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Question Number 41157 Answers: 2 Comments: 3

Question Number 41198 Answers: 2 Comments: 3

evaluate ln(−1)

$$\mathrm{evaluate}\:\boldsymbol{\mathrm{ln}}\left(−\mathrm{1}\right) \\ $$

Question Number 41151 Answers: 1 Comments: 2

Proof that : (d^n /dx^n )(cos x) = cos (x+((nπ)/2)) (d^n /dx^n )(sin x) = sin (x+((nπ)/2)) where n∈Z.

$$\mathrm{Proof}\:\mathrm{that}\::\:\frac{\mathrm{d}^{\mathrm{n}} }{\mathrm{d}{x}^{{n}} }\left(\mathrm{cos}\:{x}\right)\:=\:\mathrm{cos}\:\left({x}+\frac{{n}\pi}{\mathrm{2}}\right) \\ $$$$\frac{\mathrm{d}^{\mathrm{n}} }{\mathrm{d}{x}^{{n}} }\left(\mathrm{sin}\:{x}\right)\:=\:\mathrm{sin}\:\left({x}+\frac{{n}\pi}{\mathrm{2}}\right) \\ $$$$\mathrm{where}\:\mathrm{n}\in\mathbb{Z}. \\ $$

Question Number 41148 Answers: 1 Comments: 0

Calculate the speed of an electron whose kinetic energy is equal to 2% of its rest mass.

$${Calculate}\:{the}\:{speed}\:{of}\:{an}\:{electron} \\ $$$${whose}\:{kinetic}\:{energy}\:{is}\:{equal}\:{to} \\ $$$$\mathrm{2\%}\:{of}\:{its}\:{rest}\:{mass}. \\ $$

Question Number 41146 Answers: 1 Comments: 1

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