Question and Answers Forum

AllQuestion and Answers: Page 1369

Question Number 75046 Answers: 0 Comments: 3

Question Number 75041 Answers: 1 Comments: 1

1) Show that for a∈]01]the function f_a :R_+ →R defined by f_a (x)=x^a is a−holder function in other way there exist K>0 such as ∀ x,y>0 ∣f_a (x)−f_a (y)∣≤K∣x−y∣^a

$$\left.\mathrm{1}\left.\right)\left.\:\mathrm{Show}\:\mathrm{that}\:\:\mathrm{for}\:\mathrm{a}\in\right]\mathrm{01}\right]\mathrm{the}\:\mathrm{function}\:\:\mathrm{f}_{\mathrm{a}} \::\mathbb{R}_{+} \rightarrow\mathbb{R}\:\mathrm{defined}\:\mathrm{by}\:\mathrm{f}_{\mathrm{a}} \left(\mathrm{x}\right)=\mathrm{x}^{\mathrm{a}} \: \\ $$$$\mathrm{is}\:\:\:\mathrm{a}−\mathrm{holder}\:\mathrm{function}\:\:\mathrm{in}\:\mathrm{other}\:\mathrm{way}\:\:\mathrm{there}\:\mathrm{exist}\:\:\mathrm{K}>\mathrm{0}\:\mathrm{such}\:\mathrm{as}\:\forall\:\mathrm{x},\mathrm{y}>\mathrm{0}\: \\ $$$$\mid\mathrm{f}_{\mathrm{a}} \left(\mathrm{x}\right)−\mathrm{f}_{\mathrm{a}} \left(\mathrm{y}\right)\mid\leqslant\mathrm{K}\mid\mathrm{x}−\mathrm{y}\mid^{\mathrm{a}} \:\: \\ $$$$ \\ $$

Question Number 75040 Answers: 1 Comments: 0

Please can you help me to to show that: cos ((47Π)/(13))=sin ((23Π)/(26))=sin((3Π)/(26))

$$\mathrm{Please}\:\mathrm{can}\:\mathrm{you}\:\mathrm{help}\:\mathrm{me}\:\mathrm{to}\: \\ $$$$\mathrm{to}\:\mathrm{show}\:\mathrm{that}: \\ $$$$\mathrm{cos}\:\frac{\mathrm{47}\Pi}{\mathrm{13}}=\mathrm{sin}\:\frac{\mathrm{23}\Pi}{\mathrm{26}}=\mathrm{sin}\frac{\mathrm{3}\Pi}{\mathrm{26}} \\ $$

Question Number 75034 Answers: 3 Comments: 0

Question Number 75033 Answers: 1 Comments: 0

(4/(11)) < (x/y) < (3/8) x, y ∈ Z^+ min {x+y} = ?

$$\frac{\mathrm{4}}{\mathrm{11}}\:<\:\frac{{x}}{{y}}\:<\:\frac{\mathrm{3}}{\mathrm{8}} \\ $$$${x},\:{y}\:\:\in\:\:\mathbb{Z}^{+} \\ $$$${min}\:\left\{{x}+{y}\right\}\:\:=\:\:? \\ $$

Question Number 75027 Answers: 1 Comments: 1

Question Number 75013 Answers: 1 Comments: 0

The largest interval for which x^(12) −x^9 +x^4 −x+1>0 is (a)−4<x≤0 (b)0<x<1 (c)−100<x<100 (d)−∞<x<∞

$${The}\:{largest}\:{interval}\:{for}\:{which} \\ $$$${x}^{\mathrm{12}} −{x}^{\mathrm{9}} +{x}^{\mathrm{4}} −{x}+\mathrm{1}>\mathrm{0}\:{is} \\ $$$$\left({a}\right)−\mathrm{4}<{x}\leqslant\mathrm{0} \\ $$$$\left({b}\right)\mathrm{0}<{x}<\mathrm{1} \\ $$$$\left({c}\right)−\mathrm{100}<{x}<\mathrm{100} \\ $$$$\left({d}\right)−\infty<{x}<\infty \\ $$

Question Number 75001 Answers: 0 Comments: 2

A block of mass 0.2kg rests on an incline plane of 30° to the horizontal with a velocity of 12m/s.If the coefficient of sliding friction is 0.16, (i)determine how far up the plane the mass travels before stoping. (ii)if the block returns,what is the velocity of the block at the bottom of the plane. (g=9.8m/s)

$${A}\:{block}\:{of}\:{mass}\:\mathrm{0}.\mathrm{2}{kg}\:{rests}\:{on}\:{an}\:{incline} \\ $$$${plane}\:{of}\:\mathrm{30}°\:{to}\:{the}\:{horizontal}\:{with}\:{a} \\ $$$${velocity}\:{of}\:\mathrm{12}{m}/{s}.{If}\:{the}\:{coefficient}\:{of} \\ $$$${sliding}\:{friction}\:{is}\:\mathrm{0}.\mathrm{16}, \\ $$$$\left({i}\right){determine}\:{how}\:{far}\:{up}\:{the}\:{plane}\:{the} \\ $$$${mass}\:{travels}\:{before}\:{stoping}. \\ $$$$\left({ii}\right){if}\:{the}\:{block}\:{returns},{what}\:{is}\:{the} \\ $$$${velocity}\:{of}\:{the}\:{block}\:{at}\:{the}\:{bottom}\:{of}\:{the} \\ $$$${plane}. \\ $$$$ \\ $$$$\left({g}=\mathrm{9}.\mathrm{8}{m}/{s}\right) \\ $$

