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Question Number 35475    Answers: 1   Comments: 0

Is Rational Number Countable? If yes how do we count it with one to one correspondence with set of natural number N?

$${Is}\:{Rational}\:{Number}\:{Countable}? \\ $$$${If}\:{yes}\:{how}\:{do}\:{we}\:{count}\:{it}\:{with}\:{one}\:{to}\:{one}\:{correspondence}\:{with}\:{set}\:{of}\:{natural}\:{number}\:\mathbb{N}? \\ $$

Question Number 35474    Answers: 0   Comments: 0

while proving F=ma newtons 2nd law we put F=1 when m=1 and a=1 and thus k=1 why not F=other value except 1...

$${while}\:{proving}\:{F}={ma}\:{newtons}\:\mathrm{2}{nd}\:{law}\:{we}\:{put} \\ $$$${F}=\mathrm{1}\:{when}\:{m}=\mathrm{1}\:{and}\:{a}=\mathrm{1}\:{and}\:{thus}\:{k}=\mathrm{1} \\ $$$${why}\:{not}\:{F}={other}\:{value}\:{except}\:\mathrm{1}... \\ $$

Question Number 35473    Answers: 0   Comments: 0

vector has both magnetude and direction...then why time and current not vector...

$${vector}\:{has}\:{both}\:{magnetude}\:{and}\:{direction}...{then} \\ $$$${why}\:{time}\:{and}\:{current}\:{not}\:{vector}... \\ $$

Question Number 35472    Answers: 1   Comments: 0

Mr. Crone started from his house at 8.00 a.m. and walked t to his office at an average speed of 4 km/h. Mettle started from Mr. Crones at 8.30 a.m. and travelled by cycle in the same direction as Mr. Crone at average speed of of 6 km/h. If the two arrive arrived at the office at the same time .(i) Find the time of arrival (ii) Find the distance between Mr. Crones house and the office

$${Mr}.\:{Crone}\:{started}\:{from}\:{his}\: \\ $$$${house}\:{at}\:\mathrm{8}.\mathrm{00}\:{a}.{m}.\:{and}\:{walked}\:{t} \\ $$$${to}\:{his}\:{office}\:{at}\:{an}\:{average}\:{speed} \\ $$$${of}\:\mathrm{4}\:{km}/{h}.\:{Mettle}\:{started}\:{from} \\ $$$${Mr}.\:{Crones}\:{at}\:\mathrm{8}.\mathrm{30}\:{a}.{m}.\:{and}\:{travelled} \\ $$$${by}\:{cycle}\:{in}\:{the}\:{same}\:{direction} \\ $$$${as}\:{Mr}.\:{Crone}\:{at}\:{average}\:{speed} \\ $$$${of}\:\:{of}\:\:\mathrm{6}\:{km}/{h}.\:{If}\:{the}\:{two}\:{arrive} \\ $$$${arrived}\:{at}\:{the}\:{office}\:{at}\:{the}\:{same}\:{time} \\ $$$$.\left({i}\right)\:{Find}\:{the}\:{time}\:{of}\:{arrival} \\ $$$$\left({ii}\right)\:{Find}\:{the}\:{distance}\:{between}\:{Mr}. \\ $$$${Crones}\:{house}\:{and}\:{the}\:{office} \\ $$

Question Number 35471    Answers: 0   Comments: 0

∫_a ^b f(x)dx=area under the curve but say why what is the meaning of ∫ ←this sign

$$\int_{{a}} ^{{b}} {f}\left({x}\right){dx}={area}\:{under}\:{the}\:{curve}\:{but}\:{say}\:{why} \\ $$$${what}\:{is}\:{the}\:{meaning}\:{of}\:\int\:\leftarrow{this}\:{sign} \\ $$

Question Number 35470    Answers: 2   Comments: 0

prove sin0^o =0 and cos0^o =1

$${prove}\:{sin}\mathrm{0}^{{o}} =\mathrm{0}\:\:{and}\:{cos}\mathrm{0}^{{o}} =\mathrm{1} \\ $$

