Question and Answers Forum

AllQuestion and Answers: Page 1315

Question Number 81993 Answers: 0 Comments: 0

calculate ∫∫_D ln(1+x+y)dxdy with D is the triangle limited by points 0,A(1,0) and B(0,1)

$${calculate}\:\int\int_{{D}} {ln}\left(\mathrm{1}+{x}+{y}\right){dxdy} \\ $$$${with}\:{D}\:{is}\:{the}\:{triangle}\:{limited}\:{by} \\ $$$${points}\:\mathrm{0},{A}\left(\mathrm{1},\mathrm{0}\right)\:{and}\:{B}\left(\mathrm{0},\mathrm{1}\right) \\ $$

Question Number 81983 Answers: 0 Comments: 4

Question Number 81980 Answers: 1 Comments: 2

Question Number 82031 Answers: 1 Comments: 0

find x,y { ((5(√(2x^2 −y^4 )) =4x−3y)),((4(√(2x^2 −y^4 )) =3x−2y)) :}

$${find}\:{x},{y} \\ $$$$\begin{cases}{\mathrm{5}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }\:=\mathrm{4}{x}−\mathrm{3}{y}}\\{\mathrm{4}\sqrt{\mathrm{2}{x}^{\mathrm{2}} −{y}^{\mathrm{4}} }\:=\mathrm{3}{x}−\mathrm{2}{y}}\end{cases} \\ $$

Question Number 82030 Answers: 1 Comments: 0

a − b + c − d = 2 a^2 − b^2 + c^2 − d^2 = 6 a^3 − b^3 + c^3 − d^3 = 20 a^4 − b^4 + c^4 − d^4 = 66 a + b + c + d = ?

$${a}\:−\:{b}\:+\:{c}\:−\:{d}\:\:=\:\:\mathrm{2} \\ $$$${a}^{\mathrm{2}} \:−\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} \:−\:{d}^{\mathrm{2}} \:\:=\:\:\mathrm{6} \\ $$$${a}^{\mathrm{3}} \:−\:{b}^{\mathrm{3}} \:+\:{c}^{\mathrm{3}} \:−\:{d}^{\mathrm{3}} \:\:=\:\:\mathrm{20} \\ $$$${a}^{\mathrm{4}} \:−\:{b}^{\mathrm{4}} \:+\:{c}^{\mathrm{4}} \:−\:{d}^{\mathrm{4}} \:\:=\:\:\mathrm{66} \\ $$$${a}\:+\:{b}\:+\:{c}\:+\:{d}\:\:=\:\:? \\ $$

Question Number 81975 Answers: 2 Comments: 5

Question Number 81972 Answers: 1 Comments: 1

Question Number 81971 Answers: 1 Comments: 0

Question Number 81970 Answers: 0 Comments: 1

find the limit as n −>∞ lim(2−^n (√x))^n

$${find}\:{the}\:{limit}\:{as}\:{n}\:−>\infty \\ $$$$ \\ $$$${lim}\left(\mathrm{2}−\:^{{n}} \sqrt{{x}}\right)^{{n}} \\ $$$$ \\ $$

Question Number 81968 Answers: 1 Comments: 1

Question Number 81966 Answers: 1 Comments: 0

(((1 + i(√3))/2) )^(2020) + (((1 − i(√3))/2) )^(2020) = A A^4 = ?

$$\left(\frac{\mathrm{1}\:+\:{i}\sqrt{\mathrm{3}}}{\mathrm{2}}\:\right)^{\mathrm{2020}} \:+\:\:\left(\frac{\mathrm{1}\:−\:{i}\sqrt{\mathrm{3}}}{\mathrm{2}}\:\right)^{\mathrm{2020}} \:\:=\:\:\:{A} \\ $$$${A}^{\mathrm{4}} \:\:=\:\:? \\ $$

