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Question Number 7211 Answers: 0 Comments: 0

Find the next time of the sequence −1, 8, 49, 68, 131, .....

$${Find}\:{the}\:{next}\:{time}\:{of}\:{the}\:{sequence}\: \\ $$$$−\mathrm{1},\:\mathrm{8},\:\mathrm{49},\:\mathrm{68},\:\mathrm{131},\:..... \\ $$

Question Number 7207 Answers: 0 Comments: 4

x^((2x/y)) × y^((y/x)) = 4 ............. (i) xy^((xy + yx)) = 16 ............ (ii) Find the value of x and y

$${x}^{\left(\mathrm{2}{x}/{y}\right)} \:\:×\:\:\:{y}^{\left({y}/{x}\right)} \:\:=\:\:\mathrm{4}\:\:\:\:\:\:.............\:\left({i}\right) \\ $$$${xy}^{\left({xy}\:+\:{yx}\right)} \:\:=\:\:\mathrm{16}\:\:\:\:\:............\:\left({ii}\right) \\ $$$$ \\ $$$${Find}\:{the}\:{value}\:{of}\:{x}\:{and}\:{y} \\ $$

Question Number 7230 Answers: 0 Comments: 2

An Interesting App: I′ve recently downloaded the app called ′Math Tricks′ from the Google Play Store. If you′d like to improve your speed and skill in the mental calculations arena, I think this app should be of interest to you. The app can throw you simple calculations that include the basic operations of addition,subtraction,division and multiplication. The application can show you tricks to calculating 52^2 or 125^2 ,for example, under 10 seconds mentally. So, check it out! I′ve seen that the levels of difficulty on the app can go as high as mentally calculating positive integers raised to the power of 9, and also finding 9th roots of positive integers! Yozzia

$${An}\:{Interesting}\:{App}: \\ $$$${I}'{ve}\:{recently}\:{downloaded}\:{the}\:{app}\:{called} \\ $$$$'{Math}\:{Tricks}'\:{from}\:{the}\:{Google}\:{Play}\:{Store}. \\ $$$${If}\:{you}'{d}\:{like}\:{to}\:{improve}\:{your}\:{speed} \\ $$$${and}\:{skill}\:{in}\:{the}\:{mental}\:{calculations} \\ $$$${arena},\:{I}\:{think}\:{this}\:{app}\:{should}\:{be}\:{of} \\ $$$${interest}\:{to}\:{you}.\:{The}\:{app}\:{can}\:{throw}\:{you}\:{simple} \\ $$$${calculations}\:{that}\:{include}\:{the}\:{basic}\:{operations} \\ $$$${of}\:{addition},{subtraction},{division}\:{and} \\ $$$${multiplication}.\:{The}\:{application}\:{can} \\ $$$${show}\:{you}\:{tricks}\:{to}\:{calculating}\:\mathrm{52}^{\mathrm{2}} \:{or} \\ $$$$\mathrm{125}^{\mathrm{2}} ,{for}\:{example},\:{under}\:\mathrm{10}\:{seconds} \\ $$$${mentally}.\:{So},\:{check}\:{it}\:{out}!\:{I}'{ve}\:{seen} \\ $$$${that}\:{the}\:{levels}\:{of}\:{difficulty}\:{on}\:{the}\: \\ $$$${app}\:{can}\:{go}\:{as}\:{high}\:{as}\:{mentally}\:{calculating}\:{positive} \\ $$$${integers}\:{raised}\:{to}\:{the}\:{power}\:{of}\:\mathrm{9}, \\ $$$${and}\:{also}\:{finding}\:\mathrm{9}{th}\:{roots}\:{of}\: \\ $$$${positive}\:{integers}! \\ $$$$ \\ $$$${Yozzia} \\ $$

Question Number 7200 Answers: 1 Comments: 4

Prove that ((sin((Θ/2)))/(((Θ/2)))) = 1

$${Prove}\:{that}\: \\ $$$$\frac{{sin}\left(\frac{\Theta}{\mathrm{2}}\right)}{\left(\frac{\Theta}{\mathrm{2}}\right)}\:\:=\:\:\mathrm{1} \\ $$

Question Number 7196 Answers: 1 Comments: 0

Question Number 7187 Answers: 0 Comments: 0

Prove that ((√(4sin^2 36−1))/2)=cos72.

$${Prove}\:{that}\:\frac{\sqrt{\mathrm{4}{sin}^{\mathrm{2}} \mathrm{36}−\mathrm{1}}}{\mathrm{2}}={cos}\mathrm{72}. \\ $$

Question Number 7193 Answers: 0 Comments: 2

Question Number 7191 Answers: 1 Comments: 0

Evaluate Σ ((sin(3n))/n) from 1 to infinity

$${Evaluate}\:\:\:\:\:\Sigma\:\frac{{sin}\left(\mathrm{3}{n}\right)}{{n}}\:\:\:\:\:{from}\:\:\mathrm{1}\:\:{to}\:\:{infinity}\: \\ $$

