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Question Number 14682 Answers: 1 Comments: 0

Question Number 14677 Answers: 1 Comments: 0

A stone of mass 100g is tied to the end of a string of 50 cm long . The stone is whirled as a conical pendulum so that it rotates in horizontal circle radius 30 cm. Determine the angular speed and the tension in the string.

$$\mathrm{A}\:\mathrm{stone}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{100g}\:\mathrm{is}\:\mathrm{tied}\:\mathrm{to}\:\mathrm{the}\:\mathrm{end}\:\mathrm{of}\:\mathrm{a}\:\mathrm{string}\:\mathrm{of}\:\mathrm{50}\:\mathrm{cm}\:\mathrm{long}\:.\:\mathrm{The}\:\mathrm{stone}\:\mathrm{is} \\ $$$$\mathrm{whirled}\:\mathrm{as}\:\mathrm{a}\:\mathrm{conical}\:\mathrm{pendulum}\:\mathrm{so}\:\mathrm{that}\:\mathrm{it}\:\mathrm{rotates}\:\mathrm{in}\:\mathrm{horizontal}\:\mathrm{circle}\:\mathrm{radius} \\ $$$$\mathrm{30}\:\mathrm{cm}.\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{angular}\:\mathrm{speed}\:\mathrm{and}\:\mathrm{the}\:\mathrm{tension}\:\mathrm{in}\:\mathrm{the}\:\mathrm{string}. \\ $$

Question Number 14667 Answers: 1 Comments: 2

Question Number 14668 Answers: 2 Comments: 3

Question Number 14664 Answers: 1 Comments: 0

What is the transformed equation of a parabola given by y=2x^2 +(8/5)x−((109)/(50)) , if the coordinate axes is rotated anticlockwise by 𝛂=tan^(−1) (3/4) .

$$\:{What}\:{is}\:{the}\:{transformed}\: \\ $$$${equation}\:{of}\:{a}\:{parabola}\:{given}\:{by} \\ $$$$\:\:\boldsymbol{{y}}=\mathrm{2}\boldsymbol{{x}}^{\mathrm{2}} +\frac{\mathrm{8}}{\mathrm{5}}\boldsymbol{{x}}−\frac{\mathrm{109}}{\mathrm{50}}\:,\:{if}\:{the} \\ $$$${coordinate}\:{axes}\:{is}\:{rotated}\: \\ $$$$\:{anticlockwise}\:{by}\:\:\boldsymbol{\alpha}=\mathrm{tan}^{−\mathrm{1}} \frac{\mathrm{3}}{\mathrm{4}}\:. \\ $$

Question Number 14661 Answers: 1 Comments: 1

Question Number 14658 Answers: 1 Comments: 0

Given that: x = ((√2) + 1)^(1/3) − ((√2) − 1)^(1/3) Show that , x^3 + 3x = 2

$$\mathrm{Given}\:\mathrm{that}: \\ $$$$\mathrm{x}\:=\:\left(\sqrt{\mathrm{2}}\:+\:\mathrm{1}\right)^{\mathrm{1}/\mathrm{3}} \:−\:\left(\sqrt{\mathrm{2}}\:−\:\mathrm{1}\right)^{\mathrm{1}/\mathrm{3}} \\ $$$$\mathrm{Show}\:\mathrm{that}\:,\:\:\:\:\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{3x}\:=\:\mathrm{2} \\ $$

Question Number 14660 Answers: 0 Comments: 2

Question Number 14646 Answers: 0 Comments: 0

Prove that: ∫_( 0) ^( 1) sin(x) cos^(−1) (x) dx > (1/e^2 )

$$\mathrm{Prove}\:\mathrm{that}:\:\:\int_{\:\mathrm{0}} ^{\:\mathrm{1}} \:\mathrm{sin}\left(\mathrm{x}\right)\:\mathrm{cos}^{−\mathrm{1}} \left(\mathrm{x}\right)\:\mathrm{dx}\:>\:\frac{\mathrm{1}}{\mathrm{e}^{\mathrm{2}} } \\ $$

