mathrm{23}°\:=\:\frac{\mathrm{2}}{\mathrm{1}−\mathrm{cot}\:\mathrm{22}°}\: \\ $$

Question Number 177787 Answers: 1 Comments: 1

Question Number 177784 Answers: 1 Comments: 0

Question Number 177775 Answers: 1 Comments: 0

∫((sin2x)/( (√(cos^4 x+1))))dx

$$\int\frac{\mathrm{sin2}{x}}{\:\sqrt{\mathrm{cos}^{\mathrm{4}} {x}+\mathrm{1}}}{dx} \\ $$

Question Number 177769 Answers: 1 Comments: 2

determiner les elements demandes dans le graphe

$${determiner}\:{les}\:{elements}\:{demandes} \\ $$$${dans}\:{le}\:{graphe} \\ $$

Question Number 177768 Answers: 1 Comments: 1

use pertfectly square numbers to find (√(11)) no calculators allowed

$${use}\:{pertfectly}\:{square}\:{numbers}\:{to}\:{find} \\ $$$$\sqrt{\mathrm{11}} \\ $$$${no}\:{calculators}\:{allowed} \\ $$

Question Number 177767 Answers: 0 Comments: 0

in AB^Δ C prove that: r_a + r_( b) +r_( c) = r +4R r_( a) : escribed circle radius corresponding to A. r : incirle radius R: circumcircle radius

$$ \\ $$$$\:\:{in}\:{A}\overset{\Delta} {{B}C}\:{prove}\:{that}: \\ $$$$\:\:\:{r}_{{a}} \:+\:{r}_{\:{b}} \:+{r}_{\:{c}} \:=\:{r}\:+\mathrm{4}{R} \\ $$$$\:\:\:\:\:{r}_{\:{a}} \::\:{escribed}\:\:{circle}\:{radius} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:{corresponding}\:{to}\:{A}. \\ $$$$\:\:\:\:{r}\::\:\:{incirle}\:{radius}\: \\ $$$$\:\:\:\:\:\:{R}:\:{circumcircle}\:{radius} \\ $$

Question Number 177763 Answers: 0 Comments: 1

Solve in R the system { ((x+y=z)),(((1/x)+(1/y)=(1/z))) :}

$${Solve}\:{in}\:\mathbb{R}\:{the}\:{system} \\ $$$$\begin{cases}{{x}+{y}={z}}\\{\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\frac{\mathrm{1}}{{z}}}\end{cases} \\ $$

Question Number 177742 Answers: 3 Comments: 0

Write the chemical formular of the following (a)Magnessium nitrate (b)Allumiun sulphate (c)carbondioxide (d)Calcium Oxide (e)Zinc carbonate (f)Lead Oxide (g) Ammonium Hydrogen carbonate

$$\mathrm{Write}\:\mathrm{the}\:\mathrm{chemical}\:\mathrm{formular}\:\mathrm{of}\: \\ $$$$\mathrm{the}\:\mathrm{following} \\ $$$$\left(\mathrm{a}\right)\mathrm{Magnessium}\:\mathrm{nitrate} \\ $$$$\left(\mathrm{b}\right)\mathrm{Allumiun}\:\mathrm{sulphate} \\ $$$$\left(\mathrm{c}\right)\mathrm{carbondioxide} \\ $$$$\left(\mathrm{d}\right)\mathrm{Calcium}\:\mathrm{Oxide} \\ $$$$\left(\mathrm{e}\right)\mathrm{Zinc}\:\mathrm{carbonate} \\ $$$$\left(\mathrm{f}\right)\mathrm{Lead}\:\mathrm{Oxide} \\ $$$$\left(\mathrm{g}\right)\:\mathrm{Ammonium}\:\mathrm{Hydrogen}\:\mathrm{carbonate} \\ $$$$ \\ $$

Question Number 177741 Answers: 2 Comments: 0

Question Number 177725 Answers: 0 Comments: 2

Find the oxidation number of the underlined element in the following (a)KCl O_3 (b)SO_3 ^(2−) (c)H_2 SO_4 (d)Na H

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{oxidation}\:\mathrm{number}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{underlined}\:\mathrm{element}\:\mathrm{in}\:\mathrm{the} \\ $$$$\:\mathrm{following} \\ $$$$\left(\mathrm{a}\right)\mathrm{K}\underline{\boldsymbol{\mathrm{Cl}}}\:\mathrm{O}_{\mathrm{3}} \\ $$$$\left(\mathrm{b}\right)\underline{\mathrm{S}O}_{\mathrm{3}} ^{\mathrm{2}−} \\ $$$$\left(\mathrm{c}\right)\mathrm{H}_{\mathrm{2}} \underline{\mathrm{S}O}_{\mathrm{4}} \\ $$$$\left(\mathrm{d}\right)\underline{\mathrm{Na}}\:\mathrm{H} \\ $$$$ \\ $$

Question Number 177711 Answers: 0 Comments: 0

(4/(20))+((4.7)/(20.30))+((4.7.10)/(20.30.40))+.....

$$\frac{\mathrm{4}}{\mathrm{20}}+\frac{\mathrm{4}.\mathrm{7}}{\mathrm{20}.\mathrm{30}}+\frac{\mathrm{4}.\mathrm{7}.\mathrm{10}}{\mathrm{20}.\mathrm{30}.\mathrm{40}}+..... \\ $$

Question Number 177698 Answers: 0 Comments: 0

In △ABC 36 R r ≤ Σ ((m_b ^2 + m_c ^2 )/(sin B sin C)) ≤ ((9 R^4 )/(2 r^2 ))

$$\mathrm{In}\:\:\bigtriangleup\mathrm{ABC} \\ $$$$\mathrm{36}\:\mathrm{R}\:\mathrm{r}\:\leqslant\:\Sigma\:\frac{\mathrm{m}_{\boldsymbol{\mathrm{b}}} ^{\mathrm{2}} \:+\:\mathrm{m}_{\boldsymbol{\mathrm{c}}} ^{\mathrm{2}} }{\mathrm{sin}\:\mathrm{B}\:\mathrm{sin}\:\mathrm{C}}\:\leqslant\:\frac{\mathrm{9}\:\mathrm{R}^{\mathrm{4}} }{\mathrm{2}\:\mathrm{r}^{\mathrm{2}} } \\ $$

Question Number 177702 Answers: 2 Comments: 0

Solve in C { ((x+y=z)),(((1/x)+(1/y)=(1/z))) :}

$${Solve}\:{in}\:\mathbb{C} \\ $$$$\begin{cases}{{x}+{y}={z}}\\{\frac{\mathrm{1}}{{x}}+\frac{\mathrm{1}}{{y}}=\frac{\mathrm{1}}{{z}}}\end{cases} \\ $$

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