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Question Number 106379 Answers: 1 Comments: 0

Question Number 106378 Answers: 2 Comments: 0

Question Number 106380 Answers: 0 Comments: 0

Question Number 106373 Answers: 1 Comments: 0

A ladder placed against a vertical walls ubtends an angle of 45 degree with thewall The distance between the footo f the ladder and the wall is 15mt calculae the length of the ladder correctto the nearest whole number.

$$ \\ $$$$\mathrm{A}\:\mathrm{ladder}\:\mathrm{placed}\:\mathrm{against}\:\mathrm{a}\:\mathrm{vertical}\:\mathrm{walls} \\ $$$$\mathrm{ubtends}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{45}\:\mathrm{degree}\:\mathrm{with}\: \\ $$$$\mathrm{thewall}\:\mathrm{The}\:\mathrm{distance}\:\mathrm{between}\:\mathrm{the}\:\mathrm{footo} \\ $$$$\mathrm{f}\:\mathrm{the}\:\mathrm{ladder}\:\mathrm{and}\:\mathrm{the}\:\mathrm{wall}\:\mathrm{is}\:\mathrm{15mt} \\ $$$$\mathrm{calculae}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ladder}\: \\ $$$$\mathrm{correctto}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{whole}\:\mathrm{number}. \\ $$

Question Number 106366 Answers: 1 Comments: 0

Question Number 106365 Answers: 2 Comments: 1

help Σ_(n=1) ^∞ (1/((2n−1)!))

$$\mathrm{help} \\ $$$$\underset{\mathrm{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\mathrm{1}}{\left(\mathrm{2n}−\mathrm{1}\right)!} \\ $$

Question Number 106364 Answers: 1 Comments: 2

0^i =?????

$$\mathrm{0}^{{i}} =????? \\ $$

Question Number 106363 Answers: 0 Comments: 0

prove that : ⌊((√(10^(2k) −1))/3)⌋ = ((10^k −1)/3)

$${prove}\:{that}\:: \\ $$$$\lfloor\frac{\sqrt{\mathrm{10}^{\mathrm{2}{k}} −\mathrm{1}}}{\mathrm{3}}\rfloor\:=\:\frac{\mathrm{10}^{{k}} \:−\mathrm{1}}{\mathrm{3}} \\ $$$$ \\ $$

Question Number 106360 Answers: 0 Comments: 0

Question Number 106356 Answers: 2 Comments: 1

find the solution set of equation ∣x^2 −5x+4∣ = x^2 −5∣x∣ + 4

$$\mathrm{find}\:\mathrm{the}\:\mathrm{solution}\:\mathrm{set}\:\mathrm{of}\:\mathrm{equation}\: \\ $$$$\mid\mathrm{x}^{\mathrm{2}} −\mathrm{5x}+\mathrm{4}\mid\:=\:\mathrm{x}^{\mathrm{2}} −\mathrm{5}\mid\mathrm{x}\mid\:+\:\mathrm{4}\: \\ $$

Question Number 106351 Answers: 0 Comments: 0

Question Number 106350 Answers: 0 Comments: 0

Question Number 106340 Answers: 0 Comments: 0

Question Number 106338 Answers: 0 Comments: 0

Question Number 106337 Answers: 3 Comments: 4

1+(5/2)+(9/4)+((13)/8)+((17)/(16))+......

$$\mathrm{1}+\frac{\mathrm{5}}{\mathrm{2}}+\frac{\mathrm{9}}{\mathrm{4}}+\frac{\mathrm{13}}{\mathrm{8}}+\frac{\mathrm{17}}{\mathrm{16}}+...... \\ $$

Question Number 106335 Answers: 0 Comments: 1

Question Number 106333 Answers: 0 Comments: 1

Question Number 106329 Answers: 2 Comments: 0

find ∫_(−5) ^5 ((√(25−x^2 )))dx whithout using trigonometric compensation

$${find}\:\int_{−\mathrm{5}} ^{\mathrm{5}} \left(\sqrt{\mathrm{25}−{x}^{\mathrm{2}} }\right){dx}\:\:{whithout}\:{using} \\ $$$${trigonometric}\:{compensation} \\ $$

