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Question Number 11536 Answers: 2 Comments: 0

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 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 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 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 11388 Answers: 0 Comments: 0

A cell supplies a current of 6 ameter through a 2 coil and a current of 0.2 ameter through 7 coil. Calculate the limits and the internal resistance of the cell

$$\mathrm{A}\:\mathrm{cell}\:\mathrm{supplies}\:\mathrm{a}\:\mathrm{current}\:\mathrm{of}\:\mathrm{6}\:\mathrm{ameter}\:\mathrm{through}\:\mathrm{a}\:\mathrm{2}\:\mathrm{coil}\:\mathrm{and}\:\mathrm{a}\:\mathrm{current}\:\mathrm{of}\:\mathrm{0}.\mathrm{2}\: \\ $$$$\mathrm{ameter}\:\mathrm{through}\:\mathrm{7}\:\mathrm{coil}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{limits}\:\mathrm{and}\:\mathrm{the}\:\mathrm{internal}\:\mathrm{resistance} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{cell} \\ $$

Question Number 11332 Answers: 0 Comments: 0

Question Number 11327 Answers: 0 Comments: 0

pl show me typing and shape drawing app for mobile.

$$\mathrm{pl}\:\mathrm{show}\:\mathrm{me}\:\mathrm{typing}\:\mathrm{and}\:\mathrm{shape}\:\mathrm{drawing}\:\mathrm{app}\:\mathrm{for}\:\mathrm{mobile}. \\ $$

Question Number 11284 Answers: 0 Comments: 0

a+2b+3c....(1) −3a−4b+2c....(2) 2a−b−c....(3) a=...?? b=...?? c=...??

$${a}+\mathrm{2}{b}+\mathrm{3}{c}....\left(\mathrm{1}\right) \\ $$$$−\mathrm{3}{a}−\mathrm{4}{b}+\mathrm{2}{c}....\left(\mathrm{2}\right) \\ $$$$\mathrm{2}{a}−{b}−{c}....\left(\mathrm{3}\right) \\ $$$${a}=...?? \\ $$$${b}=...?? \\ $$$${c}=...?? \\ $$

Question Number 11283 Answers: 0 Comments: 0

2a+b+4c....(1) a+3c....(2) −3a−4b−c....(4) a=..?? b=..?? c=..??

$$\mathrm{2}{a}+{b}+\mathrm{4}{c}....\left(\mathrm{1}\right) \\ $$$${a}+\mathrm{3}{c}....\left(\mathrm{2}\right) \\ $$$$−\mathrm{3}{a}−\mathrm{4}{b}−{c}....\left(\mathrm{4}\right) \\ $$$${a}=..?? \\ $$$${b}=..?? \\ $$$${c}=..?? \\ $$

Question Number 11272 Answers: 1 Comments: 0

Question Number 11266 Answers: 0 Comments: 1

Question Number 11262 Answers: 1 Comments: 0

The k^(th) term of a sequence is K, the m^(th) term of M and n^(th) term is N. Show that if it is a geometic, (m−n) log K + (n−k) log M + (k−m) log N = 0.

$$\mathrm{The}\:\mathrm{k}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{of}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{is}\:\mathrm{K},\:\mathrm{the}\:\mathrm{m}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{of}\:\:\mathrm{M}\:\mathrm{and}\:\mathrm{n}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{is}\:\mathrm{N}.\:\mathrm{Show}\:\mathrm{that}\:\mathrm{if}\:\mathrm{it}\:\mathrm{is}\:\mathrm{a}\:\mathrm{geometic}, \\ $$$$\left(\mathrm{m}−\mathrm{n}\right)\:\mathrm{log}\:\mathrm{K}\:+\:\left(\mathrm{n}−\mathrm{k}\right)\:\mathrm{log}\:\mathrm{M}\:+\:\left(\mathrm{k}−\mathrm{m}\right)\:\mathrm{log}\:\mathrm{N}\:=\:\mathrm{0}.\: \\ $$

Question Number 11256 Answers: 1 Comments: 0

In the arithmetic progression, u_(1 ) =1.Given that u_(7 ) , u_(11) and u_(17) are in geometric progression, find the value of each.

$$\mathrm{In}\:\mathrm{the}\:\mathrm{arithmetic}\:\mathrm{progression},\:\mathrm{u}_{\mathrm{1}\:} =\mathrm{1}.\mathrm{Given}\:\mathrm{that}\:\mathrm{u}_{\mathrm{7}\:} ,\:\mathrm{u}_{\mathrm{11}} \mathrm{and}\:\mathrm{u}_{\mathrm{17}} \:\mathrm{are}\:\mathrm{in}\:\mathrm{geometric}\: \\ $$$$\mathrm{progression},\:\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{each}. \\ $$

