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Question Number 13155    Answers: 2   Comments: 0

Question Number 13154    Answers: 2   Comments: 0

Find the smallest number such that when divided by 18 the remainder is 17, When divided by 20 the remainder is 19. and when divided by 24 the remainder is 23.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{smallest}\:\mathrm{number}\:\mathrm{such}\:\mathrm{that}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{18}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{17}, \\ $$$$\mathrm{When}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{20}\:\mathrm{the}\:\mathrm{remainder}\:\mathrm{is}\:\mathrm{19}.\:\mathrm{and}\:\mathrm{when}\:\mathrm{divided}\:\mathrm{by}\:\mathrm{24}\:\mathrm{the}\:\mathrm{remainder}\: \\ $$$$\mathrm{is}\:\mathrm{23}.\: \\ $$

Question Number 13153    Answers: 1   Comments: 3

Question Number 13152    Answers: 1   Comments: 0

Solve: 5^(log(x)) + logx^5 = 25

$$\mathrm{Solve}:\:\:\mathrm{5}^{\mathrm{log}\left(\mathrm{x}\right)} \:+\:\mathrm{logx}^{\mathrm{5}} \:=\:\mathrm{25} \\ $$

Question Number 13151    Answers: 1   Comments: 0

Question Number 13145    Answers: 1   Comments: 0

((64))^(1/(3)^(1/(√5)) ) = x How to write x into fraction exponent form?

$$\sqrt[{\sqrt[{\sqrt{\mathrm{5}}}]{\mathrm{3}}}]{\mathrm{64}}\:=\:{x} \\ $$$$\mathrm{How}\:\mathrm{to}\:\mathrm{write}\:{x}\:\mathrm{into}\:\mathrm{fraction}\:\mathrm{exponent}\:\mathrm{form}? \\ $$

Question Number 13143    Answers: 0   Comments: 1

Find the point (x,y) which lies 8 unit from the origin, along the terminal line of 155°.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{point}\:\left(\mathrm{x},\mathrm{y}\right)\:\mathrm{which}\:\mathrm{lies}\:\mathrm{8}\:\mathrm{unit}\:\mathrm{from}\:\mathrm{the}\:\mathrm{origin},\:\:\mathrm{along}\:\mathrm{the}\:\mathrm{terminal}\:\mathrm{line} \\ $$$$\mathrm{of}\:\mathrm{155}°.\: \\ $$

Question Number 13142    Answers: 0   Comments: 1

Find the height PQ of a tower of an observant at a point O, 135 m from the foot of the tower. Determine the angle of elevation of the tower.

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{height}\:\mathrm{PQ}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tower}\:\mathrm{of}\:\mathrm{an}\:\mathrm{observant}\:\mathrm{at}\:\mathrm{a}\:\mathrm{point}\:\mathrm{O},\:\mathrm{135}\:\mathrm{m}\:\mathrm{from}\:\mathrm{the} \\ $$$$\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tower}.\:\mathrm{Determine}\:\mathrm{the}\:\mathrm{angle}\:\mathrm{of}\:\mathrm{elevation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tower}. \\ $$

Question Number 13141    Answers: 1   Comments: 3

Question Number 13140    Answers: 2   Comments: 1

Question Number 13223    Answers: 0   Comments: 1

If a, b, c are sides of triangle show that (1 + ((b−c)/a))^a (1 + ((c−a)/b))^b (1 + ((a−b)/c))^c < 1

$$\mathrm{If}\:{a},\:{b},\:{c}\:\mathrm{are}\:\mathrm{sides}\:\mathrm{of}\:\mathrm{triangle}\:\mathrm{show}\:\mathrm{that} \\ $$$$\left(\mathrm{1}\:+\:\frac{{b}−{c}}{{a}}\right)^{{a}} \left(\mathrm{1}\:+\:\frac{{c}−{a}}{{b}}\right)^{{b}} \left(\mathrm{1}\:+\:\frac{{a}−{b}}{{c}}\right)^{{c}} \:<\:\mathrm{1} \\ $$

Question Number 13128    Answers: 0   Comments: 0

If [x] stands for the greatest integer function, the value of ∫_( 4) ^( 10) (([x^2 ])/([x^2 −28x+196]+[x^2 ])) dx is

$$\mathrm{If}\:\:\left[{x}\right]\:\mathrm{stands}\:\mathrm{for}\:\mathrm{the}\:\mathrm{greatest}\:\mathrm{integer} \\ $$$$\mathrm{function},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\: \\ $$$$\underset{\:\mathrm{4}} {\overset{\:\:\:\:\mathrm{10}} {\int}}\:\frac{\left[{x}^{\mathrm{2}} \right]}{\left[{x}^{\mathrm{2}} −\mathrm{28}{x}+\mathrm{196}\right]+\left[{x}^{\mathrm{2}} \right]}\:{dx}\:\mathrm{is} \\ $$

Question Number 13127    Answers: 0   Comments: 0

Question Number 13121    Answers: 1   Comments: 0

Find the value of : (2/(15)) + (2/(35)) + (2/(63)) + (2/(99)) + ... + (2/(9999))

