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GeometryQuestion and Answers: Page 107

Question Number 10829 Answers: 2 Comments: 0

lim_(x→1) ∫_( 1) ^( x) ((e^t^2 (dt))/(x^2 − 1)) (a) 1 (b) 0 (c) e/2 (d) e

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\:\int_{\:\mathrm{1}} ^{\:\mathrm{x}} \:\:\:\frac{\mathrm{e}^{\mathrm{t}^{\mathrm{2}} } \:\left(\mathrm{dt}\right)}{\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{1}}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{1}\:\left(\mathrm{b}\right)\:\mathrm{0}\:\left(\mathrm{c}\right)\:\mathrm{e}/\mathrm{2}\:\left(\mathrm{d}\right)\:\mathrm{e} \\ $$

Question Number 10760 Answers: 1 Comments: 1

A block of mass 2.0kg resting on a smooth horizontal plane is acted upon simultaneously by two forces 10N due north and 10N due east. The magnitude of the acceleration produce by the force on the block.

$$\mathrm{A}\:\mathrm{block}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{2}.\mathrm{0kg}\:\mathrm{resting}\:\mathrm{on}\:\mathrm{a}\:\mathrm{smooth}\:\mathrm{horizontal}\:\mathrm{plane}\:\mathrm{is}\:\mathrm{acted} \\ $$$$\mathrm{upon}\:\mathrm{simultaneously}\:\mathrm{by}\:\mathrm{two}\:\mathrm{forces}\:\mathrm{10N}\:\mathrm{due}\:\mathrm{north}\:\mathrm{and}\:\mathrm{10N}\:\mathrm{due}\:\mathrm{east}. \\ $$$$\mathrm{The}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{acceleration}\:\mathrm{produce}\:\mathrm{by}\:\mathrm{the}\:\mathrm{force}\:\mathrm{on}\:\mathrm{the}\:\mathrm{block}. \\ $$

Question Number 10667 Answers: 1 Comments: 0

prove that the quadrilateral formed by angle bisectors of a cyclic quadrilateral is also cyclic.

$${prove}\:{that}\:{the}\:{quadrilateral}\:{formed} \\ $$$${by}\:{angle}\:{bisectors}\:{of}\:{a}\:{cyclic}\: \\ $$$${quadrilateral}\:{is}\:{also}\:{cyclic}. \\ $$

Question Number 10639 Answers: 1 Comments: 3

A manometer wire of lenght 60 cm is maintained under a tension of value 20V and an a.c is passed through the wire. If the density of the wire is 4000kgm^(−3) and it diamerter is 2mm. Calculate the frequency of the a.c

$$\mathrm{A}\:\mathrm{manometer}\:\mathrm{wire}\:\mathrm{of}\:\mathrm{lenght}\:\mathrm{60}\:\mathrm{cm}\:\mathrm{is}\:\mathrm{maintained}\:\mathrm{under} \\ $$$$\mathrm{a}\:\mathrm{tension}\:\mathrm{of}\:\mathrm{value}\:\mathrm{20V}\:\mathrm{and}\:\mathrm{an}\:\mathrm{a}.\mathrm{c}\:\mathrm{is}\:\mathrm{passed}\:\mathrm{through} \\ $$$$\mathrm{the}\:\mathrm{wire}.\:\mathrm{If}\:\mathrm{the}\:\mathrm{density}\:\mathrm{of}\:\mathrm{the}\:\mathrm{wire}\:\mathrm{is}\:\mathrm{4000kgm}^{−\mathrm{3}} \:\mathrm{and}\:\mathrm{it}\: \\ $$$$\mathrm{diamerter}\:\mathrm{is}\:\mathrm{2mm}.\:\mathrm{Calculate}\:\mathrm{the}\:\mathrm{frequency}\:\mathrm{of}\:\mathrm{the}\:\mathrm{a}.\mathrm{c} \\ $$

Question Number 10620 Answers: 1 Comments: 1

Question Number 11183 Answers: 1 Comments: 0

Question Number 10513 Answers: 0 Comments: 1

e^((−2×10^(−2) /2))

$${e}^{\left(−\mathrm{2}×\mathrm{10}^{−\mathrm{2}} /\mathrm{2}\right)} \\ $$

Question Number 10480 Answers: 2 Comments: 0

d/dx(cos^2 xdy/dx)=0

$${d}/{dx}\left(\mathrm{cos}\:^{\mathrm{2}} {xdy}/{dx}\right)=\mathrm{0} \\ $$$$ \\ $$