Question Number 35469    Answers: 0   Comments: 0

find distance between (x_(1,) y_1 ) and (x_2 ,y_2 ) when x axis and y axis inclined ai angle θ

$${find}\:{distance}\:{between}\:\left({x}_{\mathrm{1},} {y}_{\mathrm{1}} \right)\:{and}\:\left({x}_{\mathrm{2}} ,{y}_{\mathrm{2}} \right)\:{when} \\ $$$${x}\:{axis}\:{and}\:{y}\:{axis}\:{inclined}\:{ai}\:{angle}\:\theta \\ $$

Question Number 35467    Answers: 1   Comments: 0

If x = 32 − 16 ÷ 2 × 4, then x=

$$\mathrm{If}\:\:{x}\:=\:\mathrm{32}\:−\:\mathrm{16}\:\boldsymbol{\div}\:\mathrm{2}\:×\:\mathrm{4},\:\mathrm{then}\:{x}= \\ $$

Question Number 35461    Answers: 1   Comments: 0

Question Number 35460    Answers: 1   Comments: 1

Find the values of k for which the equation (((k −3)),((10 −k+1)) ) ((x),(y) ) = (((k−1)),(8) ) have a) a unique solution b) no solution c)an infinite solution hence Find the image of the point (3,1) after reflection in the line with equation a) x=1 b) y= −1 c) y+x= 1

$${Find}\:{the}\:{values}\:{of}\:{k}\:{for}\:{which} \\ $$$${the}\:{equation}\: \\ $$$$\begin{pmatrix}{{k}\:\:\:\:\:\:\:\:\:−\mathrm{3}}\\{\mathrm{10}\:\:\:\:\:\:\:−{k}+\mathrm{1}}\end{pmatrix}\begin{pmatrix}{{x}}\\{{y}}\end{pmatrix}\:=\:\begin{pmatrix}{{k}−\mathrm{1}}\\{\mathrm{8}}\end{pmatrix} \\ $$$${have} \\ $$$$\left.{a}\right)\:{a}\:\:{unique}\:{solution} \\ $$$$\left.{b}\right)\:{no}\:{solution} \\ $$$$\left.{c}\right){an}\:{infinite}\:{solution} \\ $$$${hence} \\ $$$${Find}\:{the}\:{image}\:{of}\:{the}\:{point}\: \\ $$$$\left(\mathrm{3},\mathrm{1}\right)\:{after}\:{reflection}\:{in}\:{the}\:{line} \\ $$$${with}\:{equation} \\ $$$$\left.{a}\left.\right)\left.\:{x}=\mathrm{1}\:\:\:\:{b}\right)\:{y}=\:−\mathrm{1}\:\:\boldsymbol{{c}}\right)\:\boldsymbol{{y}}+\boldsymbol{{x}}=\:\mathrm{1} \\ $$

Question Number 35456    Answers: 2   Comments: 0

∫(dx/(x(x^(2018) +1)))

$$\int\frac{{dx}}{{x}\left({x}^{\mathrm{2018}} +\mathrm{1}\right)} \\ $$

Question Number 35446    Answers: 1   Comments: 1

Question Number 35440    Answers: 1   Comments: 2

find the value of ∫_0 ^∞ (dx/((2x^2 +1)^2 ))

$${find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{dx}}{\left(\mathrm{2}{x}^{\mathrm{2}} \:\:+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 35439    Answers: 0   Comments: 1

Question Number 35438    Answers: 0   Comments: 1

let m>0 and 0<a<b 1) calculate ∫_0 ^∞ ((cos(mx))/((x^2 +a^2 )(x^2 +b^2 )))dx 2)find the value of ∫_0 ^∞ ((cos(2x))/((x^2 +1)(x^2 +3)))dx

$${let}\:{m}>\mathrm{0}\:{and}\:\mathrm{0}<{a}<{b}\: \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\:\:\frac{{cos}\left({mx}\right)}{\left({x}^{\mathrm{2}} \:+{a}^{\mathrm{2}} \right)\left({x}^{\mathrm{2}} \:+{b}^{\mathrm{2}} \right)}{dx} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\:\frac{{cos}\left(\mathrm{2}{x}\right)}{\left({x}^{\mathrm{2}} +\mathrm{1}\right)\left({x}^{\mathrm{2}} \:\:+\mathrm{3}\right)}{dx} \\ $$

