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Question Number 39689 Answers: 1 Comments: 2

In Lambert W Function How would i simplify x = − ((W(((−ln(4))/8)))/(ln(4))) To get the values

$${In}\:{Lambert}\:{W}\:{Function} \\ $$$$ \\ $$$${How}\:{would}\:{i}\:{simplify} \\ $$$$ \\ $$$${x}\:=\:−\:\frac{{W}\left(\frac{−{ln}\left(\mathrm{4}\right)}{\mathrm{8}}\right)}{{ln}\left(\mathrm{4}\right)} \\ $$$${To}\:{get}\:{the}\:{values} \\ $$$$ \\ $$

Question Number 39949 Answers: 2 Comments: 1

f(x)=2arctan((√((1−x)/x))) f′(x)=?

$${f}\left({x}\right)=\mathrm{2}{arctan}\left(\sqrt{\frac{\mathrm{1}−{x}}{{x}}}\right) \\ $$$${f}'\left({x}\right)=? \\ $$

Question Number 39678 Answers: 1 Comments: 1

Question Number 39671 Answers: 1 Comments: 0

Three function are given f(x)=(√x) g(x)=x+5 and h(x)=x^2 +5 .Express h(x) interms of f(x) and g(x).

$${Three}\:{function}\:{are}\:{given}\:{f}\left({x}\right)=\sqrt{{x}} \\ $$$${g}\left({x}\right)={x}+\mathrm{5}\:{and}\:{h}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{5}\:.{Express} \\ $$$${h}\left({x}\right)\:{interms}\:{of}\:{f}\left({x}\right)\:{and}\:{g}\left({x}\right). \\ $$

Question Number 39666 Answers: 1 Comments: 1

Question Number 39669 Answers: 1 Comments: 0

Question Number 39660 Answers: 0 Comments: 2

let S_n = ∫_0 ^n ((x(−1)^([x]) )/((x+1 −[x])^3 ))dx 1) calculate S_n 2) find lim_(n→+∞) S_n

$${let}\:\:{S}_{{n}} \:\:=\:\int_{\mathrm{0}} ^{{n}} \:\:\:\:\:\frac{{x}\left(−\mathrm{1}\right)^{\left[{x}\right]} }{\left({x}+\mathrm{1}\:−\left[{x}\right]\right)^{\mathrm{3}} }{dx} \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:\:{S}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:{S}_{{n}} \\ $$

Question Number 39655 Answers: 1 Comments: 1

Question Number 39727 Answers: 0 Comments: 1

If the average of 4 kids age is 3c and the average of two of them is 33. find the value of c.

$${If}\:{the}\:{average}\:{of}\:\mathrm{4}\:{kids}\:{age}\:{is} \\ $$$$\mathrm{3}{c}\:{and}\:{the}\:{average}\:{of}\:{two}\: \\ $$$${of}\:{them}\:{is}\:\mathrm{33}.\:{find}\:{the}\:{value} \\ $$$${of}\:{c}. \\ $$

Question Number 39651 Answers: 1 Comments: 0

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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

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

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