Question Number 14633 Answers: 3 Comments: 1

Solve the equation: (1 − tanθ)(1 + sin2θ) = 1 + tanθ

$$\mathrm{Solve}\:\mathrm{the}\:\mathrm{equation}: \\ $$$$\left(\mathrm{1}\:−\:\mathrm{tan}\theta\right)\left(\mathrm{1}\:+\:\mathrm{sin2}\theta\right)\:=\:\mathrm{1}\:+\:\mathrm{tan}\theta \\ $$

Question Number 14632 Answers: 2 Comments: 0

Find the general solution of the equation 3^(sin 2x + 2 cos^2 x) + 3^(1 − sin 2x + 2 sin^2 x) = 28

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{general}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{equation} \\ $$$$\mathrm{3}^{\mathrm{sin}\:\mathrm{2}{x}\:+\:\mathrm{2}\:\mathrm{cos}^{\mathrm{2}} \:{x}} \:+\:\mathrm{3}^{\mathrm{1}\:−\:\mathrm{sin}\:\mathrm{2}{x}\:+\:\mathrm{2}\:\mathrm{sin}^{\mathrm{2}} \:{x}} \:=\:\mathrm{28} \\ $$

Question Number 14630 Answers: 0 Comments: 2

solve the eqn dr/dθ=[r(a^2 −r^2 )/a^2 +r^2 ]cotθ hint. let a^2 +r^2 =a^2 −r^2 +2r^2 .

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{eqn} \\ $$$$\mathrm{dr}/\mathrm{d}\theta=\left[\mathrm{r}\left(\mathrm{a}^{\mathrm{2}} −\mathrm{r}^{\mathrm{2}} \right)/\mathrm{a}^{\mathrm{2}} +\mathrm{r}^{\mathrm{2}} \right]\mathrm{cot}\theta \\ $$$$\mathrm{hint}.\:\mathrm{let}\:\mathrm{a}^{\mathrm{2}} +\mathrm{r}^{\mathrm{2}} =\mathrm{a}^{\mathrm{2}} −\mathrm{r}^{\mathrm{2}} +\mathrm{2r}^{\mathrm{2}} . \\ $$

Question Number 14882 Answers: 0 Comments: 6

Two vectors a^→ and b^→ are parallel and have same magnitude. Then they (1) have same direction, but they are not equal (2) are equal (3) are not equal (4) may or may not be equal

$$\mathrm{Two}\:\mathrm{vectors}\:\overset{\rightarrow} {{a}}\:\mathrm{and}\:\overset{\rightarrow} {{b}}\:\mathrm{are}\:\mathrm{parallel}\:\mathrm{and} \\ $$$$\mathrm{have}\:\mathrm{same}\:\mathrm{magnitude}.\:\mathrm{Then}\:\mathrm{they} \\ $$$$\left(\mathrm{1}\right)\:\mathrm{have}\:\mathrm{same}\:\mathrm{direction},\:\mathrm{but}\:\mathrm{they}\:\mathrm{are} \\ $$$$\mathrm{not}\:\mathrm{equal} \\ $$$$\left(\mathrm{2}\right)\:\mathrm{are}\:\mathrm{equal} \\ $$$$\left(\mathrm{3}\right)\:\mathrm{are}\:\mathrm{not}\:\mathrm{equal} \\ $$$$\left(\mathrm{4}\right)\:\mathrm{may}\:\mathrm{or}\:\mathrm{may}\:\mathrm{not}\:\mathrm{be}\:\mathrm{equal} \\ $$

Question Number 14879 Answers: 1 Comments: 0

Find the value of x, satisfying sin^2 x + sin x − 2 ≥ 0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:{x},\:\mathrm{satisfying} \\ $$$$\mathrm{sin}^{\mathrm{2}} \:{x}\:+\:\mathrm{sin}\:{x}\:−\:\mathrm{2}\:\geqslant\:\mathrm{0} \\ $$

Question Number 14878 Answers: 0 Comments: 3

Find the number of solution of equation x sin x = 2

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{number}\:\mathrm{of}\:\mathrm{solution}\:\mathrm{of}\:\mathrm{equation} \\ $$$${x}\:\mathrm{sin}\:{x}\:=\:\mathrm{2} \\ $$

Question Number 14876 Answers: 0 Comments: 0