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Question Number 39764 Answers: 0 Comments: 0

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Question Number 39756 Answers: 1 Comments: 1

A force F = 2t i + 5j acts on a particle of mass 2kg. find the velocity and the magnitude of the impulse that acts on the particle within the time range 1s ≤ t ≤ 3s

$${A}\:{force}\:{F}\:=\:\mathrm{2}{t}\:\boldsymbol{{i}}\:+\:\mathrm{5}\boldsymbol{{j}}\:{acts}\:{on} \\ $$$${a}\:{particle}\:{of}\:{mass}\:\mathrm{2}{kg}.\:{find} \\ $$$${the}\:{velocity}\:{and}\:{the}\:{magnitude} \\ $$$${of}\:{the}\:{impulse}\:{that}\:{acts}\:{on}\: \\ $$$${the}\:{particle}\:{within}\:{the}\:{time} \\ $$$${range}\:\:\mathrm{1}\boldsymbol{{s}}\:\leqslant\:\boldsymbol{{t}}\:\leqslant\:\mathrm{3}\boldsymbol{{s}} \\ $$

Question Number 39700 Answers: 0 Comments: 1

given that f(x)= x^3 − 3x^2 + ax + b and (x−1) is a factor of f(x) also the maximum value of f(x) at poin where x = 1 is 12 find a) (dy/d) (f(x)) b) the values of a and b c) factorise f(x) completely d) hence evaluate ∫_3 ^4 [f(x)] dx

$${given}\:{that}\:{f}\left({x}\right)=\:{x}^{\mathrm{3}} \:−\:\mathrm{3}{x}^{\mathrm{2}} \:+\:{ax}\:+\:{b} \\ $$$${and}\:\left({x}−\mathrm{1}\right)\:{is}\:{a}\:{factor}\:{of}\:{f}\left({x}\right) \\ $$$${also}\:{the}\:{maximum}\:{value}\:{of} \\ $$$${f}\left({x}\right)\:{at}\:{poin}\:{where}\:{x}\:=\:\mathrm{1} \\ $$$${is}\:\mathrm{12}\:{find}\: \\ $$$$\left.{a}\right)\:\frac{{dy}}{{d}}\:\left({f}\left({x}\right)\right) \\ $$$$\left.{b}\right)\:{the}\:{values}\:{of}\:{a}\:{and}\:{b} \\ $$$$\left.{c}\right)\:{factorise}\:{f}\left({x}\right)\:{completely} \\ $$$$\left.{d}\right)\:{hence}\:{evaluate}\:\int_{\mathrm{3}} ^{\mathrm{4}} \left[{f}\left({x}\right)\right]\:{dx} \\ $$

Question Number 39696 Answers: 1 Comments: 3

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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 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 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 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 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 39464 Answers: 1 Comments: 0

Domain of the explicit form of the function y represented implicitly by the equation (1+x)cosy−x^2 =0 is (a) (−1,1] (b) (−1, 1−(√)5/2] (c) [1−(√)5/2, 1+(√)5/2] (d) [0, 1+(√)5/2]

$${Domain}\:\:{of}\:\:{the}\:\:{explicit}\:\:{form}\:\:{of} \\ $$$${the}\:\:{function}\:\:\:{y}\:\:\:{represented}\: \\ $$$${implicitly}\:\:\:{by}\:\:{the}\:\:{equation}\: \\ $$$$\left(\mathrm{1}+{x}\right){cosy}−{x}^{\mathrm{2}} =\mathrm{0}\:\:{is} \\ $$$$\left({a}\right)\:\:\left(−\mathrm{1},\mathrm{1}\right]\:\:\:\:\:\:\:\:\:\:\left({b}\right)\:\:\:\:\left(−\mathrm{1},\:\mathrm{1}−\sqrt{}\mathrm{5}/\mathrm{2}\right] \\ $$$$\left({c}\right)\:\:\:\left[\mathrm{1}−\sqrt{}\mathrm{5}/\mathrm{2},\:\mathrm{1}+\sqrt{}\mathrm{5}/\mathrm{2}\right] \\ $$$$\left({d}\right)\:\:\left[\mathrm{0},\:\mathrm{1}+\sqrt{}\mathrm{5}/\mathrm{2}\right] \\ $$

Question Number 39395 Answers: 0 Comments: 2

Given that θ is an obtuse angle find tan θ if cos θ =(3/5)

$${Given}\:{that}\:\theta\:{is}\:{an}\:{obtuse}\: \\ $$$${angle}\:{find}\:{tan}\:\theta\:{if} \\ $$$${cos}\:\theta\:=\frac{\mathrm{3}}{\mathrm{5}} \\ $$$$ \\ $$

Question Number 39337 Answers: 0 Comments: 0

tan^(−1) 2 + tan^(−1) 3=cosec^(−1) x ,then x is equal to (a) 4 (b) (√2) (d) −(√2) (d) none of these

$${tan}^{−\mathrm{1}} \:\mathrm{2}\:+\:{tan}^{−\mathrm{1}} \:\mathrm{3}={cosec}^{−\mathrm{1}} {x}\:\:,{then} \\ $$$${x}\:\:{is}\:\:{equal}\:\:{to} \\ $$$$\:\left({a}\right)\:\:\:\mathrm{4}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({b}\right)\:\:\sqrt{\mathrm{2}}\:\: \\ $$$$\left({d}\right)\:−\sqrt{\mathrm{2}}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({d}\right)\:{none}\:{of}\:{these} \\ $$

Question Number 39289 Answers: 1 Comments: 0

Find the value of x if the matrix (((3x 5x)),((x 3)) ) (((x 1)),((3 x)) ) has no inverse

$${Find}\:{the}\:{value}\:{of}\:{x}\:{if}\: \\ $$$${the}\:{matrix}\: \\ $$$$ \\ $$$$\begin{pmatrix}{\mathrm{3}{x}\:\:\:\:\:\:\:\:\mathrm{5}{x}}\\{{x}\:\:\:\:\:\:\:\:\:\:\:\:\:\:\mathrm{3}}\end{pmatrix}\begin{pmatrix}{{x}\:\:\:\:\:\:\mathrm{1}}\\{\mathrm{3}\:\:\:\:\:\:\:\:\:{x}}\end{pmatrix}\: \\ $$$${has}\:{no}\:{inverse} \\ $$

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