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Question Number 39651 Answers: 1 Comments: 0

Question Number 39650 Answers: 1 Comments: 0

If f be a linear function f (6)−f(12) =2 What is f(12)−f(2).

$${If}\:{f}\:{be}\:{a}\:{linear}\:{function}\:{f}\:\left(\mathrm{6}\right)−{f}\left(\mathrm{12}\right) \\ $$$$=\mathrm{2}\:{What}\:{is}\:{f}\left(\mathrm{12}\right)−{f}\left(\mathrm{2}\right). \\ $$$$ \\ $$

Question Number 39649 Answers: 1 Comments: 1

Question Number 39640 Answers: 1 Comments: 0

John′s age is 3x years 3 years after he was 27 years old what was his age 3 years before hence find the sum of the family ages Σ_(x=1) ^(60) (3x)^(3x−1)

$${John}'{s}\:{age}\:{is}\:\mathrm{3}{x}\:{years}\:\mathrm{3}\:{years} \\ $$$${after}\:{he}\:{was}\:\mathrm{27}\:{years}\:{old} \\ $$$${what}\:{was}\:{his}\:{age}\:\mathrm{3}\:{years}\:{before} \\ $$$${hence}\:{find}\:{the}\:{sum}\:{of}\:{the} \\ $$$${family}\:{ages}\:\underset{{x}=\mathrm{1}} {\overset{\mathrm{60}} {\sum}}\left(\mathrm{3}{x}\right)^{\mathrm{3}{x}−\mathrm{1}} \\ $$

Question Number 39639 Answers: 1 Comments: 0

Question Number 39638 Answers: 1 Comments: 0

Question Number 39636 Answers: 1 Comments: 0

let P_α (x) =x^3 +2α x −3 1) determine the roots of P_α 2) determine the roots of P_(−1)

$${let}\:{P}_{\alpha} \left({x}\right)\:={x}^{\mathrm{3}} \:\:+\mathrm{2}\alpha\:{x}\:−\mathrm{3} \\ $$$$\left.\mathrm{1}\right)\:{determine}\:{the}\:{roots}\:{of}\:{P}_{\alpha} \\ $$$$\left.\mathrm{2}\right)\:{determine}\:{the}\:{roots}\:{of}\:\:{P}_{−\mathrm{1}} \\ $$

Question Number 39635 Answers: 1 Comments: 1

calculate lim_(x→1) ((1+cos(πx))/(x^2 − sin(((πx)/2))))

$${calculate}\:\:{lim}_{{x}\rightarrow\mathrm{1}} \:\frac{\mathrm{1}+{cos}\left(\pi{x}\right)}{{x}^{\mathrm{2}} −\:{sin}\left(\frac{\pi{x}}{\mathrm{2}}\right)} \\ $$

Question Number 39633 Answers: 0 Comments: 3

find the value of f(x) = ∫_0 ^π ln(x^2 −2x cosθ +1)dθ with x fromR.

$${find}\:{the}\:{value}\:{of}\: \\ $$$${f}\left({x}\right)\:=\:\int_{\mathrm{0}} ^{\pi} {ln}\left({x}^{\mathrm{2}} \:−\mathrm{2}{x}\:{cos}\theta\:+\mathrm{1}\right){d}\theta\:\:{with}\:{x}\:{fromR}. \\ $$

Question Number 39632 Answers: 0 Comments: 0

let S_n = Σ_(k=1) ^n (1/(k(√k))) find a equivalent of S_n (n→+∞)

$${let}\:{S}_{{n}} \:=\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{{k}\sqrt{{k}}} \\ $$$${find}\:{a}\:{equivalent}\:\:{of}\:{S}_{{n}} \:\:\:\:\:\left({n}\rightarrow+\infty\right) \\ $$

Question Number 39631 Answers: 0 Comments: 0

let S_n = Σ_(k=1) ^n (1/(√k)) find a equivalent of S_n when n →+∞

$${let}\:{S}_{{n}} \:\:=\:\sum_{{k}=\mathrm{1}} ^{{n}} \:\:\frac{\mathrm{1}}{\sqrt{{k}}} \\ $$$${find}\:{a}\:{equivalent}\:{of}\:{S}_{{n}} \:{when}\:{n}\:\rightarrow+\infty \\ $$

Question Number 39626 Answers: 2 Comments: 1

Question Number 39623 Answers: 0 Comments: 0

Two equal charges q_1 =q_(2 ) =−6μC are on the y−axis at y_1 =3cm and y_2 =−3cm. i)What is the magnitude and direction of the electric field on the x−axis at x= 4cm, ii)if a test charge q_0 =2μC is plqced at x=4cm,find the force the net charge experiences.