Question Number 81963 Answers: 1 Comments: 2

if tan (x)+sec (x) = (7/8) find cot (x)+cosec (x) =

$${if}\:\mathrm{tan}\:\left({x}\right)+\mathrm{sec}\:\left({x}\right)\:=\:\frac{\mathrm{7}}{\mathrm{8}} \\ $$$${find}\:\mathrm{cot}\:\left({x}\right)+\mathrm{cosec}\:\left({x}\right)\:=\: \\ $$

Question Number 82130 Answers: 0 Comments: 5

In an arrangement of the word VIOLENT, find the chances that the vowels I, O, E occupy the odd positions.

$$\mathrm{In}\:\mathrm{an}\:\mathrm{arrangement}\:\mathrm{of}\:\mathrm{the}\:\mathrm{word}\:\:\mathrm{VIOLENT},\:\mathrm{find}\:\mathrm{the}\:\mathrm{chances} \\ $$$$\mathrm{that}\:\mathrm{the}\:\mathrm{vowels}\:\:\:\mathrm{I},\:\mathrm{O},\:\mathrm{E}\:\:\:\mathrm{occupy}\:\mathrm{the}\:\mathrm{odd}\:\mathrm{positions}. \\ $$

Question Number 81954 Answers: 0 Comments: 6

soit α∈]0;π[. determiner: 1)le module et l′argument de: a)1−e^(iα) ,b)1+e^(i𝛂) 2)deduire le module et l′argument de a) ((1−e^(iα) )/(1+e^(iα) )), b)(1−e^(iα) )(1+e^(iα) ) rochinel930@gmail.c

$$\left.\:{soit}\:\alpha\in\right]\mathrm{0};\pi\left[.\:{determiner}:\right. \\ $$$$\left.\mathrm{1}\right){le}\:{module}\:{et}\:{l}'{argument}\:{de}: \\ $$$$\left.\boldsymbol{{a}}\left.\right)\mathrm{1}−\boldsymbol{{e}}^{\boldsymbol{{i}}\alpha} ,\boldsymbol{{b}}\right)\mathrm{1}+\boldsymbol{{e}}^{\boldsymbol{{i}\alpha}} \\ $$$$\left.\mathrm{2}\right)\boldsymbol{{deduire}}\:\boldsymbol{{le}}\:\boldsymbol{{module}}\:\boldsymbol{{et}}\:\boldsymbol{{l}}'\boldsymbol{{argument}}\:\boldsymbol{{de}} \\ $$$$\left.\:\left.\boldsymbol{{a}}\right)\:\frac{\mathrm{1}−\boldsymbol{{e}}^{\boldsymbol{{i}}\alpha} }{\mathrm{1}+{e}^{{i}\alpha} },\:{b}\right)\left(\mathrm{1}−{e}^{{i}\alpha} \right)\left(\mathrm{1}+{e}^{{i}\alpha} \right) \\ $$$$\:\boldsymbol{{rochinel}}\mathrm{930}@{gmail}.\boldsymbol{{c}} \\ $$

Question Number 81944 Answers: 2 Comments: 0

show that cot(40°)−cot(50°)=2tan(10°) cos(70°) cos(50^° ) cos(10^° )=((√3)/8)

$${show}\:{that}\: \\ $$$${cot}\left(\mathrm{40}°\right)−{cot}\left(\mathrm{50}°\right)=\mathrm{2}{tan}\left(\mathrm{10}°\right) \\ $$$${cos}\left(\mathrm{70}°\right)\:{cos}\left(\mathrm{50}^{°} \right)\:{cos}\left(\mathrm{10}^{°} \right)=\frac{\sqrt{\mathrm{3}}}{\mathrm{8}} \\ $$

Question Number 81943 Answers: 0 Comments: 0

Evaluate: (((√(30 + (√8) + (√5)))/((√8) + (√5))))^(1/4)

$$\mathrm{Evaluate}:\:\:\:\:\left(\frac{\sqrt{\mathrm{30}\:+\:\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}}{\sqrt{\mathrm{8}}\:+\:\sqrt{\mathrm{5}}}\right)^{\mathrm{1}/\mathrm{4}} \\ $$