Question Number 74997 Answers: 1 Comments: 1

Question Number 74995 Answers: 1 Comments: 1

find ∫_0 ^(π/2) Log cosx dx

$$\mathrm{find}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \mathrm{Log}\:\mathrm{cos}{x}\:{dx} \\ $$

Question Number 74994 Answers: 0 Comments: 6

Question Number 74980 Answers: 1 Comments: 0

Prove that for n∈N^∗ Σ_(p=0) ^(n−1) [x+(p/n)]=[nx]

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{for}\:\mathrm{n}\in\mathbb{N}^{\ast} \\ $$$$\:\underset{\mathrm{p}=\mathrm{0}} {\overset{\mathrm{n}−\mathrm{1}} {\sum}}\:\left[\mathrm{x}+\frac{\mathrm{p}}{\mathrm{n}}\right]=\left[\mathrm{nx}\right] \\ $$

Question Number 74970 Answers: 2 Comments: 13

x+y+z=1 x^2 +y^2 +z^2 =2 x^3 +y^3 +z^3 =3 find x^4 +y^4 +z^4 =? x^5 +y^5 +z^5 =? x^6 +y^6 +z^6 =? ...... x^n +y^n +z^n =?

$${x}+{y}+{z}=\mathrm{1} \\ $$$${x}^{\mathrm{2}} +{y}^{\mathrm{2}} +{z}^{\mathrm{2}} =\mathrm{2} \\ $$$${x}^{\mathrm{3}} +{y}^{\mathrm{3}} +{z}^{\mathrm{3}} =\mathrm{3} \\ $$$$ \\ $$$${find} \\ $$$${x}^{\mathrm{4}} +{y}^{\mathrm{4}} +{z}^{\mathrm{4}} =? \\ $$$${x}^{\mathrm{5}} +{y}^{\mathrm{5}} +{z}^{\mathrm{5}} =? \\ $$$${x}^{\mathrm{6}} +{y}^{\mathrm{6}} +{z}^{\mathrm{6}} =? \\ $$$$...... \\ $$$${x}^{{n}} +{y}^{{n}} +{z}^{{n}} =? \\ $$

Question Number 74966 Answers: 1 Comments: 2

If sin 2A=λsin 2B Prove that ((tan (A+B))/(tan (A−B)))=((λ+1)/(λ−1)) .

$${If}\:\:\mathrm{sin}\:\mathrm{2}{A}=\lambda\mathrm{sin}\:\mathrm{2}{B} \\ $$$${Prove}\:{that}\:\:\frac{\mathrm{tan}\:\left({A}+{B}\right)}{\mathrm{tan}\:\left({A}−{B}\right)}=\frac{\lambda+\mathrm{1}}{\lambda−\mathrm{1}}\:. \\ $$

Question Number 74959 Answers: 1 Comments: 1

f(x)=∣x+5∣−∣x−2∣−∣x+6∣ find f′(x)

$${f}\left({x}\right)=\mid{x}+\mathrm{5}\mid−\mid{x}−\mathrm{2}\mid−\mid{x}+\mathrm{6}\mid \\ $$$$ \\ $$$${find}\:{f}'\left({x}\right) \\ $$

Question Number 74948 Answers: 1 Comments: 0

The hhpotenuse of a right angled triangle has its ends at the points (1,3) and (−4,1) . Find an equation of the legs (perpendicar sides) of the triangle.

$$\mathrm{The}\:\mathrm{hhpotenuse}\:\mathrm{of}\:\mathrm{a}\:\mathrm{right}\:\mathrm{angled}\:\mathrm{triangle} \\ $$$$\mathrm{has}\:\mathrm{its}\:\mathrm{ends}\:\mathrm{at}\:\mathrm{the}\:\mathrm{points}\:\left(\mathrm{1},\mathrm{3}\right)\:\mathrm{and}\:\left(−\mathrm{4},\mathrm{1}\right) \\ $$$$.\:\mathrm{Find}\:\mathrm{an}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{legs}\:\left(\mathrm{perpendicar}\right. \\ $$$$\left.\:\mathrm{sides}\right)\:\mathrm{of}\:\mathrm{the}\:\mathrm{triangle}. \\ $$

Question Number 74947 Answers: 1 Comments: 0