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\::\:\:\frac{\mathrm{2}}{\mathrm{15}}\:+\:\frac{\mathrm{2}}{\mathrm{35}}\:+\:\frac{\mathrm{2}}{\mathrm{63}}\:+\:\frac{\mathrm{2}}{\mathrm{99}}\:+\:...\:+\:\frac{\mathrm{2}}{\mathrm{9999}} \\ $$

Question Number 13117    Answers: 1   Comments: 0

Question Number 13107    Answers: 1   Comments: 0

A man moves 20m north then 12m east and finally 15m south. His displacement from the starting point is ?

$$\mathrm{A}\:\mathrm{man}\:\mathrm{moves}\:\mathrm{20m}\:\mathrm{north}\:\mathrm{then}\:\mathrm{12m}\:\mathrm{east}\:\mathrm{and}\:\mathrm{finally}\:\mathrm{15m}\:\mathrm{south}.\:\:\mathrm{His}\:\mathrm{displacement} \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{starting}\:\mathrm{point}\:\mathrm{is}\:? \\ $$

Question Number 13103    Answers: 2   Comments: 0

∫_( −1) ^2 (( ∣ x ∣ )/x) dx =

$$\:\underset{\:−\mathrm{1}} {\overset{\mathrm{2}} {\int}}\:\frac{\:\mid\:{x}\:\mid\:}{{x}}\:{dx}\:=\: \\ $$

Question Number 13102    Answers: 0   Comments: 4

Find the sum of the nth term : 1^6 + 2^6 + 3^6 + 4^6 + ... + n^6

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{nth}\:\mathrm{term}\:\::\:\:\mathrm{1}^{\mathrm{6}} \:+\:\mathrm{2}^{\mathrm{6}} \:+\:\mathrm{3}^{\mathrm{6}} \:+\:\mathrm{4}^{\mathrm{6}} \:+\:...\:+\:\mathrm{n}^{\mathrm{6}} \\ $$

Question Number 13099    Answers: 2   Comments: 0

If f(x + 5) = g(2x −1) Find 2f^(−1) (x) (A) g^(−1) (x) + 11 (D) g^(−1) (x/2) + 6 (B) g^(−1) (x) + 9 (E) g^(−1) (2x) + 6 (C) g^(−1) (x) + 6

$$\mathrm{If}\:{f}\left({x}\:+\:\mathrm{5}\right)\:=\:{g}\left(\mathrm{2}{x}\:−\mathrm{1}\right) \\ $$$$\mathrm{Find}\:\mathrm{2}{f}^{−\mathrm{1}} \left({x}\right) \\ $$$$ \\ $$$$\left(\mathrm{A}\right)\:{g}^{−\mathrm{1}} \left({x}\right)\:+\:\mathrm{11}\:\:\:\:\:\:\:\:\left(\mathrm{D}\right)\:{g}^{−\mathrm{1}} \left({x}/\mathrm{2}\right)\:+\:\mathrm{6} \\ $$$$\left(\mathrm{B}\right)\:{g}^{−\mathrm{1}} \left({x}\right)\:+\:\mathrm{9}\:\:\:\:\:\:\:\:\:\:\:\left(\mathrm{E}\right)\:{g}^{−\mathrm{1}} \left(\mathrm{2}{x}\right)\:+\:\mathrm{6} \\ $$$$\left(\mathrm{C}\right)\:{g}^{−\mathrm{1}} \left({x}\right)\:+\:\mathrm{6} \\ $$

Question Number 13098    Answers: 1   Comments: 0

Question Number 13097    Answers: 1   Comments: 0

S=Σ_(x_2 =1) ^x_1 Σ_(x_3 =1) ^x_2 ∙∙∙Σ_(x_n =1) ^x_(n−1) Σ_(t=1) ^x_n t Can you evaluate S?

$${S}=\underset{{x}_{\mathrm{2}} =\mathrm{1}} {\overset{{x}_{\mathrm{1}} } {\sum}}\underset{{x}_{\mathrm{3}} =\mathrm{1}} {\overset{{x}_{\mathrm{2}} } {\sum}}\centerdot\centerdot\centerdot\underset{{x}_{{n}} =\mathrm{1}} {\overset{{x}_{{n}−\mathrm{1}} } {\sum}}\underset{{t}=\mathrm{1}} {\overset{{x}_{{n}} } {\sum}}{t} \\ $$$$\mathrm{Can}\:\mathrm{you}\:\mathrm{evaluate}\:{S}? \\ $$

Question Number 13091    Answers: 1   Comments: 0

A motor car moves with a velocity of 20m/s on a rough horizontal road and covers a displacement of 50m. Find the coefficient of dynamic friction between the tyre and the ground (g = 10m/s^2 ).