Question Number 81942 Answers: 1 Comments: 0

Question Number 81937 Answers: 0 Comments: 2

Solve the PDE by method of separating variables (∂^2 u/∂x^2 ) + 2t(∂^2 u/(∂x∂t)) − 4u = 0

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{PDE}\:\mathrm{by}\:\mathrm{method}\:\mathrm{of}\:\mathrm{separating}\:\mathrm{variables} \\ $$$$\frac{\partial^{\mathrm{2}} {u}}{\partial{x}^{\mathrm{2}} }\:+\:\mathrm{2}{t}\frac{\partial^{\mathrm{2}} {u}}{\partial{x}\partial{t}}\:−\:\mathrm{4}{u}\:=\:\mathrm{0} \\ $$

Question Number 81927 Answers: 2 Comments: 0

One man adds 3 litres of water to 12 litres of milk and another 4 litres of water to 10 litres of milk. What is the ratio of the strengths of milk in the two mixtures?

$$\mathrm{One}\:\mathrm{man}\:\mathrm{adds}\:\mathrm{3}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{water}\:\mathrm{to}\:\mathrm{12}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{milk} \\ $$$$\mathrm{and}\:\mathrm{another}\:\mathrm{4}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{water}\:\mathrm{to}\:\mathrm{10}\:\mathrm{litres}\:\mathrm{of}\:\mathrm{milk}. \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{strengths}\:\mathrm{of}\:\mathrm{milk}\:\mathrm{in}\:\mathrm{the} \\ $$$$\mathrm{two}\:\mathrm{mixtures}? \\ $$

Question Number 81926 Answers: 1 Comments: 1

3 integers are chosen at random from the first 20 integers. The probability that their ptoduct is even, is

$$\mathrm{3}\:\mathrm{integers}\:\mathrm{are}\:\mathrm{chosen}\:\mathrm{at}\:\mathrm{random}\:\mathrm{from} \\ $$$$\mathrm{the}\:\mathrm{first}\:\mathrm{20}\:\mathrm{integers}.\:\mathrm{The}\:\mathrm{probability} \\ $$$$\mathrm{that}\:\mathrm{their}\:\mathrm{ptoduct}\:\mathrm{is}\:\mathrm{even},\:\mathrm{is} \\ $$

Question Number 81925 Answers: 1 Comments: 0

If A and B are two indpendent events, the probability that both A and B occur is (1/8) and the probability that neither of them occurs is (3/8) . The probability of the occurrence of A is

$$\mathrm{If}\:{A}\:\mathrm{and}\:{B}\:\mathrm{are}\:\mathrm{two}\:\mathrm{indpendent}\:\mathrm{events}, \\ $$$$\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{both}\:{A}\:\mathrm{and}\:{B}\:\mathrm{occur} \\ $$$$\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{8}}\:\mathrm{and}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{neither}\:\mathrm{of} \\ $$$$\mathrm{them}\:\mathrm{occurs}\:\mathrm{is}\:\frac{\mathrm{3}}{\mathrm{8}}\:.\:\mathrm{The}\:\mathrm{probability}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{occurrence}\:\mathrm{of}\:{A}\:\mathrm{is} \\ $$

Question Number 81921 Answers: 1 Comments: 0

Question Number 81911 Answers: 1 Comments: 4

Question Number 81910 Answers: 0 Comments: 1

a_1 =1 a_2 =2 a_(n+1) =(n+1)a_n −2a_(n−1) find a_n =?

$${a}_{\mathrm{1}} =\mathrm{1} \\ $$$${a}_{\mathrm{2}} =\mathrm{2} \\ $$$${a}_{{n}+\mathrm{1}} =\left({n}+\mathrm{1}\right){a}_{{n}} −\mathrm{2}{a}_{{n}−\mathrm{1}} \\ $$$${find}\:{a}_{{n}} =? \\ $$

Question Number 81906 Answers: 0 Comments: 1

Question Number 81889 Answers: 1 Comments: 0

Pg 1310 Pg 1311 Pg 1312 Pg 1313 Pg 1314 Pg 1315 Pg 1316 Pg 1317 Pg 1318 Pg 1319

Contact: info@tinkutara.com