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Question Number 41141    Answers: 0   Comments: 1

If X= [(3,(−4)),(1,(−1)) ], the value of X^n is

$$\mathrm{If}\:{X}=\begin{bmatrix}{\mathrm{3}}&{−\mathrm{4}}\\{\mathrm{1}}&{−\mathrm{1}}\end{bmatrix},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{X}^{{n}} \mathrm{is} \\ $$

Question Number 41139    Answers: 1   Comments: 1

Question Number 41138    Answers: 0   Comments: 3

A parallelogram, the length of whose sides are 12 cm and 8 cm, has one diagonal 10 cm long. Find the length of the other diagonal.

$$\mathrm{A}\:\mathrm{parallelogram},\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{whose}\: \\ $$$$\mathrm{sides}\:\mathrm{are}\:\mathrm{12}\:\mathrm{cm}\:\mathrm{and}\:\mathrm{8}\:\mathrm{cm},\:\mathrm{has}\:\mathrm{one}\: \\ $$$$\mathrm{diagonal}\:\:\:\mathrm{10}\:\mathrm{cm}\:\mathrm{long}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{length} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{other}\:\mathrm{diagonal}. \\ $$

Question Number 41137    Answers: 0   Comments: 0

Question Number 41136    Answers: 1   Comments: 0

let f(x)=2x−(√(x−1)) find ∫ f^(−1) (x)dx .

$${let}\:{f}\left({x}\right)=\mathrm{2}{x}−\sqrt{{x}−\mathrm{1}} \\ $$$${find}\:\:\int\:{f}^{−\mathrm{1}} \left({x}\right){dx}\:. \\ $$

Question Number 41135    Answers: 1   Comments: 0

find f(x)=∫_0 ^1 arctan(xt)dt x from R

$${find}\:{f}\left({x}\right)=\int_{\mathrm{0}} ^{\mathrm{1}} {arctan}\left({xt}\right){dt}\:\:{x}\:{from}\:{R}\: \\ $$

Question Number 41117    Answers: 2   Comments: 0

Question Number 41121    Answers: 0   Comments: 0

Radio Karneston broadcasts at 891kHz. A student made a radio to receive the station using an L-C oscillator circuit with an inductor of fixed inductance,0.16mH and a variable⊛ capacitor.At what value of capacitance will the student receive the station?

$${Radio}\:{Karneston}\:{broadcasts}\:{at}\:\mathrm{891}{kHz}. \\ $$$${A}\:{student}\:{made}\:{a}\:{radio}\:{to}\:{receive} \\ $$$${the}\:{station}\:{using}\:{an}\:{L}-{C}\:{oscillator} \\ $$$${circuit}\:{with}\:{an}\:{inductor}\:{of}\:{fixed} \\ $$$${inductance},\mathrm{0}.\mathrm{16}{mH}\:{and}\:{a}\:{variable}\circledast \\ $$$${capacitor}.{At}\:{what}\:{value}\:{of} \\ $$$${capacitance}\:{will}\:{the}\:{student}\:{receive} \\ $$$${the}\:{station}? \\ $$

Question Number 41122    Answers: 0   Comments: 0

A lamp is connected in series with a parallel plate capacitor and a source of alternating current.When the plates seperation is increased,the⊛ lamp dims.Please explain this observation.

$${A}\:{lamp}\:{is}\:{connected}\:{in}\:{series}\:{with} \\ $$$${a}\:{parallel}\:{plate}\:{capacitor}\:{and}\:{a}\:{source} \\ $$$${of}\:{alternating}\:{current}.{When}\:{the} \\ $$$${plates}\:{seperation}\:{is}\:{increased},{the}\circledast \\ $$$${lamp}\:{dims}.{Please}\:{explain}\:{this} \\ $$$${observation}. \\ $$

Question Number 41108    Answers: 1   Comments: 0

evaluate ∫x^i dx where i=(√(−1))

$$\boldsymbol{\mathrm{evaluate}}\:\int\boldsymbol{{x}}^{\boldsymbol{{i}}} \boldsymbol{{dx}} \\ $$$$\boldsymbol{\mathrm{where}}\:\boldsymbol{{i}}=\sqrt{−\mathrm{1}} \\ $$

Question Number 41103    Answers: 1   Comments: 6

Question Number 41101    Answers: 1   Comments: 2

Find a general formula for m such that f(x)=∣sin x∣+sin ∣x∣ be not differentiable at x=m.

$${Find}\:{a}\:{general}\:{formula}\:{for}\:{m} \\ $$$${such}\:{that}\:{f}\left({x}\right)=\mid\mathrm{sin}\:{x}\mid+\mathrm{sin}\:\mid{x}\mid \\ $$$${be}\:{not}\:{differentiable}\:{at}\:{x}={m}. \\ $$