Question Number 106325 Answers: 0 Comments: 0

Question Number 106319 Answers: 1 Comments: 2

Question Number 106318 Answers: 0 Comments: 0

∫_0 ^(log(2)) ((e^x −4)/(x +2))dx = ..... {(a)log(2) (b)1−log(2) (c) 1−2log(2) (d)−log(2)}

$$\int_{\mathrm{0}} ^{\mathrm{log}\left(\mathrm{2}\right)} \frac{{e}^{{x}} \:−\mathrm{4}}{{x}\:+\mathrm{2}}{dx}\:\:\:=\:..... \\ $$$$\left\{\left({a}\right){log}\left(\mathrm{2}\right)\:\:\:\:\:\:\:\left({b}\right)\mathrm{1}−{log}\left(\mathrm{2}\right)\:\:\:\:\:\:\:\left({c}\right)\right. \\ $$$$\left.\mathrm{1}−\mathrm{2}{log}\left(\mathrm{2}\right)\:\:\:\:\:\:\:\:\left({d}\right)−{log}\left(\mathrm{2}\right)\right\} \\ $$

Question Number 106315 Answers: 1 Comments: 0

show that ⊛∀ (x_1 ,x_2 ,.....,x_(n ) )∈R^n (Σ_(k=1) ^n x_k )^2 ≤nΣ_(k=1) ^n x_k ^2 ⊛a,b>0 p(x)=x^n +ax+b=0 could not have more than 3 reals solutions

$$\boldsymbol{{show}}\:\boldsymbol{{that}} \\ $$$$\circledast\forall\:\left(\boldsymbol{{x}}_{\mathrm{1}} ,\boldsymbol{{x}}_{\mathrm{2}} ,.....,\boldsymbol{{x}}_{\boldsymbol{{n}}\:} \right)\in\mathbb{R}^{\boldsymbol{{n}}} \\ $$$$\left(\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{x}}_{\boldsymbol{{k}}} \right)^{\mathrm{2}} \leqslant\boldsymbol{{n}}\underset{\boldsymbol{{k}}=\mathrm{1}} {\overset{\boldsymbol{{n}}} {\sum}}\boldsymbol{{x}}_{\boldsymbol{{k}}} ^{\mathrm{2}} \\ $$$$\circledast\boldsymbol{{a}},\boldsymbol{{b}}>\mathrm{0} \\ $$$$\boldsymbol{{p}}\left(\boldsymbol{{x}}\right)=\boldsymbol{{x}}^{\boldsymbol{{n}}} +\boldsymbol{{ax}}+\boldsymbol{{b}}=\mathrm{0} \\ $$$$\boldsymbol{{could}}\:\boldsymbol{{not}}\:\boldsymbol{{have}}\:\boldsymbol{{more}}\:\boldsymbol{{than}}\:\mathrm{3} \\ $$$$\boldsymbol{{reals}}\:\boldsymbol{{solutions}} \\ $$

Question Number 106314 Answers: 3 Comments: 0

Question Number 106313 Answers: 1 Comments: 0

lim_(x→1) ((x∣x−1∣)/(x^2 −1))

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\frac{\mathrm{x}\mid\mathrm{x}−\mathrm{1}\mid}{\mathrm{x}^{\mathrm{2}} −\mathrm{1}} \\ $$

Question Number 106309 Answers: 1 Comments: 0

If g(x)= x+(√x) and lim_(x→2) ((f(x)−f(2))/(x^2 +ax+b))=(4/3) find the value of (f○g)′(1).

$$\mathrm{If}\:\mathrm{g}\left(\mathrm{x}\right)=\:\mathrm{x}+\sqrt{\mathrm{x}}\:\mathrm{and}\:\underset{{x}\rightarrow\mathrm{2}} {\mathrm{lim}}\:\frac{\mathrm{f}\left(\mathrm{x}\right)−\mathrm{f}\left(\mathrm{2}\right)}{\mathrm{x}^{\mathrm{2}} +\mathrm{ax}+\mathrm{b}}=\frac{\mathrm{4}}{\mathrm{3}} \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\left(\mathrm{f}\circ\mathrm{g}\right)'\left(\mathrm{1}\right). \\ $$

Question Number 106305 Answers: 1 Comments: 0

what is probability of 5 coming up at least one if a die is rolled 3 times

$$\mathrm{what}\:\mathrm{is}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{5}\:\mathrm{coming}\:\mathrm{up}\:\mathrm{at}\:\mathrm{least}\:\mathrm{one}\:\mathrm{if}\:\mathrm{a}\:\mathrm{die}\: \\ $$$$\mathrm{is}\:\mathrm{rolled}\:\mathrm{3}\:\mathrm{times}\: \\ $$

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