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Question Number 29260    Answers: 0   Comments: 0

The eriodic time of a simple pendulum is given by T=2π(√(L/g)). if L=100±0.1cm(s.e) and the time s for 10 ossilations are: 48.2,48.2,48.7,48.5,48.4,48.2,48.4, 48.6,48.5,48.2. calcukate g and the standard error involved.

$${The}\:{eriodic}\:{time}\:{of}\:{a}\:{simple} \\ $$$${pendulum}\:{is}\:{given}\:{by}\:{T}=\mathrm{2}\pi\sqrt{\frac{{L}}{{g}}}. \\ $$$${if}\:{L}=\mathrm{100}\pm\mathrm{0}.\mathrm{1}{cm}\left({s}.{e}\right)\:{and}\:{the} \\ $$$${time}\:{s}\:{for}\:\mathrm{10}\:{ossilations}\:{are}: \\ $$$$\mathrm{48}.\mathrm{2},\mathrm{48}.\mathrm{2},\mathrm{48}.\mathrm{7},\mathrm{48}.\mathrm{5},\mathrm{48}.\mathrm{4},\mathrm{48}.\mathrm{2},\mathrm{48}.\mathrm{4}, \\ $$$$\mathrm{48}.\mathrm{6},\mathrm{48}.\mathrm{5},\mathrm{48}.\mathrm{2}. \\ $$$${calcukate}\:{g}\:{and}\:{the}\:{standard} \\ $$$${error}\:{involved}. \\ $$

Question Number 29259    Answers: 1   Comments: 0

solve the equation 2x+3y=5 3x+4y=4

$${solve}\:{the}\:{equation} \\ $$$$\mathrm{2}{x}+\mathrm{3}{y}=\mathrm{5} \\ $$$$\mathrm{3}{x}+\mathrm{4}{y}=\mathrm{4}\: \\ $$

Question Number 29308    Answers: 2   Comments: 0

Solve: w^3 = − 16

$$\mathrm{Solve}:\:\:\:\mathrm{w}^{\mathrm{3}} \:=\:−\:\mathrm{16} \\ $$

Question Number 29249    Answers: 1   Comments: 1

Question Number 29241    Answers: 1   Comments: 0

Question Number 29242    Answers: 0   Comments: 0

Question Number 29254    Answers: 1   Comments: 1

Question Number 29222    Answers: 1   Comments: 0

3x−4y=12, xy=2

$$\mathrm{3}{x}−\mathrm{4}{y}=\mathrm{12},\:{xy}=\mathrm{2} \\ $$

Question Number 29217    Answers: 1   Comments: 0

The velocity of a physical system is given by V={(√((p+1/n)))}/x where p=pressure. Find the dimensions of n and x

$${The}\:{velocity}\:{of}\:{a}\:{physical}\:{system} \\ $$$${is}\:{given}\:{by}\:{V}=\left\{\sqrt{\left({p}+\mathrm{1}/{n}\right)}\right\}/{x} \\ $$$${where}\:{p}={pressure}.\:{Find}\:{the} \\ $$$${dimensions}\:{of}\:{n}\:{and}\:{x} \\ $$

Question Number 29216    Answers: 1   Comments: 0

A horizontal force of 0.8N is required to pull a 5kg block across a table top at a constant speed. With the block initially at rest,a 20g bullet fired horizontally into the block to slide 1.5m before coming to rest again.Determine the speed v of the bullet,where the bullet is assumed to be embedded in the block.

$${A}\:{horizontal}\:{force}\:{of}\:\mathrm{0}.\mathrm{8}{N}\:{is} \\ $$$${required}\:{to}\:{pull}\:{a}\:\mathrm{5}{kg}\:{block}\:{across} \\ $$$${a}\:{table}\:{top}\:{at}\:{a}\:{constant}\:{speed}. \\ $$$${With}\:{the}\:{block}\:{initially}\:{at}\:{rest},{a} \\ $$$$\mathrm{20}{g}\:{bullet}\:{fired}\:{horizontally}\:{into} \\ $$$${the}\:{block}\:{to}\:{slide}\:\mathrm{1}.\mathrm{5}{m}\:{before} \\ $$$${coming}\:{to}\:{rest}\:{again}.{Determine} \\ $$$${the}\:{speed}\:{v}\:{of}\:{the}\:{bullet},{where} \\ $$$${the}\:{bullet}\:{is}\:{assumed}\:{to}\:{be} \\ $$$${embedded}\:{in}\:{the}\:{block}. \\ $$

Question Number 29213    Answers: 0   Comments: 1

Two masses m and 2m,approach each l along a path at right angle to each other and move off at 2m/s at angle 37° to the original direction of mass m. What where the initial speeds of the two particles?

$${Two}\:{masses}\:{m}\:{and}\:\mathrm{2}{m},{approach} \\ $$$${each}\:{l}\:{along}\:{a}\:{path}\:{at}\:{right} \\ $$$${angle}\:{to}\:{each}\:{other}\:{and}\:{move}\:{off} \\ $$$${at}\:\mathrm{2}{m}/{s}\:{at}\:{angle}\:\mathrm{37}°\:{to}\:{the} \\ $$$${original}\:{direction}\:{of}\:{mass}\:{m}. \\ $$$${What}\:{where}\:{the}\:{initial}\:{speeds}\:{of} \\ $$$${the}\:{two}\:{particles}? \\ $$