$$\mathrm{A}\:\mathrm{motor}\:\mathrm{car}\:\mathrm{moves}\:\mathrm{with}\:\mathrm{a}\:\mathrm{velocity}\:\mathrm{of}\:\mathrm{20m}/\mathrm{s}\:\mathrm{on}\:\mathrm{a}\:\mathrm{rough}\:\mathrm{horizontal}\:\mathrm{road}\:\mathrm{and} \\ $$$$\mathrm{covers}\:\mathrm{a}\:\mathrm{displacement}\:\mathrm{of}\:\mathrm{50m}.\:\mathrm{Find}\:\mathrm{the}\:\mathrm{coefficient}\:\mathrm{of}\:\mathrm{dynamic}\:\mathrm{friction}\:\mathrm{between} \\ $$$$\mathrm{the}\:\mathrm{tyre}\:\mathrm{and}\:\mathrm{the}\:\mathrm{ground}\:\:\left(\mathrm{g}\:=\:\mathrm{10m}/\mathrm{s}^{\mathrm{2}} \right). \\ $$

Question Number 13081    Answers: 2   Comments: 0

{ ((x+y+z=[1]_5 )),((xy=[2]_5 )),((yz=[1]_5 )) :} Solve system on Z_5

$$\begin{cases}{{x}+{y}+{z}=\left[\mathrm{1}\right]_{\mathrm{5}} }\\{{xy}=\left[\mathrm{2}\right]_{\mathrm{5}} }\\{{yz}=\left[\mathrm{1}\right]_{\mathrm{5}} }\end{cases} \\ $$$${Solve}\:{system}\:{on}\:\mathbb{Z}_{\mathrm{5}} \\ $$

Question Number 13075    Answers: 0   Comments: 5

S(x) is the sum of 49 terms of AP The first term is (1/2)x^3 and the difference is (7 − x) If S(x) maximum, the value of 10^(th) term is ...

$${S}\left({x}\right)\:\mathrm{is}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{49}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{AP} \\ $$$$\mathrm{The}\:\mathrm{first}\:\mathrm{term}\:\mathrm{is}\:\frac{\mathrm{1}}{\mathrm{2}}{x}^{\mathrm{3}} \:\mathrm{and}\:\mathrm{the}\:\mathrm{difference} \\ $$$$\mathrm{is}\:\left(\mathrm{7}\:−\:{x}\right) \\ $$$$\mathrm{If}\:{S}\left({x}\right)\:\mathrm{maximum},\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{10}^{\mathrm{th}} \:\mathrm{term}\:\mathrm{is}\:... \\ $$

Question Number 13059    Answers: 2   Comments: 0

please help for ∫_(−3π ) ^( 3π) sin^(2009) x dx

$$\mathrm{please}\:\mathrm{help}\:\mathrm{for} \\ $$$$\int_{−\mathrm{3}\pi\:} ^{\:\:\:\mathrm{3}\pi} \mathrm{sin}^{\mathrm{2009}} \mathrm{x}\:\mathrm{dx} \\ $$

Question Number 13054    Answers: 1   Comments: 0

An object is placed between a converging lens and a plane mirror. Explain how two real images of the object may be produced by the system. If the focal length of the lens is 15cm and the object is 20cm from both the lens and the mirror.Calculate the distance of the two images from the lens.. pls help me with this....

$$\mathrm{An}\:\mathrm{object}\:\mathrm{is}\:\mathrm{placed}\:\mathrm{between}\:\mathrm{a}\: \\ $$$$\mathrm{converging}\:\mathrm{lens}\:\mathrm{and}\:\mathrm{a}\:\mathrm{plane}\:\mathrm{mirror}. \\ $$$$\mathrm{Explain}\:\mathrm{how}\:\mathrm{two}\:\mathrm{real}\:\mathrm{images}\:\mathrm{of}\:\mathrm{the} \\ $$$$\mathrm{object}\:\mathrm{may}\:\mathrm{be}\:\mathrm{produced}\:\mathrm{by}\:\mathrm{the}\: \\ $$$$\mathrm{system}. \\ $$$$\mathrm{If}\:\mathrm{the}\:\mathrm{focal}\:\mathrm{length}\:\mathrm{of}\:\mathrm{the}\:\mathrm{lens}\:\mathrm{is}\:\mathrm{15cm} \\ $$$$\mathrm{and}\:\mathrm{the}\:\mathrm{object}\:\mathrm{is}\:\mathrm{20cm}\:\mathrm{from}\:\mathrm{both}\: \\ $$$$\mathrm{the}\:\mathrm{lens}\:\mathrm{and}\:\mathrm{the}\:\mathrm{mirror}.\mathrm{Calculate} \\ $$$$\mathrm{the}\:\mathrm{distance}\:\mathrm{of}\:\mathrm{the}\:\mathrm{two}\:\mathrm{images}\: \\ $$$$\mathrm{from}\:\mathrm{the}\:\mathrm{lens}.. \\ $$$$ \\ $$$$ \\ $$$$ \\ $$$$\mathrm{pls}\:\mathrm{help}\:\mathrm{me}\:\mathrm{with}\:\mathrm{this}....\: \\ $$

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