$${Two}\:{equal}\:{charges}\:{q}_{\mathrm{1}} ={q}_{\mathrm{2}\:} =−\mathrm{6}\mu{C} \\ $$$${are}\:{on}\:{the}\:{y}−{axis}\:{at}\:{y}_{\mathrm{1}} =\mathrm{3}{cm}\:{and} \\ $$$${y}_{\mathrm{2}} =−\mathrm{3}{cm}. \\ $$$$\left.{i}\right){What}\:{is}\:{the}\:{magnitude}\:{and} \\ $$$${direction}\:{of}\:{the}\:{electric}\:{field}\:{on}\:{the} \\ $$$${x}−{axis}\:{at}\:{x}=\:\mathrm{4}{cm}, \\ $$$$\left.{ii}\right){if}\:{a}\:{test}\:{charge}\:{q}_{\mathrm{0}} =\mathrm{2}\mu{C}\:{is}\:{plqced} \\ $$$${at}\:{x}=\mathrm{4}{cm},{find}\:{the}\:{force}\:{the}\:{net} \\ $$$${charge}\:{experiences}. \\ $$

Question Number 39622 Answers: 0 Comments: 0

Two charges Q_0 and 3Q_0 are at l distance apart.These two charges are free to move but do not because is a third charge nearby.What must be the charge for the first two to be in equilibrium?

$${Two}\:{charges}\:{Q}_{\mathrm{0}} \:{and}\:\mathrm{3}{Q}_{\mathrm{0}} \:{are}\:{at}\:{l} \\ $$$${distance}\:{apart}.{These}\:{two}\:{charges} \\ $$$${are}\:{free}\:{to}\:{move}\:{but}\:{do}\:{not}\:{because} \\ $$$${is}\:{a}\:{third}\:{charge}\:{nearby}.{What}\:{must} \\ $$$${be}\:{the}\:{charge}\:{for}\:{the}\:{first}\:{two}\:{to}\:{be} \\ $$$${in}\:{equilibrium}? \\ $$

Question Number 39612 Answers: 1 Comments: 4

Question Number 39611 Answers: 1 Comments: 0

write the expression of electrostatic force between two charges Q_(1 ) and Q_2 separated by distance r. for the following condition 1)in air 2)when die electric present between them 3)when die electric partially fill space betweenp them

$${write}\:{the}\:{expression}\:{of}\:{electrostatic}\:{force} \\ $$$${between}\:{two}\:{charges}\:{Q}_{\mathrm{1}\:} {and}\:{Q}_{\mathrm{2}} \:{separated}\:{by} \\ $$$${distance}\:{r}.\:{for}\:{the}\:{following}\:{condition} \\ $$$$\left.\mathrm{1}\right){in}\:{air} \\ $$$$\left.\mathrm{2}\right){when}\:{die}\:{electric}\:{present}\:{between}\:{them} \\ $$$$\left.\mathrm{3}\right){when}\:{die}\:{electric}\:{partially}\:{fill}\:{space}\:{betweenp} \\ $$$${them} \\ $$

Question Number 39607 Answers: 3 Comments: 0

find the minimum and maximum value of the quadratic functions a) 4x^2 + 5x + 1 b) x + (2/x) = 3 c) x^2 − (x/4) + 6 hence draw each draw

$${find}\:{the}\: \\ $$$${minimum}\:{and}\:{maximum}\:{value} \\ $$$${of}\:{the}\:{quadratic}\:{functions} \\ $$$$\left.{a}\right)\:\mathrm{4}{x}^{\mathrm{2}} \:+\:\mathrm{5}{x}\:+\:\mathrm{1} \\ $$$$\left.{b}\right)\:{x}\:+\:\frac{\mathrm{2}}{{x}}\:=\:\mathrm{3} \\ $$$$\left.{c}\right)\:{x}^{\mathrm{2}} \:−\:\frac{{x}}{\mathrm{4}}\:+\:\mathrm{6} \\ $$$${hence}\:{draw}\:{each}\:{draw} \\ $$

Question Number 39591 Answers: 1 Comments: 0

Given the lines l_1 :−3mx + 3y = 9 and l_(2 ) : y = mx + c find the value of m and c if the point (1,2) lie on both lines. hence the tangent of the curve y = (mx + c)^2 when it moves across the x−axis

$${Given}\:{the}\:{lines}\: \\ $$$${l}_{\mathrm{1}} :−\mathrm{3}{mx}\:+\:\mathrm{3}{y}\:=\:\mathrm{9}\: \\ $$$${and}\:{l}_{\mathrm{2}\:} :\:{y}\:=\:{mx}\:+\:{c} \\ $$$${find}\:{the}\:{value}\:{of}\:\:{m}\:{and}\:{c}\:{if} \\ $$$${the}\:{point}\:\left(\mathrm{1},\mathrm{2}\right)\:{lie}\:{on}\:{both}\:{lines}. \\ $$$${hence}\:{the}\:{tangent}\:{of}\:{the} \\ $$$${curve}\:{y}\:=\:\left({mx}\:+\:{c}\right)^{\mathrm{2}} \\ $$$${when}\:{it}\:{moves}\:{across}\:{the}\:{x}−{axis} \\ $$

