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Question Number 11436 Answers: 0 Comments: 1

∫_0 ^(𝛑/4) sinx×cos^7 x dx. solves...

$$ \\ $$$$\underset{\mathrm{0}} {\overset{\frac{\boldsymbol{\pi}}{\mathrm{4}}} {\int}}\boldsymbol{\mathrm{sinx}}×\boldsymbol{\mathrm{cos}}^{\mathrm{7}} \boldsymbol{\mathrm{x}}\:\boldsymbol{\mathrm{dx}}. \\ $$$$\boldsymbol{\mathrm{solves}}... \\ $$

Question Number 11433 Answers: 1 Comments: 5

for r=(1/θ), show that the arc length between θ=3π^(−1) and θ=nπ^(−1) (where n>3) is aproxiately equal to the length of the line y=3π^(−1) between the same bounds. Or show otherwise.

$$\mathrm{for}\:{r}=\frac{\mathrm{1}}{\theta},\:\mathrm{show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{arc}\:\mathrm{length}\:\mathrm{between} \\ $$$$\theta=\mathrm{3}\pi^{−\mathrm{1}} \:\:\mathrm{and}\:\theta={n}\pi^{−\mathrm{1}} \:\:\:\left(\mathrm{where}\:\:{n}>\mathrm{3}\right)\:\:\mathrm{is}\:\mathrm{aproxiately} \\ $$$$\mathrm{equal}\:\mathrm{to}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{line}\:{y}=\mathrm{3}\pi^{−\mathrm{1}} \\ $$$$\mathrm{between}\:\mathrm{the}\:\mathrm{same}\:\mathrm{bounds}.\:\mathrm{Or}\:\mathrm{show}\:\mathrm{otherwise}. \\ $$$$ \\ $$

Question Number 11429 Answers: 1 Comments: 0

∫_0 ^3 ((2x+3)/(2x+1))dx=𝛂+ln7. 𝛂=? please......

$$\underset{\mathrm{0}} {\overset{\mathrm{3}} {\int}}\frac{\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{3}}{\mathrm{2}\boldsymbol{\mathrm{x}}+\mathrm{1}}\boldsymbol{\mathrm{dx}}=\boldsymbol{\alpha}+\boldsymbol{\mathrm{ln}}\mathrm{7}. \\ $$$$\boldsymbol{\alpha}=? \\ $$$$\boldsymbol{\mathrm{please}}...... \\ $$

Question Number 11425 Answers: 1 Comments: 0

Question Number 11423 Answers: 0 Comments: 0

please solve. ax^4 + bx^3 + cx^2 + dx + e = 0

$$\mathrm{please}\:\mathrm{solve}.\: \\ $$$$\mathrm{ax}^{\mathrm{4}} \:+\:\mathrm{bx}^{\mathrm{3}} \:+\:\mathrm{cx}^{\mathrm{2}} \:+\:\mathrm{dx}\:+\:\mathrm{e}\:=\:\mathrm{0} \\ $$

Question Number 11420 Answers: 2 Comments: 1

please ∫_0 ^∞ ((xlogx)/((1+x^2 )^2 ))dx=

$${please} \\ $$$$ \\ $$$$\int_{\mathrm{0}} ^{\infty} \frac{{xlogx}}{\left(\mathrm{1}+{x}^{\mathrm{2}} \right)^{\mathrm{2}} }{dx}= \\ $$

Question Number 11419 Answers: 0 Comments: 1

If A = {whole numbers} and B={natural numbers}, then A△B=___.

$$\mathrm{If}\:\mathrm{A}\:=\:\left\{\mathrm{whole}\:\mathrm{numbers}\right\}\:\mathrm{and}\: \\ $$$$\mathrm{B}=\left\{\mathrm{natural}\:\mathrm{numbers}\right\},\:\mathrm{then}\:\mathrm{A}\bigtriangleup\mathrm{B}=\_\_\_. \\ $$

Question Number 11417 Answers: 0 Comments: 0

A = log (5x + 1)(3x + 5) B = (1/(log (5x+ 1)(x − 1))) If A + B ≥ 1, x must be ...

$${A}\:=\:\mathrm{log}\:\left(\mathrm{5}{x}\:+\:\mathrm{1}\right)\left(\mathrm{3}{x}\:+\:\mathrm{5}\right) \\ $$$${B}\:=\:\frac{\mathrm{1}}{\mathrm{log}\:\left(\mathrm{5}{x}+\:\mathrm{1}\right)\left({x}\:−\:\mathrm{1}\right)} \\ $$$$\mathrm{If}\:{A}\:+\:{B}\:\geqslant\:\mathrm{1},\:{x}\:\mathrm{must}\:\mathrm{be}\:... \\ $$