Question Number 35430    Answers: 1   Comments: 1

Question Number 35429    Answers: 1   Comments: 1

find ∫_0 ^1 ((2x−1)/(√(x^2 +6))) dx

$${find}\:\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\:\:\:\frac{\mathrm{2}{x}−\mathrm{1}}{\sqrt{{x}^{\mathrm{2}} \:\:+\mathrm{6}}}\:{dx} \\ $$

Question Number 35428    Answers: 1   Comments: 1

find ∫ ((x+3)/(√(x^2 +x −1)))dx

$${find}\:\:\:\:\:\int\:\:\:\:\frac{{x}+\mathrm{3}}{\sqrt{{x}^{\mathrm{2}} \:+{x}\:−\mathrm{1}}}{dx} \\ $$

Question Number 35427    Answers: 1   Comments: 1

calculate ∫_2 ^5 (e^(√(x+1)) /(√(x+1)))dx

$${calculate}\:\:\:\int_{\mathrm{2}} ^{\mathrm{5}} \:\:\:\frac{{e}^{\sqrt{{x}+\mathrm{1}}} }{\sqrt{{x}+\mathrm{1}}}{dx} \\ $$

Question Number 35425    Answers: 1   Comments: 0

Given that a number is a factor of 144 and the square of the number added to five times the number is ≥ −6 find the number

$$\:{Given}\:{that}\:{a}\:{number}\:{is}\:{a}\:{factor}\: \\ $$$${of}\:\mathrm{144}\:{and}\:{the}\:{square}\:{of}\:{the}\:{number} \\ $$$${added}\:{to}\:{five}\:{times}\:{the}\:{number} \\ $$$${is}\:\geqslant\:−\mathrm{6}\:{find}\:{the}\:{number} \\ $$

Question Number 35426    Answers: 1   Comments: 2

find the value of x if the inverse of the matrix (((x+5 2)),((7 x)) ) is (((0 0)),((0 0)) )

$${find}\:{the}\:{value}\:{of}\:{x}\:{if}\:{the}\:{inverse} \\ $$$${of}\:{the}\:{matrix}\:\begin{pmatrix}{{x}+\mathrm{5}\:\:\:\:\:\:\:\:\mathrm{2}}\\{\mathrm{7}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{x}}\end{pmatrix}\:{is} \\ $$$$\begin{pmatrix}{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\mathrm{0}}\end{pmatrix} \\ $$

Question Number 35422    Answers: 0   Comments: 2

Question Number 35416    Answers: 1   Comments: 2

let −1≤x≤1 simplify A=sin{ arcsinx +2arcsin)(1−x)}

$${let}\:−\mathrm{1}\leqslant{x}\leqslant\mathrm{1}\:{simplify} \\ $$$$\left.{A}={sin}\left\{\:{arcsinx}\:\:+\mathrm{2}{arcsin}\right)\left(\mathrm{1}−{x}\right)\right\} \\ $$

Question Number 35412    Answers: 1   Comments: 2

evaluate ∫(√((t^2 +1+(3/4)t))) dt

$$\boldsymbol{\mathrm{evaluate}}\:\int\sqrt{\left(\boldsymbol{\mathrm{t}}^{\mathrm{2}} +\mathrm{1}+\frac{\mathrm{3}}{\mathrm{4}}\boldsymbol{\mathrm{t}}\right)}\:\boldsymbol{\mathrm{dt}} \\ $$

Question Number 35646    Answers: 1   Comments: 2

Question Number 35645    Answers: 1   Comments: 0

sketch the graph of f(x)=2−x−x^2 then state its domain and range

$$\boldsymbol{\mathrm{sketch}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{graph}}\:\boldsymbol{\mathrm{of}} \\ $$$$\boldsymbol{\mathrm{f}}\left(\boldsymbol{{x}}\right)=\mathrm{2}−\boldsymbol{{x}}−\boldsymbol{{x}}^{\mathrm{2}} \\ $$$$\boldsymbol{\mathrm{then}}\:\boldsymbol{\mathrm{state}}\:\boldsymbol{\mathrm{its}}\:\boldsymbol{\mathrm{domain}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{range}} \\ $$

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