Question Number 10477 Answers: 0 Comments: 0

maximum and minimum value of 12x^(5−5x^4_(+40x^3_(+6) ) )

$${maximum}\:{and}\:{minimum}\:{value}\:{of}\: \\ $$$$\mathrm{12}{x}^{\mathrm{5}−\mathrm{5}{x}^{\mathrm{4}_{+\mathrm{40}{x}^{\mathrm{3}_{+\mathrm{6}} } } } } \\ $$

Question Number 10435 Answers: 1 Comments: 1

Question Number 10426 Answers: 0 Comments: 0

good morning!!!! we have f(x)=x^2 +2x g(x)=−2x^2 −3x+2 and d(m)=mx+2m 1)determine the coordonate of M_1 and M_2 intersection points respectively of (Cf) and d(m) or(Cg) and d(m)

$${good}\:{morning}!!!! \\ $$$${we}\:{have}\:\:{f}\left({x}\right)={x}^{\mathrm{2}} +\mathrm{2}{x}\:\:\:{g}\left({x}\right)=−\mathrm{2}{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2} \\ $$$${and}\:{d}\left({m}\right)={mx}+\mathrm{2}{m} \\ $$$$\left.\mathrm{1}\right){determine}\:{the}\:{coordonate}\:{of}\:{M}_{\mathrm{1}} \:{and}\:{M}_{\mathrm{2}} \: \\ $$$${intersection}\:{points}\:{respectively}\:{of}\:\left({Cf}\right)\:{and}\:{d}\left({m}\right) \\ $$$${or}\left({Cg}\right)\:{and}\:{d}\left({m}\right) \\ $$$$ \\ $$$$ \\ $$

Question Number 10415 Answers: 1 Comments: 0

find all the possible values of cos θ such that 2cot^2 θ + cos θ=0

$${find}\:{all}\:{the}\:{possible}\:{values}\:{of}\:\mathrm{cos}\:\theta\:{such}\:{that}\:\mathrm{2cot}\:^{\mathrm{2}} \theta\:+\:\mathrm{cos}\:\theta=\mathrm{0} \\ $$$$ \\ $$

Question Number 10303 Answers: 0 Comments: 1

Question Number 10222 Answers: 2 Comments: 1

solve simultaneously. m^4 + n^4 = 9m^2 n^2 + 1 ...... (i) m + n = 4 ........ (ii)

$$\mathrm{solve}\:\mathrm{simultaneously}. \\ $$$$\mathrm{m}^{\mathrm{4}} \:+\:\mathrm{n}^{\mathrm{4}} \:=\:\mathrm{9m}^{\mathrm{2}} \mathrm{n}^{\mathrm{2}} \:+\:\mathrm{1}\:\:\:\:\:\:\:......\:\left(\mathrm{i}\right) \\ $$$$\mathrm{m}\:+\:\mathrm{n}\:=\:\mathrm{4}\:........\:\left(\mathrm{ii}\right) \\ $$

Question Number 10200 Answers: 0 Comments: 0

Question Number 10195 Answers: 1 Comments: 1

The number of integral solutions of the equation 7(y+(1/y))−2(y^2 +(1/y^2 ))=9 are?

$${The}\:{number}\:{of}\:{integral}\:{solutions}\:{of}\:{the}\:{equation}\: \\ $$$$\mathrm{7}\left({y}+\frac{\mathrm{1}}{{y}}\right)−\mathrm{2}\left({y}^{\mathrm{2}} +\frac{\mathrm{1}}{{y}^{\mathrm{2}} }\right)=\mathrm{9}\:\mathrm{are}? \\ $$

Question Number 10181 Answers: 0 Comments: 0

Let A be a subset of {0;1;∙∙∙;1997} containing more than 1000 elements. Prove that A contains either a power of 2 or two distinct integers whose sum is a power of 2.

$${Let}\:{A}\:{be}\:{a}\:{subset}\:{of}\:\left\{\mathrm{0};\mathrm{1};\centerdot\centerdot\centerdot;\mathrm{1997}\right\}\: \\ $$$${containing}\:{more}\:{than}\:\mathrm{1000}\:{elements}. \\ $$$${Prove}\:{that}\:{A}\:{contains}\:{either}\:{a}\:{power} \\ $$$${of}\:\mathrm{2}\:{or}\:{two}\:{distinct}\:{integers}\:{whose}\: \\ $$$${sum}\:{is}\:{a}\:{power}\:{of}\:\mathrm{2}. \\ $$

Question Number 10166 Answers: 1 Comments: 1