Question Number 7178 Answers: 0 Comments: 2

Question Number 7189 Answers: 0 Comments: 2

Evaluate : Σ ((sin(n))/n) , From 1 to infinity.

$${Evaluate}\:\:\::\:\:\:\Sigma\:\frac{{sin}\left({n}\right)}{{n}}\:\:,\:\:\:{From}\:\:\:\mathrm{1}\:{to}\:\:{infinity}. \\ $$

Question Number 7184 Answers: 0 Comments: 0

Show that ∫(2^x /((1+(√5))^x +(3+(√5))^x ))dx=(1/(ln(1+(√5))−ln2))(ln[1+((((√5)−1)/2))^x ]−((((√5)−1)/2))^x )+C

$${Show}\:{that} \\ $$$$\int\frac{\mathrm{2}^{{x}} }{\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)^{{x}} +\left(\mathrm{3}+\sqrt{\mathrm{5}}\right)^{{x}} }{dx}=\frac{\mathrm{1}}{{ln}\left(\mathrm{1}+\sqrt{\mathrm{5}}\right)−{ln}\mathrm{2}}\left({ln}\left[\mathrm{1}+\left(\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\right)^{{x}} \right]−\left(\frac{\sqrt{\mathrm{5}}−\mathrm{1}}{\mathrm{2}}\right)^{{x}} \right)+{C} \\ $$$$ \\ $$

Question Number 7168 Answers: 0 Comments: 2

I have five envelopes numbered 3,4,5,6,7 all hidden in a box, i picked an envelope . If its prime then i get the square of that number in Naira. Otherwise (without replacement) i picked another envelope and then get the sum of the squares of the two numbers picked (in Naira) what is the chance of me getting N25 ?

$${I}\:{have}\:{five}\:{envelopes}\:{numbered}\:\mathrm{3},\mathrm{4},\mathrm{5},\mathrm{6},\mathrm{7}\:{all}\:{hidden}\:{in}\:{a} \\ $$$${box},\:{i}\:{picked}\:{an}\:{envelope}\:.\:\:{If}\:{its}\:{prime}\:{then}\:{i}\:{get}\:{the}\: \\ $$$${square}\:{of}\:{that}\:{number}\:{in}\:{Naira}.\:{Otherwise}\:\left({without}\:\right. \\ $$$$\left.{replacement}\right)\:{i}\:{picked}\:{another}\:{envelope}\:{and}\:{then}\:{get}\:{the} \\ $$$${sum}\:{of}\:{the}\:{squares}\:{of}\:{the}\:{two}\:{numbers}\:{picked}\:\left({in}\:{Naira}\right) \\ $$$${what}\:{is}\:{the}\:{chance}\:{of}\:{me}\:{getting}\:\:{N}\mathrm{25}\:\:? \\ $$$$ \\ $$

Question Number 7165 Answers: 0 Comments: 0

30 teams participated in the football tournament . At the end of the competition it turned out that in Any group of three teams it is possible to single out two teams which score equal point in three games. within this group (3 points are given for the victory, 1 point for the draw , 0 point for the defeat ). what is the least possible number of draws that can occur in such a tournament ? please help me. Please help .. thanks.

$$\mathrm{30}\:{teams}\:{participated}\:{in}\:{the}\:{football}\:{tournament}\:.\:{At}\:{the}\: \\ $$$${end}\:{of}\:{the}\:{competition}\:{it}\:{turned}\:{out}\:{that}\:{in} \\ $$$${Any}\:{group}\:{of}\:{three}\:\:{teams}\:{it}\:{is}\:{possible}\:{to}\:{single}\:{out}\:{two} \\ $$$${teams}\:{which}\:{score}\:{equal}\:{point}\:{in}\:{three}\:{games}.\: \\ $$$${within}\:{this}\:{group}\:\left(\mathrm{3}\:{points}\:{are}\:{given}\:{for}\:{the}\:{victory},\:\right. \\ $$$$\left.\mathrm{1}\:{point}\:{for}\:{the}\:{draw}\:,\:\mathrm{0}\:{point}\:{for}\:{the}\:{defeat}\:\right).\: \\ $$$${what}\:{is}\:{the}\:{least}\:{possible}\:{number}\:{of}\:{draws}\:{that}\:{can}\:{occur} \\ $$$${in}\:{such}\:{a}\:{tournament}\:? \\ $$$$ \\ $$$$ \\ $$$${please}\:{help}\:{me}. \\ $$$${Please}\:{help}\:..\:{thanks}. \\ $$

Question Number 7164 Answers: 1 Comments: 0

Question Number 7163 Answers: 0 Comments: 2

Question Number 7161 Answers: 1 Comments: 3

If ax^2 + bx + c = 0, prove that. x = ((2c)/(− b ± (√(b^2 − 4ac))))

$${If}\:\:{ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0},\:\:{prove}\:{that}. \\ $$$${x}\:=\:\frac{\mathrm{2}{c}}{−\:{b}\:\pm\:\sqrt{{b}^{\mathrm{2}} \:−\:\mathrm{4}{ac}}}\: \\ $$