Question Number 41096    Answers: 0   Comments: 1

Question Number 41095    Answers: 1   Comments: 0

For all real values of x solve the inequality ∣((1−x^3 )/(x^6 −2x^3 +5))∣≤(1/4)

$${For}\:{all}\:{real}\:{values}\:{of}\:{x}\:{solve}\:{the} \\ $$$${inequality} \\ $$$$\:\mid\frac{\mathrm{1}−{x}^{\mathrm{3}} }{{x}^{\mathrm{6}} −\mathrm{2}{x}^{\mathrm{3}} +\mathrm{5}}\mid\leqslant\frac{\mathrm{1}}{\mathrm{4}} \\ $$

Question Number 41086    Answers: 1   Comments: 0

A woman is four times older than her daughter. Six years ago the product of their ages is 136. How old is the woman?

$$\mathrm{A}\:\mathrm{woman}\:\mathrm{is}\:\mathrm{four}\:\mathrm{times}\:\mathrm{older}\:\mathrm{than}\: \\ $$$$\mathrm{her}\:\mathrm{daughter}.\:\mathrm{Six}\:\mathrm{years}\:\mathrm{ago}\:\mathrm{the} \\ $$$$\mathrm{product}\:\mathrm{of}\:\mathrm{their}\:\mathrm{ages}\:\mathrm{is}\:\mathrm{136}. \\ $$$$\mathrm{How}\:\mathrm{old}\:\mathrm{is}\:\mathrm{the}\:\mathrm{woman}? \\ $$

Question Number 41084    Answers: 1   Comments: 0

∫ (x^3 /(x^6 + 1)) dx

$$\int\:\frac{\mathrm{x}^{\mathrm{3}} }{\mathrm{x}^{\mathrm{6}} \:+\:\mathrm{1}}\:\mathrm{dx} \\ $$

Question Number 41079    Answers: 1   Comments: 0

In a triangle the length of the two larger sides are 24 and 22, respectively. If the angles are in AP, then the third side is

$$\mathrm{In}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{the}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two} \\ $$$$\mathrm{larger}\:\mathrm{sides}\:\mathrm{are}\:\mathrm{24}\:\mathrm{and}\:\mathrm{22},\:\mathrm{respectively}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{angles}\:\mathrm{are}\:\mathrm{in}\:\mathrm{AP},\:\mathrm{then}\:\mathrm{the}\:\mathrm{third} \\ $$$$\mathrm{side}\:\mathrm{is} \\ $$

Question Number 41078    Answers: 1   Comments: 3

∫_0 ^1 ((sin x + 2cos x)/(3sin x + 4cos x))dx

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{\mathrm{sin}\:{x}\:+\:\mathrm{2cos}\:{x}}{\mathrm{3sin}\:{x}\:+\:\mathrm{4cos}\:{x}}{dx} \\ $$

Question Number 41066    Answers: 1   Comments: 0

Question Number 41063    Answers: 0   Comments: 1

Question Number 41062    Answers: 0   Comments: 3

Question Number 41054    Answers: 0   Comments: 1

calculate ∫_0 ^(π/2) (x^2 /(sin^2 x))dx .

$${calculate}\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:\:\frac{{x}^{\mathrm{2}} }{{sin}^{\mathrm{2}} {x}}{dx}\:. \\ $$

Question Number 41053    Answers: 4   Comments: 1

let I = ∫_0 ^(π/2) cos^6 x dx and J = ∫_0 ^(π/2) sin^6 xdx 1)cslculate I +J and I−J 2)find the value of I and J

$${let}\:{I}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{cos}^{\mathrm{6}} {x}\:{dx}\:{and} \\ $$$${J}\:=\:\int_{\mathrm{0}} ^{\frac{\pi}{\mathrm{2}}} \:{sin}^{\mathrm{6}} {xdx} \\ $$$$\left.\mathrm{1}\right){cslculate}\:{I}\:+{J}\:\:{and}\:{I}−{J} \\ $$$$\left.\mathrm{2}\right){find}\:{the}\:{value}\:{of}\:{I}\:{and}\:{J} \\ $$

Question Number 41052    Answers: 0   Comments: 1

find the value of ∫_(π/6) ^(π/4) (x/(1+cos^2 x))dxr

$${find}\:{the}\:{value}\:{of}\:\:\int_{\frac{\pi}{\mathrm{6}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{x}}{\mathrm{1}+{cos}^{\mathrm{2}} {x}}{dxr} \\ $$

Question Number 41051    Answers: 0   Comments: 1

find the value of Σ_(n=1) ^∞ ((2n+3)/(n^2 (n+1)^2 ))

$${find}\:{the}\:{value}\:{of}\:\:\sum_{{n}=\mathrm{1}} ^{\infty} \:\frac{\mathrm{2}{n}+\mathrm{3}}{{n}^{\mathrm{2}} \left({n}+\mathrm{1}\right)^{\mathrm{2}} } \\ $$

Question Number 41049    Answers: 0   Comments: 2

calculate ∫_(−(π/4)) ^(π/4) (x^2 /(cos^2 x))dx

$${calculate}\:\:\:\int_{−\frac{\pi}{\mathrm{4}}} ^{\frac{\pi}{\mathrm{4}}} \:\:\frac{{x}^{\mathrm{2}} }{{cos}^{\mathrm{2}} {x}}{dx} \\ $$

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