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Question Number 39173 Answers: 0 Comments: 0

Given that A and B are two independent Events where P(A) = (4/5) and P(A ∪ B) = ((13)/5) . find a) P(A∩B) b) P(A∣B). hence draw tree Diagram for each posible out come

$${Given}\:{that}\:{A}\:{and}\:{B}\:{are}\:{two} \\ $$$${independent}\:{Events}\: \\ $$$${where}\:{P}\left({A}\right)\:=\:\frac{\mathrm{4}}{\mathrm{5}}\:{and}\: \\ $$$${P}\left({A}\:\cup\:{B}\right)\:=\:\frac{\mathrm{13}}{\mathrm{5}}\:. \\ $$$$\left.{find}\:{a}\right)\:{P}\left({A}\cap{B}\right) \\ $$$$\left.\:\:\:\:\:\:\:\:\:{b}\right)\:{P}\left({A}\mid{B}\right). \\ $$$${hence}\:{draw}\:{tree}\:{Diagram} \\ $$$${for}\:{each}\:{posible}\:{out}\:{come} \\ $$

Question Number 39172 Answers: 1 Comments: 1

find the angle between 3i − 4j and i − j

$${find}\:{the}\:{angle}\:{between}\: \\ $$$$\mathrm{3}{i}\:−\:\mathrm{4}{j}\:{and}\:{i}\:−\:{j} \\ $$

Question Number 39171 Answers: 1 Comments: 0

Given that y = 3x^4 and x increases at the rate of 34% . find the percentage increase in y. [hint: using Bionomial method]

$${Given}\:{that}\: \\ $$$${y}\:=\:\mathrm{3}{x}^{\mathrm{4}} \:{and}\:{x}\:{increases} \\ $$$${at}\:{the}\:{rate}\:{of}\:\mathrm{34\%}\:. \\ $$$${find}\:{the}\:{percentage}\:{increase} \\ $$$${in}\:{y}. \\ $$$$\left[{hint}:\:{using}\:{Bionomial}\:\right. \\ $$$$\left.{method}\right] \\ $$

Question Number 39166 Answers: 1 Comments: 1

Find the value of k if (2,k) ,(3,4) and (6,4) are collinear. hence find the equation on the line 3i − j with the above points

$${Find}\:{the}\:{value}\:{of}\:{k}\:{if} \\ $$$$\left(\mathrm{2},{k}\right)\:,\left(\mathrm{3},\mathrm{4}\right)\:{and}\:\left(\mathrm{6},\mathrm{4}\right)\:{are} \\ $$$${collinear}. \\ $$$${hence}\:{find}\:{the}\:{equation}\:{on} \\ $$$${the}\:{line}\:\mathrm{3}{i}\:−\:{j}\:{with}\:{the}\:{above} \\ $$$${points} \\ $$

Question Number 39170 Answers: 0 Comments: 0

Find the value of k if (d/dx)(f(x))= 6 when x = −1 and f(x) = 3x^3 − kx^2 + 1 if f(2) = 8 find one factor of f(x) and hence Evaluate lim_(x→∞) (f(x)).

$${Find}\:{the}\:{value}\:{of}\:{k}\:{if}\: \\ $$$$\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)=\:\mathrm{6}\:{when}\:{x}\:=\:−\mathrm{1}\: \\ $$$${and}\:{f}\left({x}\right)\:=\:\mathrm{3}{x}^{\mathrm{3}} \:−\:{kx}^{\mathrm{2}} \:+\:\mathrm{1}\: \\ $$$${if}\:{f}\left(\mathrm{2}\right)\:=\:\mathrm{8}\:{find}\:{one}\:{factor}\:{of} \\ $$$${f}\left({x}\right)\:{and}\:{hence}\:{Evaluate} \\ $$$$\underset{{x}\rightarrow\infty} {{lim}}\left({f}\left({x}\right)\right). \\ $$