Question Number 11255 Answers: 1 Comments: 0

If the sum of the first 4 terms of an A.P., is p, the sum of the first 8 terms is q and the sum of the first 12 terms is r, express (3p+r) in terms of q.

$$\mathrm{If}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{4}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}.,\:\mathrm{is}\:\mathrm{p},\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{8}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{q}\:\mathrm{and}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first} \\ $$$$\mathrm{12}\:\mathrm{terms}\:\mathrm{is}\:\mathrm{r},\:\mathrm{express}\:\left(\mathrm{3p}+\mathrm{r}\right)\:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{q}. \\ $$

Question Number 11089 Answers: 0 Comments: 1

for each n∈N, f_n (x)=nx(1−x^2 )^n for each x, 0≤x≤1 and a_n =∫_0 ^1 f_n (x)dx if s_n =sin(πa_n ), for each n∈N, then li_(n→∼) m s_n =....???

$${for}\:{each}\:{n}\in\mathbb{N},\:{f}_{{n}} \left({x}\right)={nx}\left(\mathrm{1}−{x}^{\mathrm{2}} \right)^{{n}} \\ $$$${for}\:{each}\:{x},\:\mathrm{0}\leqslant{x}\leqslant\mathrm{1}\:{and}\:{a}_{{n}} =\int_{\mathrm{0}} ^{\mathrm{1}} {f}_{{n}} \left({x}\right){dx} \\ $$$${if}\:{s}_{{n}} ={sin}\left(\pi{a}_{{n}} \right),\:{for}\:{each}\:{n}\in\mathbb{N},\:{then} \\ $$$${l}\underset{{n}\rightarrow\sim} {{i}m}\:{s}_{{n}} =....??? \\ $$

Question Number 11088 Answers: 0 Comments: 0

S={(n/(2m)) + ((6m)/n) : n,m∈N} inf(S)=...??? and sup(S)=...???

$${S}=\left\{\frac{{n}}{\mathrm{2}{m}}\:+\:\frac{\mathrm{6}{m}}{{n}}\::\:{n},{m}\in\mathbb{N}\right\} \\ $$$${inf}\left({S}\right)=...???\:{and}\:{sup}\left({S}\right)=...??? \\ $$

Question Number 11087 Answers: 0 Comments: 0

a<(π/2) if M<1 with ∣cos x−cos y∣≤M∣x−y∣ to each x,y∈[0,a] M=....???

$${a}<\frac{\pi}{\mathrm{2}} \\ $$$${if}\:{M}<\mathrm{1}\:{with}\:\mid{cos}\:{x}−{cos}\:{y}\mid\leqslant{M}\mid{x}−{y}\mid \\ $$$${to}\:{each}\:{x},{y}\in\left[\mathrm{0},{a}\right] \\ $$$${M}=....??? \\ $$

Question Number 11069 Answers: 0 Comments: 1

Question Number 10989 Answers: 1 Comments: 0

find the image of the point(5,2) under a rotation of 90° clockwise

$${find}\:{the}\:{image}\:{of}\:{the}\:{point}\left(\mathrm{5},\mathrm{2}\right)\: \\ $$$${under}\:{a}\:{rotation}\:{of}\:\mathrm{90}°\:{clockwise} \\ $$

Question Number 10914 Answers: 1 Comments: 0

A 200 N force inclined at 40° above the horizontal , drag load along the horizontal floor. coefficient of the kinetic friction between the load is 0.30 and the load experiences an acceleration of 1.2 m/s^2 , What is the mass of the load.

$$\mathrm{A}\:\mathrm{200}\:\mathrm{N}\:\mathrm{force}\:\mathrm{inclined}\:\mathrm{at}\:\mathrm{40}°\:\mathrm{above}\:\mathrm{the}\:\mathrm{horizontal}\:,\:\mathrm{drag}\:\mathrm{load}\:\mathrm{along}\:\mathrm{the} \\ $$$$\mathrm{horizontal}\:\mathrm{floor}.\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{the}\:\mathrm{kinetic}\:\mathrm{friction}\:\mathrm{between}\:\mathrm{the}\:\mathrm{load}\:\mathrm{is}\:\mathrm{0}.\mathrm{30}\: \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{load}\:\mathrm{experiences}\:\mathrm{an}\:\mathrm{acceleration}\:\mathrm{of}\:\mathrm{1}.\mathrm{2}\:\mathrm{m}/\mathrm{s}^{\mathrm{2}} , \\ $$$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{the}\:\mathrm{load}. \\ $$

Question Number 10908 Answers: 1 Comments: 0

Question Number 10900 Answers: 0 Comments: 1

Question Number 10899 Answers: 1 Comments: 0

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