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GeometryQuestion and Answers: Page 115

Question Number 11864 Answers: 2 Comments: 0

∫_7 ^(10) x^2 dx/x^2 −3x+2=

$$\underset{\mathrm{7}} {\overset{\mathrm{10}} {\int}}{x}^{\mathrm{2}} {dx}/{x}^{\mathrm{2}} −\mathrm{3}{x}+\mathrm{2}= \\ $$

Question Number 11827 Answers: 1 Comments: 0

∫x^2 dcosx=?

$$\int\mathrm{x}^{\mathrm{2}} \mathrm{dcosx}=? \\ $$

Question Number 11759 Answers: 1 Comments: 0

A quadrilateral with consecutive sides of lenght 7, 15, 15, and d is inscribed in a circle with its diameter d. Find the radius of circle

$$\mathrm{A}\:\mathrm{quadrilateral}\:\mathrm{with}\:\mathrm{consecutive}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{lenght}\:\mathrm{7},\:\mathrm{15},\:\mathrm{15},\:\mathrm{and}\:{d} \\ $$$$\mathrm{is}\:\mathrm{inscribed}\:\mathrm{in}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{with}\:\mathrm{its}\:\mathrm{diameter}\:{d}. \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{radius}\:\mathrm{of}\:\mathrm{circle} \\ $$

Question Number 11740 Answers: 0 Comments: 0

Metal pellets of mass 0.1 kg are fired into an iron plate of large mass m and specific heat capacity c at a temperature of 15°C . 25% of the kinetic energy of the pellets is converted thermal energy and the plate temperature rises to 16°C. The average speed of the pellets before hitting the plate was ?

$$\mathrm{Metal}\:\mathrm{pellets}\:\mathrm{of}\:\mathrm{mass}\:\mathrm{0}.\mathrm{1}\:\mathrm{kg}\:\mathrm{are}\:\mathrm{fired}\:\mathrm{into}\:\mathrm{an}\:\mathrm{iron}\:\mathrm{plate}\:\mathrm{of}\:\mathrm{large}\:\mathrm{mass}\:\mathrm{m} \\ $$$$\mathrm{and}\:\mathrm{specific}\:\mathrm{heat}\:\mathrm{capacity}\:\mathrm{c}\:\mathrm{at}\:\mathrm{a}\:\mathrm{temperature}\:\mathrm{of}\:\mathrm{15}°\mathrm{C}\:.\:\mathrm{25\%}\:\mathrm{of}\:\mathrm{the}\:\mathrm{kinetic} \\ $$$$\mathrm{energy}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pellets}\:\mathrm{is}\:\mathrm{converted}\:\mathrm{thermal}\:\mathrm{energy}\:\mathrm{and}\:\mathrm{the}\:\mathrm{plate}\:\mathrm{temperature} \\ $$$$\mathrm{rises}\:\mathrm{to}\:\mathrm{16}°\mathrm{C}.\:\mathrm{The}\:\mathrm{average}\:\mathrm{speed}\:\mathrm{of}\:\mathrm{the}\:\mathrm{pellets}\:\mathrm{before}\:\mathrm{hitting}\:\mathrm{the}\:\mathrm{plate}\:\mathrm{was}\:? \\ $$

Question Number 11781 Answers: 3 Comments: 0

sin(2θ) + 7cos(2θ) = 6 find θ

$$\mathrm{sin}\left(\mathrm{2}\theta\right)\:+\:\mathrm{7cos}\left(\mathrm{2}\theta\right)\:=\:\mathrm{6} \\ $$$$\mathrm{find}\:\theta \\ $$

Question Number 11632 Answers: 1 Comments: 0

Question Number 11594 Answers: 1 Comments: 0

please how can demonstred sin(2x)_ /cos(2x)=2sin(2x)

$${please}\:{how}\:{can}\:{demonstred}\: \\ $$$${sin}\left(\mathrm{2}{x}\underset{} {\right)}/{cos}\left(\mathrm{2}{x}\right)=\mathrm{2}{sin}\left(\mathrm{2}{x}\right) \\ $$

Question Number 11403 Answers: 0 Comments: 1

how can demonstred that cos(2x)−sin(2x)−1=−cos^2 x

$${how}\:{can}\:{demonstred}\:{that}\: \\ $$$${cos}\left(\mathrm{2}{x}\right)−{sin}\left(\mathrm{2}{x}\right)−\mathrm{1}=−{cos}^{\mathrm{2}} {x} \\ $$

Question Number 11344 Answers: 0 Comments: 1

n_c_n =((n!)/((n−n)!n!))

$${n}_{{c}_{{n}} } =\frac{{n}!}{\left({n}−{n}\right)!{n}!} \\ $$

Question Number 11343 Answers: 0 Comments: 1

n_c_n =((n1)/((n−n)))

$${n}_{\boldsymbol{\mathrm{c}}_{\boldsymbol{\mathrm{n}}} } =\frac{{n}\mathrm{1}}{\left({n}−{n}\right)} \\ $$

Question Number 11221 Answers: 0 Comments: 4

Question Number 11148 Answers: 1 Comments: 0

∫((x dx)/((x+1))^(1/3) )=....???

$$\int\frac{{x}\:{dx}}{\sqrt[{\mathrm{3}}]{{x}+\mathrm{1}}}=....??? \\ $$

Question Number 11078 Answers: 1 Comments: 0

$$ \\ $$$$ \\ $$$$ \\ $$$$ \\ $$

Question Number 10815 Answers: 0 Comments: 0

Evalute ∫(x^(2 ) + 9)^9 dx .

$${Evalute}\:\:\int\left({x}^{\mathrm{2}\:} \:\:+\:\mathrm{9}\right)^{\mathrm{9}} \:{dx}\:. \\ $$

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

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

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