Question and Answers Forum

OthersQuestion and Answers: Page 110

Question Number 38059 Answers: 1 Comments: 0

Prove that Σ(x_i −x^− )=0

$${Prove}\:{that}\:\Sigma\left({x}_{{i}} −\overset{−} {{x}}\right)=\mathrm{0} \\ $$

Question Number 38051 Answers: 0 Comments: 0

A manufactual plans to build two types of tables. For table A,the cost of material is 20 000 bucks, the number of man hours needed to complete it is 10, and the profit is 15 000 bucks. Table B requires materials costing 12000 bucks,15 man hour of labour and makes same profit as table A. The total money avialable for materials is 500 000 bucks and labour avialable is 330 man hours.Find the maximum profit that can be made and the number of each type of table that should be made to produces it.

$${A}\:{manufactual}\:{plans}\:{to}\:{build}\:{two} \\ $$$${types}\:{of}\:{tables}.\:{For}\:{table}\:{A},{the}\:{cost} \\ $$$${of}\:{material}\:{is}\:\mathrm{20}\:\mathrm{000}\:{bucks},\:{the}\: \\ $$$${number}\:{of}\:{man}\:{hours}\:{needed}\:{to}\: \\ $$$${complete}\:{it}\:{is}\:\mathrm{10},\:{and}\:{the}\:{profit}\: \\ $$$${is}\:\mathrm{15}\:\mathrm{000}\:{bucks}.\:{Table}\:{B}\:{requires} \\ $$$${materials}\:{costing}\:\mathrm{12000}\:{bucks},\mathrm{15} \\ $$$${man}\:{hour}\:{of}\:{labour}\:{and}\:{makes} \\ $$$${same}\:{profit}\:{as}\:{table}\:{A}. \\ $$$$\:\:{The}\:{total}\:{money}\:{avialable}\:{for}\:{materials} \\ $$$${is}\:\mathrm{500}\:\mathrm{000}\:{bucks}\:{and}\:{labour}\:{avialable} \\ $$$${is}\:\mathrm{330}\:{man}\:{hours}.{Find}\:{the}\:{maximum} \\ $$$${profit}\:{that}\:{can}\:{be}\:{made}\:{and}\:{the}\:{number}\:{of}\:{each} \\ $$$${type}\:{of}\:{table}\:{that}\:{should}\:{be}\:{made}\:{to}\:{produces} \\ $$$${it}. \\ $$

Question Number 38049 Answers: 1 Comments: 0

Find the equation of the two lines throught (2,−3) which makes 45° with the line 2x − y = 2..hence find the cosine of the acute between the lines l_1 : y− 2x + 5=0 and l_2 : y − x + 6 (leave your answer in surd form)

$${Find}\:{the}\:{equation}\:{of}\:{the}\:{two}\:{lines} \\ $$$${throught}\:\left(\mathrm{2},−\mathrm{3}\right)\:{which}\:{makes}\:\mathrm{45}° \\ $$$${with}\:{the}\:{line}\:\mathrm{2}{x}\:−\:{y}\:=\:\mathrm{2}..{hence} \\ $$$${find}\:{the}\:{cosine}\:{of}\:{the}\:{acute}\:{between} \\ $$$${the}\:{lines}\:{l}_{\mathrm{1}} :\:{y}−\:\mathrm{2}{x}\:+\:\mathrm{5}=\mathrm{0}\:{and}\: \\ $$$${l}_{\mathrm{2}} :\:{y}\:−\:{x}\:+\:\mathrm{6}\:\left({leave}\:{your}\:{answer}\:{in}\right. \\ $$$$\left.{surd}\:{form}\right) \\ $$

Question Number 38012 Answers: 3 Comments: 1

The roots of the equation 2x^2 − x + 3 = 0 are α and β if the roots of 3x^2 + px + q=0 are α + (1/α) and β + (1/(β )) find the value of p and q.