Question Number 29212    Answers: 1   Comments: 1

A block of wood of mass 0.6kg is balanced on top of vertical port 2m high.A 10g bullet is fired horizontally into the block and the embedded bullet land at a 4m from the base of the port.Find the initial velocity of the bullet.

$${A}\:{block}\:{of}\:{wood}\:{of}\:{mass}\:\mathrm{0}.\mathrm{6}{kg}\:{is} \\ $$$${balanced}\:{on}\:{top}\:{of}\:{vertical}\:{port} \\ $$$$\mathrm{2}{m}\:{high}.{A}\:\mathrm{10}{g}\:{bullet}\:{is}\:{fired} \\ $$$${horizontally}\:{into}\:{the}\:{block}\:{and} \\ $$$${the}\:{embedded}\:{bullet}\:{land}\:{at}\:{a}\:\mathrm{4}{m} \\ $$$${from}\:{the}\:{base}\:{of}\:{the}\:{port}.{Find} \\ $$$${the}\:{initial}\:{velocity}\:{of}\:{the}\:{bullet}. \\ $$

Question Number 29209    Answers: 1   Comments: 4

Question Number 29202    Answers: 1   Comments: 0

Find area between by y=1 and y=((1−x^2 )/(1+x^2 )) .

$${Find}\:{area}\:{between}\:{by}\:{y}=\mathrm{1}\:\:{and} \\ $$$${y}=\frac{\mathrm{1}−{x}^{\mathrm{2}} }{\mathrm{1}+{x}^{\mathrm{2}} }\:. \\ $$

Question Number 29201    Answers: 2   Comments: 0

Question Number 29198    Answers: 1   Comments: 1

Question Number 29196    Answers: 0   Comments: 0

Let s = n_c_1 − (1+(1/2))n_c_2 +(1+(1/2)+(1/3))n_c_3 +.......+(−1)^(n−1) (1+(1/2)+(1/3)+....+(1/n))n_c_n then prove that s×n =1.

$$\mathrm{Let}\:\mathrm{s}\:=\:\mathrm{n}_{\mathrm{c}_{\mathrm{1}} } \:−\:\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}\right)\mathrm{n}_{\mathrm{c}_{\mathrm{2}} } \:+\left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}\right)\mathrm{n}_{\mathrm{c}_{\mathrm{3}} } \\ $$$$+.......+\left(−\mathrm{1}\right)^{\mathrm{n}−\mathrm{1}} \left(\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+....+\frac{\mathrm{1}}{\mathrm{n}}\right)\mathrm{n}_{\mathrm{c}_{\mathrm{n}} } \\ $$$$\mathrm{then}\:\mathrm{prove}\:\mathrm{that}\:\mathrm{s}×\mathrm{n}\:=\mathrm{1}. \\ $$

Question Number 29231    Answers: 1   Comments: 0

Question Number 29180    Answers: 1   Comments: 0

lim_(x → a) ((((x)^(1/m) − (a)^(1/m) )/((x)^(1/n) − (a)^(1/n) ))) Don′t use L′hospital rules :-)

$$\underset{\mathrm{x}\:\rightarrow\:\mathrm{a}} {\mathrm{lim}}\:\left(\frac{\sqrt[{\mathrm{m}}]{\mathrm{x}}\:−\:\sqrt[{\mathrm{m}}]{\mathrm{a}}}{\sqrt[{\mathrm{n}}]{\mathrm{x}}\:−\:\sqrt[{\mathrm{n}}]{\mathrm{a}}}\right) \\ $$$$\left.\mathrm{Don}'\mathrm{t}\:\mathrm{use}\:\mathrm{L}'\mathrm{hospital}\:\mathrm{rules}\::-\right) \\ $$

Question Number 29173    Answers: 1   Comments: 0

find cos(5α) interms of cosα then find the value of cos((π/(10))).

$${find}\:{cos}\left(\mathrm{5}\alpha\right)\:{interms}\:{of}\:{cos}\alpha\:{then}\:{find}\:{the}\:{value}\:{of} \\ $$$${cos}\left(\frac{\pi}{\mathrm{10}}\right). \\ $$

Question Number 29172    Answers: 1   Comments: 0

Question Number 29171    Answers: 0   Comments: 0

Question Number 29170    Answers: 0   Comments: 0

Question Number 29169    Answers: 0   Comments: 1

factorize inside R[x] the polynomial p(x)= x^8 −1.

$${factorize}\:{inside}\:{R}\left[{x}\right]\:{the}\:{polynomial} \\ $$$${p}\left({x}\right)=\:{x}^{\mathrm{8}} −\mathrm{1}. \\ $$

Question Number 29168    Answers: 0   Comments: 1

Question Number 29167    Answers: 0   Comments: 1

let give S_n = Σ_(k=1) ^(n−1) sin(((kπ)/n)) find lim_(n→+∞) (S_n /n) .

$${let}\:{give}\:{S}_{{n}} =\:\sum_{{k}=\mathrm{1}} ^{{n}−\mathrm{1}} {sin}\left(\frac{{k}\pi}{{n}}\right)\:\:{find}\:{lim}_{{n}\rightarrow+\infty} \:\:\frac{{S}_{{n}} }{{n}}\:\:. \\ $$

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