Question Number 7159 Answers: 0 Comments: 2

log_2 Π_(x=1) ^(2015) Π_(y=1) ^(2015) (1+e^((2𝛑ixy)/(2015)) ) = ?

$$\boldsymbol{{log}}_{\mathrm{2}} \underset{\boldsymbol{{x}}=\mathrm{1}} {\overset{\mathrm{2015}} {\prod}}\:\underset{\boldsymbol{{y}}=\mathrm{1}} {\overset{\mathrm{2015}} {\prod}}\left(\mathrm{1}+\boldsymbol{{e}}^{\frac{\mathrm{2}\boldsymbol{\pi{ixy}}}{\mathrm{2015}}} \right)\:=\:? \\ $$

Question Number 7157 Answers: 1 Comments: 0

If a and b are positive numbers what is the value of ∫_0 ^∞ ((e^(ax) − e^(bx) )/((1 + e^(ax) )(1 + e^(bx) ))) dx

$${If}\:{a}\:{and}\:{b}\:{are}\:{positive}\:{numbers} \\ $$$${what}\:{is}\:{the}\:{value}\:{of}\: \\ $$$$\int_{\mathrm{0}} ^{\infty} \:\frac{{e}^{{ax}} \:−\:{e}^{{bx}} }{\left(\mathrm{1}\:+\:{e}^{{ax}} \right)\left(\mathrm{1}\:+\:{e}^{{bx}} \right)}\:{dx}\: \\ $$

Question Number 7150 Answers: 0 Comments: 1

Question Number 7149 Answers: 0 Comments: 0

Find last digit P P=(2017^k +2016)(2016^m +2015)(2015^n +2014) where k,m,n∈N Help me!!!

$$\mathrm{Find}\:\mathrm{last}\:\mathrm{digit}\:\mathrm{P} \\ $$$$\:\mathrm{P}=\left(\mathrm{2017}^{\boldsymbol{\mathrm{k}}} +\mathrm{2016}\right)\left(\mathrm{2016}^{\boldsymbol{\mathrm{m}}} +\mathrm{2015}\right)\left(\mathrm{2015}^{\boldsymbol{\mathrm{n}}} +\mathrm{2014}\right) \\ $$$$\mathrm{where}\:\boldsymbol{\mathrm{k}},\boldsymbol{\mathrm{m}},\boldsymbol{\mathrm{n}}\in{N} \\ $$$$\:\:\:\: \\ $$$$\:\:\:\:{Help}\:{me}!!! \\ $$

Question Number 7147 Answers: 0 Comments: 2

Question Number 7142 Answers: 1 Comments: 0

The sides of a triangle are x cm, (x − 4) cm, (x − 8)cm respectively . if the cosine o the largest is (1/5) , calculate the angles of triangle.

$${The}\:{sides}\:{of}\:{a}\:{triangle}\:{are}\:{x}\:{cm},\:\left({x}\:−\:\mathrm{4}\right)\:{cm},\:\left({x}\:−\:\mathrm{8}\right){cm} \\ $$$${respectively}\:.\:{if}\:{the}\:{cosine}\:{o}\:{the}\:{largest}\:{is}\:\frac{\mathrm{1}}{\mathrm{5}}\:,\: \\ $$$${calculate}\:{the}\:{angles}\:{of}\:\:{triangle}. \\ $$$$ \\ $$

Question Number 7139 Answers: 0 Comments: 0

Question Number 7138 Answers: 1 Comments: 0

Question Number 7135 Answers: 0 Comments: 0

Prove that (3/((2)^(1/5) +(3)^(1/5) +(5)^(1/5) )) > (((2)^(1/4) +(3)^(1/4) +(5)^(1/4) )/(((√2)+(√3)+(√5))((2)^(1/3) +(3)^(1/3) +(5)^(1/3) ))) How to prove it ?

$$\boldsymbol{\mathrm{Prove}}\:\boldsymbol{\mathrm{that}} \\ $$$$\:\frac{\mathrm{3}}{\sqrt[{\mathrm{5}}]{\mathrm{2}}+\sqrt[{\mathrm{5}}]{\mathrm{3}}+\sqrt[{\mathrm{5}}]{\mathrm{5}}}\:>\:\frac{\sqrt[{\mathrm{4}}]{\mathrm{2}}+\sqrt[{\mathrm{4}}]{\mathrm{3}}+\sqrt[{\mathrm{4}}]{\mathrm{5}}}{\left(\sqrt{\mathrm{2}}+\sqrt{\mathrm{3}}+\sqrt{\mathrm{5}}\right)\left(\sqrt[{\mathrm{3}}]{\mathrm{2}}+\sqrt[{\mathrm{3}}]{\mathrm{3}}+\sqrt[{\mathrm{3}}]{\mathrm{5}}\right)} \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\: \\ $$$$\:\:\:{How}\:{to}\:{prove}\:{it}\:? \\ $$

Question Number 7145 Answers: 0 Comments: 1

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