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Question Number 11473 Answers: 1 Comments: 1

Show that the graph of y = x^3 + 2x^2 + x + 1 , between x = − 1 and x = 2 lies entirely above the x − axis

$$\mathrm{Show}\:\mathrm{that}\:\mathrm{the}\:\mathrm{graph}\:\mathrm{of}\:\:\mathrm{y}\:=\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{2x}^{\mathrm{2}} \:+\:\mathrm{x}\:+\:\mathrm{1}\:,\:\mathrm{between}\:\mathrm{x}\:=\:−\:\mathrm{1}\:\mathrm{and}\:\mathrm{x}\:=\:\mathrm{2} \\ $$$$\mathrm{lies}\:\mathrm{entirely}\:\mathrm{above}\:\mathrm{the}\:\mathrm{x}\:−\:\mathrm{axis} \\ $$

Question Number 11459 Answers: 2 Comments: 0

If ((4x^2 −4xy+3y^2 )/(2y^2 +2xy−5x^2 ))=1 if the ((x+y)/(x−y)) what is th value?

Question Number 11456 Answers: 2 Comments: 3

sin x − cos x = a, (π/4) ≤ x ≤ (π/2) Which statement is correct? (1) sin^2 x − cos^2 x = −(1/2)(√(3 + 2a^2 − a^4 )) (2) sin^4 x + cos^4 x = (1/8)(−3a^4 + 6a^2 + 5) (3) sin 2x = ((1 − a^2 )/2) (4) tan^2 x + cot^2 x = ((−3a^4 − 2a^2 + 8a + 13 )/(2(a^4 + 2a^2 + 1)))

$$\mathrm{sin}\:{x}\:−\:\mathrm{cos}\:{x}\:=\:{a},\:\:\frac{\pi}{\mathrm{4}}\:\leqslant\:{x}\:\leqslant\:\frac{\pi}{\mathrm{2}} \\ $$$$\mathrm{Which}\:\mathrm{statement}\:\mathrm{is}\:\mathrm{correct}? \\ $$$$\left(\mathrm{1}\right)\:\mathrm{sin}^{\mathrm{2}} \:{x}\:−\:\mathrm{cos}^{\mathrm{2}} \:{x}\:=\:−\frac{\mathrm{1}}{\mathrm{2}}\sqrt{\mathrm{3}\:+\:\mathrm{2}{a}^{\mathrm{2}} \:−\:{a}^{\mathrm{4}} } \\ $$$$\left(\mathrm{2}\right)\:\mathrm{sin}^{\mathrm{4}} \:{x}\:+\:\mathrm{cos}^{\mathrm{4}} \:{x}\:=\:\frac{\mathrm{1}}{\mathrm{8}}\left(−\mathrm{3}{a}^{\mathrm{4}} \:+\:\mathrm{6}{a}^{\mathrm{2}} \:+\:\mathrm{5}\right) \\ $$$$\left(\mathrm{3}\right)\:\mathrm{sin}\:\mathrm{2}{x}\:=\:\frac{\mathrm{1}\:−\:{a}^{\mathrm{2}} }{\mathrm{2}} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{tan}^{\mathrm{2}} \:{x}\:+\:\mathrm{cot}^{\mathrm{2}} \:{x}\:=\:\frac{−\mathrm{3}{a}^{\mathrm{4}} \:−\:\mathrm{2}{a}^{\mathrm{2}} \:+\:\mathrm{8}{a}\:+\:\mathrm{13}\:}{\mathrm{2}\left({a}^{\mathrm{4}} \:+\:\mathrm{2}{a}^{\mathrm{2}} \:+\:\mathrm{1}\right)} \\ $$

Question Number 11453 Answers: 0 Comments: 0

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Question Number 11444 Answers: 2 Comments: 0

If lim_(x→0) (((√(px + q)) − 2)/x) = 1 What is the value of p + q ?

$$\mathrm{If}\:\:\underset{{x}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{px}\:+\:{q}}\:−\:\mathrm{2}}{{x}}\:=\:\mathrm{1} \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:{p}\:+\:{q}\:? \\ $$

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

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

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