Question Number 11416 Answers: 1 Comments: 0

Question Number 11413 Answers: 1 Comments: 0

Find the length of the arc of the hyperbolic spiral rθ=a lying between r=a and r=2a.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{arc}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hyperbolic} \\ $$$$\mathrm{spiral}\:\:\mathrm{r}\theta=\mathrm{a}\:\:\mathrm{lying}\:\mathrm{between}\:\:\mathrm{r}=\mathrm{a}\:\:\mathrm{and}\: \\ $$$$\mathrm{r}=\mathrm{2a}. \\ $$

Question Number 11408 Answers: 1 Comments: 0

Question Number 11406 Answers: 1 Comments: 0

Evaluate: ∫_( 1) ^( 3) ((x − 1)/((x + 1)^2 )) dx

$$\mathrm{Evaluate}:\:\:\:\:\:\:\:\int_{\:\mathrm{1}} ^{\:\mathrm{3}} \:\:\frac{\mathrm{x}\:−\:\mathrm{1}}{\left(\mathrm{x}\:+\:\mathrm{1}\right)^{\mathrm{2}} }\:\mathrm{dx} \\ $$

Question Number 11405 Answers: 1 Comments: 0

Find the magnitude of two forces such that if they act at right angle their resultant is (√(10)) , and (√(13)) if they act at an angle of 60°.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{two}\:\mathrm{forces}\:\mathrm{such}\:\mathrm{that}\:\mathrm{if}\:\mathrm{they}\:\mathrm{act}\:\mathrm{at}\:\mathrm{right}\:\mathrm{angle}\:\mathrm{their} \\ $$$$\mathrm{resultant}\:\mathrm{is}\:\sqrt{\mathrm{10}}\:,\:\mathrm{and}\:\sqrt{\mathrm{13}}\:\mathrm{if}\:\mathrm{they}\:\mathrm{act}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{60}°.\: \\ $$

Question Number 11403 Answers: 0 Comments: 1

how can demonstred that cos(2x)−sin(2x)−1=−cos^2 x

$${how}\:{can}\:{demonstred}\:{that}\: \\ $$$${cos}\left(\mathrm{2}{x}\right)−{sin}\left(\mathrm{2}{x}\right)−\mathrm{1}=−{cos}^{\mathrm{2}} {x} \\ $$

Question Number 11399 Answers: 1 Comments: 0

The sum of the first and last term of an A.P is 51. And the sum of the progression is 255. Find the last term of the A.P.

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{and}\:\mathrm{last}\:\mathrm{term}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}\:\mathrm{is}\:\mathrm{51}.\:\mathrm{And}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{progression}\:\mathrm{is}\:\mathrm{255}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{last}\:\mathrm{term}\:\mathrm{of}\:\mathrm{the}\:\mathrm{A}.\mathrm{P}. \\ $$

Question Number 11398 Answers: 0 Comments: 0

Solve for x : 625^(x − 5) = 200(√x^3 )

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:: \\ $$$$\mathrm{625}^{\mathrm{x}\:−\:\mathrm{5}} \:=\:\mathrm{200}\sqrt{\mathrm{x}^{\mathrm{3}} } \\ $$

Question Number 11395 Answers: 0 Comments: 1

Prove that those functions below don′t have limit a) lim_((x,y)→(0,0)) ((xy)/(x^2 + y^2 )) b) lim_((x,y)→(0,0)) ((xy + y^3 )/(x^2 + y^2 ))

$$\mathrm{Prove}\:\mathrm{that}\:\mathrm{those}\:\mathrm{functions}\:\mathrm{below}\:\mathrm{don}'\mathrm{t}\:\mathrm{have}\:\mathrm{limit} \\ $$$$\left.\mathrm{a}\right)\:\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\:\frac{{xy}}{{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} } \\ $$$$ \\ $$$$\left.{b}\right)\:\:\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\:\:\frac{{xy}\:+\:{y}^{\mathrm{3}} }{{x}^{\mathrm{2}} \:+\:{y}^{\mathrm{2}} } \\ $$

Question Number 11394 Answers: 0 Comments: 0

Find equation of the hyperbolas that intersect 3x^2 −4y^2 =5xy and 3y^2 −4x^2 =2x+5.

$$\mathrm{Find}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{hyperbolas}\:\mathrm{that}\: \\ $$$$\mathrm{intersect}\:\mathrm{3x}^{\mathrm{2}} −\mathrm{4y}^{\mathrm{2}} =\mathrm{5xy}\:\mathrm{and}\: \\ $$$$\mathrm{3y}^{\mathrm{2}} −\mathrm{4x}^{\mathrm{2}} =\mathrm{2x}+\mathrm{5}. \\ $$

Question Number 11393 Answers: 0 Comments: 0

Question Number 11389 Answers: 1 Comments: 0

Given that the mean relative atomic mass of chlorine contain two isotopes of mass numbe 35 and 37. What is the percentage of composition of the isotope of mass number 37

$$\mathrm{Given}\:\mathrm{that}\:\mathrm{the}\:\mathrm{mean}\:\mathrm{relative}\:\mathrm{atomic}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{chlorine}\:\mathrm{contain}\:\mathrm{two}\:\mathrm{isotopes} \\ $$$$\mathrm{of}\:\mathrm{mass}\:\mathrm{numbe}\:\mathrm{35}\:\mathrm{and}\:\mathrm{37}.\:\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{percentage}\:\mathrm{of}\:\mathrm{composition}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{isotope}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{number}\:\mathrm{37}\: \\ $$