Question Number 39588 Answers: 1 Comments: 0

if cos A= (3/5) and tan B = ((12)/5) where A and B are reflex angles find without using tables,the value of a) sin (A − B) b) tan(A−B) c) cos (A + B).

$${if}\:{cos}\:{A}=\:\frac{\mathrm{3}}{\mathrm{5}}\:{and}\:{tan}\:{B}\:=\:\frac{\mathrm{12}}{\mathrm{5}} \\ $$$${where}\:{A}\:{and}\:{B}\:{are}\:{reflex}\:{angles} \\ $$$${find}\:{without}\:{using}\:{tables},{the} \\ $$$${value}\:{of} \\ $$$$\left.{a}\left.\right)\:{sin}\:\left({A}\:−\:{B}\right)\:{b}\right)\:{tan}\left({A}−{B}\right) \\ $$$$\left.{c}\right)\:{cos}\:\left({A}\:+\:{B}\right). \\ $$

Question Number 39587 Answers: 4 Comments: 0

Solve for x in the range 0 ≤ x ≤2π the equations a) cos(x + (π/3)) = 0 b) sin x = cos x. c) sin 2x + 2sin x = 1 + cos x

$${Solve}\:{for}\:{x}\:{in}\:{the}\:{range}\:\mathrm{0}\:\leqslant\:{x}\:\leqslant\mathrm{2}\pi \\ $$$${the}\:{equations} \\ $$$$\left.{a}\right)\:{cos}\left({x}\:+\:\frac{\pi}{\mathrm{3}}\right)\:=\:\mathrm{0}\: \\ $$$$\left.{b}\right)\:{sin}\:{x}\:=\:{cos}\:{x}. \\ $$$$\left.{c}\right)\:{sin}\:\mathrm{2}{x}\:+\:\mathrm{2}{sin}\:{x}\:=\:\mathrm{1}\:+\:{cos}\:{x} \\ $$$$ \\ $$

Question Number 39586 Answers: 2 Comments: 0

show that a) ((1 + 2sin2θ − cos2θ)/(1+sin2θ + cos 2θ)) = tan θ b) tan^2 A − tan^2 B = ((sin^2 A−sin^2 B)/(cos^2 A cos^2 B))

$${show}\:{that}\: \\ $$$$\left.{a}\right)\:\frac{\mathrm{1}\:+\:\mathrm{2}{sin}\mathrm{2}\theta\:−\:{cos}\mathrm{2}\theta}{\mathrm{1}+{sin}\mathrm{2}\theta\:+\:{cos}\:\mathrm{2}\theta}\:=\:{tan}\:\theta \\ $$$$\left.{b}\right)\:{tan}^{\mathrm{2}} {A}\:−\:{tan}^{\mathrm{2}} {B}\:=\:\frac{{sin}^{\mathrm{2}} {A}−{sin}^{\mathrm{2}} {B}}{{cos}^{\mathrm{2}} {A}\:{cos}^{\mathrm{2}} {B}} \\ $$$$ \\ $$$$ \\ $$

Question Number 39582 Answers: 1 Comments: 0

Question Number 39573 Answers: 1 Comments: 1

Point charges 88μC,−55μC and 70μC are placed in a straight line. The central one is 0.75m from each of the others.Calculate the net force on each due to the other two.

$${Point}\:{charges}\:\mathrm{88}\mu{C},−\mathrm{55}\mu{C}\:{and} \\ $$$$\mathrm{70}\mu{C}\:{are}\:{placed}\:{in}\:{a}\:{straight}\:{line}. \\ $$$${The}\:{central}\:{one}\:{is}\:\mathrm{0}.\mathrm{75}{m}\:{from} \\ $$$${each}\:{of}\:{the}\:{others}.{Calculate}\:{the} \\ $$$${net}\:{force}\:{on}\:{each}\:{due}\:{to}\:{the}\:{other} \\ $$$${two}. \\ $$

Question Number 39559 Answers: 2 Comments: 1

Question Number 39529 Answers: 0 Comments: 5

Question Number 39520 Answers: 1 Comments: 1

if (1+x)^n =Σ_(i=0) ^n a_i x^i and (1+x)^(n+1) =Σ_(i=0) ^(n+1) b_i x^i calculate ((∐_(i=0) ^n a_i )/(Π_(i=0) ^(n+1) b_i )) .

$${if}\:\left(\mathrm{1}+{x}\right)^{{n}} \:=\sum_{{i}=\mathrm{0}} ^{{n}} \:{a}_{{i}} {x}^{{i}} \:\:\:\:{and} \\ $$$$\left(\mathrm{1}+{x}\right)^{{n}+\mathrm{1}} \:=\sum_{{i}=\mathrm{0}} ^{{n}+\mathrm{1}} \:{b}_{{i}} \:{x}^{{i}} \:\:{calculate} \\ $$$$\frac{\coprod_{{i}=\mathrm{0}} ^{{n}} \:{a}_{{i}} }{\prod_{{i}=\mathrm{0}} ^{{n}+\mathrm{1}} \:{b}_{{i}} }\:. \\ $$

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