$${The}\:{roots}\:{of}\:{the}\:{equation} \\ $$$$\mathrm{2}{x}^{\mathrm{2}} \:−\:{x}\:+\:\mathrm{3}\:=\:\mathrm{0}\:{are}\:\alpha\:{and}\:\beta \\ $$$${if}\:{the}\:{roots}\:{of}\:\mathrm{3}{x}^{\mathrm{2}} \:+\:{px}\:+\:{q}=\mathrm{0}\: \\ $$$${are}\:\alpha\:+\:\frac{\mathrm{1}}{\alpha}\:{and}\:\beta\:+\:\frac{\mathrm{1}}{\beta\:}\:{find}\:{the}\:{value} \\ $$$${of}\:{p}\:{and}\:{q}. \\ $$$$\: \\ $$

Question Number 38011 Answers: 2 Comments: 0

Show that ((sin2A)/(1+ cos2A)) = TanA

$${Show}\:{that}\: \\ $$$$\:\:\frac{{sin}\mathrm{2}{A}}{\mathrm{1}+\:{cos}\mathrm{2}{A}}\:=\:{TanA} \\ $$

Question Number 37972 Answers: 1 Comments: 0

The distance S metres is given as a funtion f(t) where is time taken... if S = t^3 + t^2 + 4 find the velocity and acceleration

$$\:{The}\:{distance}\:{S}\:{metres}\:{is}\: \\ $$$${given}\:{as}\:{a}\:{funtion}\: \\ $$$${f}\left({t}\right)\:{where}\:{is}\:{time}\:{taken}... \\ $$$${if}\:{S}\:=\:{t}^{\mathrm{3}} \:+\:{t}^{\mathrm{2}} \:+\:\mathrm{4} \\ $$$${find}\:{the}\:{velocity}\:{and}\:{acceleration} \\ $$

Question Number 37948 Answers: 0 Comments: 1

If x ∈R show that (2+i)e^((1+3i)) +(2−i)e^((1−3i)) is also real.

$${If}\:{x}\:\in\mathbb{R} \\ $$$${show}\:{that}\:\left(\mathrm{2}+{i}\right){e}^{\left(\mathrm{1}+\mathrm{3}{i}\right)} +\left(\mathrm{2}−{i}\right){e}^{\left(\mathrm{1}−\mathrm{3}{i}\right)} \:{is}\:{also}\:{real}. \\ $$

Question Number 37940 Answers: 1 Comments: 0

Which of the following expressions are positive for all real values of x? a) x^2 − 2x + 5 b) x^2 −2x−1 c) x^2 +4x+2 d) 2x^2 −6x + 5

$${Which}\:{of}\:{the}\:{following}\: \\ $$$${expressions}\:{are}\:{positive}\:{for} \\ $$$${all}\:{real}\:{values}\:{of}\:\:{x}? \\ $$$$\left.{a}\left.\right)\:{x}^{\mathrm{2}} −\:\mathrm{2}{x}\:+\:\mathrm{5}\:\:\:{b}\right)\:{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{1}\: \\ $$$$\left.{c}\left.\right)\:{x}^{\mathrm{2}} +\mathrm{4}{x}+\mathrm{2}\:\:\:\:\:\:{d}\right)\:\mathrm{2}{x}^{\mathrm{2}} −\mathrm{6}{x}\:+\:\mathrm{5} \\ $$

Question Number 37915 Answers: 1 Comments: 0

If y=4x^2 −1 , then find ((85)/(169))+Σ_(i=1) ^(84) (1/(y(i)))

$$\mathrm{If}\:{y}=\mathrm{4}{x}^{\mathrm{2}} −\mathrm{1}\:,\:\mathrm{then}\:\mathrm{find} \\ $$$$\frac{\mathrm{85}}{\mathrm{169}}+\underset{{i}=\mathrm{1}} {\overset{\mathrm{84}} {\Sigma}}\:\frac{\mathrm{1}}{{y}\left({i}\right)}\: \\ $$