Question Number 39127 Answers: 0 Comments: 1

Given the lines l_1 : x + y = 5 and l_2 : y = 4x and l_3 ; 4x + y − 1 =0 show that l_(2 ) is perpendicular to l_3 . find the point coordinates if x + 2y = 5 is colliner to l_1

$${Given}\:{the}\:{lines} \\ $$$${l}_{\mathrm{1}} :\:\:{x}\:+\:{y}\:=\:\mathrm{5}\:{and}\:{l}_{\mathrm{2}} :\:{y}\:=\:\mathrm{4}{x} \\ $$$${and}\:{l}_{\mathrm{3}} ;\:\mathrm{4}{x}\:+\:{y}\:−\:\mathrm{1}\:=\mathrm{0} \\ $$$${show}\:{that}\:{l}_{\mathrm{2}\:} \:{is}\:{perpendicular} \\ $$$${to}\:{l}_{\mathrm{3}} . \\ $$$${find}\:{the}\:{point}\:{coordinates} \\ $$$${if}\:{x}\:+\:\mathrm{2}{y}\:=\:\mathrm{5}\:{is}\:{colliner}\:{to}\:{l}_{\mathrm{1}} \\ $$

Question Number 39144 Answers: 1 Comments: 0

f(x) = 3x^3 − 2x + k has factor (x − 1) find the value of k. with these value evaluate a) (d/(dx ))(f(x)_ ) b) ∫_5 ^2 (f(x))

$${f}\left({x}\right)\:=\:\mathrm{3}{x}^{\mathrm{3}} \:−\:\mathrm{2}{x}\:+\:{k}\:{has}\: \\ $$$${factor}\:\left({x}\:−\:\mathrm{1}\right)\:\: \\ $$$${find}\:{the}\:{value}\:{of}\:{k}. \\ $$$${with}\:{these}\:{value}\: \\ $$$${evaluate} \\ $$$$\left.{a}\right)\:\frac{{d}}{{dx}\:}\left({f}\left({x}\right)_{} \right) \\ $$$$\left.{b}\right)\:\int_{\mathrm{5}} ^{\mathrm{2}} \left({f}\left({x}\right)\right) \\ $$

Question Number 39021 Answers: 0 Comments: 0

calculate A_n = ∫_0 ^1 sin(narctanx)dx with n integr natural. 2) find nature of Σ_n A_n

$${calculate}\:\:{A}_{{n}} =\:\int_{\mathrm{0}} ^{\mathrm{1}} \:{sin}\left({narctanx}\right){dx}\:\:{with}\:{n}\:{integr}\:{natural}. \\ $$$$\left.\mathrm{2}\right)\:{find}\:{nature}\:{of}\:\sum_{{n}} \:\:{A}_{{n}} \\ $$

Question Number 39013 Answers: 0 Comments: 1

Given the matrices A = ((3,5),(2,4) ) and I = ((1,0),(0,1) ) find matrix B if BA= I find A′ the reflection on the line y = x and A′′ the enlargement with matrix (((2 0)),((0 2)) ).

$${Given}\:{the}\:{matrices} \\ $$$${A}\:=\:\begin{pmatrix}{\mathrm{3}}&{\mathrm{5}}\\{\mathrm{2}}&{\mathrm{4}}\end{pmatrix}\:{and}\:{I}\:=\:\begin{pmatrix}{\mathrm{1}}&{\mathrm{0}}\\{\mathrm{0}}&{\mathrm{1}}\end{pmatrix} \\ $$$${find}\:{matrix}\:{B}\:{if}\: \\ $$$${BA}=\:{I} \\ $$$${find}\:{A}'\:{the}\:{reflection}\:{on}\:{the} \\ $$$${line}\:{y}\:=\:{x}\:{and}\:{A}''\:{the}\:{enlargement} \\ $$$${with}\:{matrix}\:\begin{pmatrix}{\mathrm{2}\:\:\:\:\:\:\:\:\:\mathrm{0}}\\{\mathrm{0}\:\:\:\:\:\:\:\:\:\:\mathrm{2}}\end{pmatrix}. \\ $$

Question Number 39003 Answers: 2 Comments: 0

Question Number 38996 Answers: 1 Comments: 1

a line with equation y = 2x + 5.the point (1,7) lie on this line.find the distance between this line and the line joining (2,3) and (6,7).