Question Number 11384 Answers: 1 Comments: 0

Out of 5 accountants and 7 bankers, a committee consisting of 2 accountants and 3 bankers is to be formed. In how many ways can this be done if (a) Any acountant and any bankers must be included (b) One particular banker must be included (c) 2 accountant cannot be in the committee

$$\mathrm{Out}\:\mathrm{of}\:\mathrm{5}\:\mathrm{accountants}\:\mathrm{and}\:\mathrm{7}\:\mathrm{bankers},\:\mathrm{a}\:\mathrm{committee}\:\mathrm{consisting}\:\mathrm{of}\: \\ $$$$\mathrm{2}\:\mathrm{accountants}\:\mathrm{and}\:\mathrm{3}\:\mathrm{bankers}\:\mathrm{is}\:\mathrm{to}\:\mathrm{be}\:\mathrm{formed}.\:\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{this} \\ $$$$\mathrm{be}\:\mathrm{done}\:\mathrm{if} \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Any}\:\mathrm{acountant}\:\mathrm{and}\:\mathrm{any}\:\mathrm{bankers}\:\mathrm{must}\:\mathrm{be}\:\mathrm{included} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{One}\:\mathrm{particular}\:\mathrm{banker}\:\mathrm{must}\:\mathrm{be}\:\mathrm{included} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{2}\:\mathrm{accountant}\:\mathrm{cannot}\:\mathrm{be}\:\mathrm{in}\:\mathrm{the}\:\mathrm{committee} \\ $$

Question Number 11383 Answers: 1 Comments: 0

There are six trains travelling between Abuja and Lagos and back. In how many ways can a man travel from abuja to Lagos by one train and return by a different train

$$\mathrm{There}\:\mathrm{are}\:\mathrm{six}\:\mathrm{trains}\:\mathrm{travelling}\:\mathrm{between}\:\mathrm{Abuja}\:\mathrm{and}\:\mathrm{Lagos}\:\mathrm{and}\:\mathrm{back}. \\ $$$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{a}\:\mathrm{man}\:\mathrm{travel}\:\mathrm{from}\:\mathrm{abuja}\:\mathrm{to}\:\mathrm{Lagos}\:\mathrm{by}\:\mathrm{one}\:\mathrm{train}\:\mathrm{and} \\ $$$$\mathrm{return}\:\mathrm{by}\:\mathrm{a}\:\mathrm{different}\:\mathrm{train} \\ $$

Question Number 11382 Answers: 0 Comments: 2

In how many ways can 24 different articles be divided into groups of 12, 8 and 4 articles respectively

$$\mathrm{In}\:\mathrm{how}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{24}\:\mathrm{different}\:\mathrm{articles}\:\mathrm{be}\:\mathrm{divided}\:\mathrm{into}\:\mathrm{groups}\:\mathrm{of} \\ $$$$\mathrm{12},\:\mathrm{8}\:\mathrm{and}\:\mathrm{4}\:\mathrm{articles}\:\mathrm{respectively} \\ $$

Question Number 11373 Answers: 1 Comments: 0

Question Number 11372 Answers: 0 Comments: 0

If G_1 and G_2 are groups , and f : G_1 →G_2 is a group homomorphism , then prove that o(G_1 ) = o(G_2 ) .

$$\mathrm{If}\:\mathrm{G}_{\mathrm{1}} \:\mathrm{and}\:\mathrm{G}_{\mathrm{2}} \:\mathrm{are}\:\mathrm{groups}\:,\:\mathrm{and}\:\mathrm{f}\::\:\mathrm{G}_{\mathrm{1}} \:\rightarrow\mathrm{G}_{\mathrm{2}} \\ $$$$\mathrm{is}\:\mathrm{a}\:\mathrm{group}\:\mathrm{homomorphism}\:,\:\mathrm{then}\:\mathrm{prove} \\ $$$$\mathrm{that}\:\mathrm{o}\left(\mathrm{G}_{\mathrm{1}} \right)\:=\:\mathrm{o}\left(\mathrm{G}_{\mathrm{2}} \right)\:. \\ $$

Question Number 11365 Answers: 0 Comments: 1

∅(n)=n−1 , n∈Z ,where ∅ is Eular phi function. True or false .And explain it .

$$\emptyset\left(\mathrm{n}\right)=\mathrm{n}−\mathrm{1}\:,\:\mathrm{n}\in\mathrm{Z}\:,\mathrm{where}\:\emptyset\:\mathrm{is}\:\mathrm{Eular}\:\mathrm{phi}\:\mathrm{function}. \\ $$$$\mathrm{True}\:\mathrm{or}\:\mathrm{false}\:.\mathrm{And}\:\mathrm{explain}\:\mathrm{it}\:. \\ $$

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