Question Number 37911 Answers: 0 Comments: 1

the function f(x) is defined by f(x) = { ((−x + 1 , for x≤3)),((kx − 8 , for x ≥ 3)) :} find the value of k .

$$\mathrm{the}\:\mathrm{function}\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by} \\ $$$${f}\left({x}\right)\:=\begin{cases}{−{x}\:+\:\mathrm{1}\:,\:{for}\:{x}\leqslant\mathrm{3}}\\{{kx}\:−\:\mathrm{8}\:,\:{for}\:{x}\:\geqslant\:\mathrm{3}}\end{cases} \\ $$$${find}\:{the}\:{value}\:{of}\:{k}\:. \\ $$

Question Number 37860 Answers: 1 Comments: 0

The distance moved by a particle in t seconds is given by s= t^3 + 3t + 1 where s is in metres.Find the velocity and Asseleration after 3 seconds. Show all steps with short statements on how the answers are gotten.

$${The}\:{distance}\:{moved}\:{by}\:{a}\:{particle} \\ $$$${in}\:{t}\:{seconds}\:{is}\:{given}\:{by} \\ $$$${s}=\:{t}^{\mathrm{3}} \:+\:\mathrm{3}{t}\:+\:\mathrm{1}\:{where}\:{s}\:{is}\:{in}\: \\ $$$${metres}.{Find}\:{the}\:{velocity}\:{and}\: \\ $$$${Asseleration}\:{after}\:\mathrm{3}\:{seconds}. \\ $$$$ \\ $$$${Show}\:{all}\:{steps}\:{with}\:{short}\:{statements} \\ $$$${on}\:{how}\:{the}\:{answers}\:{are}\:{gotten}. \\ $$

Question Number 37845 Answers: 0 Comments: 0

Question Number 37838 Answers: 0 Comments: 5

let f(x)= e^(−2x) arctan(x^2 ) 1)calculate f^((n)) (x) 2) find f^((n)) (0) 3) developp f at integr serie

$${let}\:{f}\left({x}\right)=\:{e}^{−\mathrm{2}{x}} \:{arctan}\left({x}^{\mathrm{2}} \right) \\ $$$$\left.\mathrm{1}\right){calculate}\:{f}^{\left({n}\right)} \left({x}\right) \\ $$$$\left.\mathrm{2}\right)\:{find}\:{f}^{\left({n}\right)} \left(\mathrm{0}\right) \\ $$$$\left.\mathrm{3}\right)\:{developp}\:{f}\:{at}\:{integr}\:{serie} \\ $$

Question Number 37796 Answers: 0 Comments: 0

Find (dy/dx) if y= (x^2 + 1)^2 and y= (1−3x^2 )^5

$${Find}\:\frac{{dy}}{{dx}}\:{if}\: \\ $$$${y}=\:\left({x}^{\mathrm{2}} +\:\mathrm{1}\right)^{\mathrm{2}} \\ $$$${and}\:{y}=\:\left(\mathrm{1}−\mathrm{3}{x}^{\mathrm{2}} \right)^{\mathrm{5}} \\ $$

Question Number 37795 Answers: 1 Comments: 0

The side of a square is increasing at a rate of 0.1cms^(−1) . Find the rate of increase of the perimeter of the square when the length of side is 4cm.

$${The}\:{side}\:{of}\:{a}\:{square}\:{is}\:{increasing} \\ $$$${at}\:{a}\:{rate}\:{of}\:\mathrm{0}.\mathrm{1}{cms}^{−\mathrm{1}} .\:{Find}\:{the} \\ $$$${rate}\:{of}\:{increase}\:{of}\:{the}\:{perimeter} \\ $$$${of}\:{the}\:{square}\:{when}\:{the}\:{length}\:{of} \\ $$$${side}\:{is}\:\mathrm{4}{cm}. \\ $$

Question Number 37768 Answers: 0 Comments: 4

quest for truth...then study the books...

$${quest}\:{for}\:{truth}...{then}\:{study}\:{the}\:{books}... \\ $$

Question Number 37755 Answers: 0 Comments: 1