$${a}\:{line}\:{with}\:{equation} \\ $$$$\:{y}\:=\:\mathrm{2}{x}\:+\:\mathrm{5}.{the}\:{point}\:\left(\mathrm{1},\mathrm{7}\right) \\ $$$${lie}\:{on}\:{this}\:{line}.{find}\:{the}\: \\ $$$${distance}\:{between}\:{this}\:{line}\: \\ $$$${and}\:{the}\:{line}\:{joining}\: \\ $$$$\left(\mathrm{2},\mathrm{3}\right)\:{and}\:\left(\mathrm{6},\mathrm{7}\right). \\ $$

Question Number 38957 Answers: 1 Comments: 1

solve for x e^(2x) + 2e^x + 1 = 0

$${solve}\:{for}\:{x}\: \\ $$$${e}^{\mathrm{2}{x}} \:+\:\mathrm{2}{e}^{{x}} \:+\:\mathrm{1}\:=\:\mathrm{0} \\ $$

Question Number 38910 Answers: 1 Comments: 0

Given a polynomial f(x) where f(x) = x^3 + ax^2 + 3x + b and ( x− 1) is a factor of f(x) and f ′(x)= 12 at point ( 2,4) find the values of a and b hence factorise f(x) completely

$${Given}\:{a}\:{polynomial}\:{f}\left({x}\right)\:{where} \\ $$$${f}\left({x}\right)\:=\:{x}^{\mathrm{3}} \:+\:{ax}\:^{\mathrm{2}} \:+\:\mathrm{3}{x}\:+\:{b} \\ $$$${and}\:\left(\:{x}−\:\mathrm{1}\right)\:{is}\:{a}\:{factor}\:{of}\:{f}\left({x}\right) \\ $$$${and}\:{f}\:'\left({x}\right)=\:\:\mathrm{12}\:{at}\:{point}\:\left(\:\mathrm{2},\mathrm{4}\right) \\ $$$${find}\:{the}\:{values}\:{of}\:{a}\:{and}\:{b} \\ $$$${hence}\:{factorise}\:{f}\left({x}\right)\:{completely} \\ $$$$ \\ $$

Question Number 38881 Answers: 1 Comments: 0

solve for 0 ≤ θ ≤π, the equations a)_ cos (2θ − (π/2))= (1/2) b) cos θ − (√3) sin θ = 0

$${solve}\:{for}\:\mathrm{0}\:\leqslant\:\theta\:\leqslant\pi,\:{the}\:{equations} \\ $$$$\left.{a}\right)_{} \:\mathrm{cos}\:\left(\mathrm{2}\theta\:−\:\frac{\pi}{\mathrm{2}}\right)=\:\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\left.{b}\right)\:\mathrm{cos}\:\theta\:−\:\sqrt{\mathrm{3}}\:{sin}\:\theta\:=\:\mathrm{0} \\ $$

Question Number 38880 Answers: 1 Comments: 0

Find the equation of the perpendicular bisector of the line segment joining the points (1,3) and (5,1)

$${Find}\:{the}\:{equation}\:{of}\:{the}\:{perpendicular} \\ $$$${bisector}\:{of}\:{the}\:{line}\:{segment}\:{joining} \\ $$$${the}\:{points}\:\left(\mathrm{1},\mathrm{3}\right)\:{and}\:\left(\mathrm{5},\mathrm{1}\right) \\ $$

Question Number 38879 Answers: 1 Comments: 0

Find the equation of the line through (2,−3) which make angles 45° with the line 2x − y = 2.

$${Find}\:{the}\:{equation}\:{of}\:{the}\:{line}\:{through} \\ $$$$\left(\mathrm{2},−\mathrm{3}\right)\:{which}\:{make}\:{angles}\:\mathrm{45}°\:{with} \\ $$$${the}\:{line}\:\mathrm{2}{x}\:−\:{y}\:=\:\mathrm{2}. \\ $$

Question Number 38878 Answers: 1 Comments: 0

Find the equation on a line joining the points A(2x,4),B(x,3) and C(4,3)