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Question Number 10211 Answers: 0 Comments: 2

without solving for x in f(x)=0, show me a different way to find the roots of f(x)=x^2 −x−1

$$\mathrm{without}\:\mathrm{solving}\:\mathrm{for}\:{x}\:\mathrm{in}\:{f}\left({x}\right)=\mathrm{0}, \\ $$$$\mathrm{show}\:\mathrm{me}\:\mathrm{a}\:\mathrm{different}\:\mathrm{way}\:\mathrm{to}\:\mathrm{find}\:\mathrm{the} \\ $$$$\mathrm{roots}\:\mathrm{of}\:{f}\left({x}\right)={x}^{\mathrm{2}} −{x}−\mathrm{1} \\ $$

Question Number 10206 Answers: 1 Comments: 0

^3 (√(49+^3 (√(49+^3 (√(49....)) )))) =x (√(4(√(4(√(4(√(4....)))))))) =y ⇒x^2 −y=?

$$\:^{\mathrm{3}} \sqrt{\mathrm{49}+^{\mathrm{3}} \sqrt{\mathrm{49}+^{\mathrm{3}} \sqrt{\mathrm{49}....}\:}}\:=\mathrm{x} \\ $$$$\sqrt{\mathrm{4}\sqrt{\mathrm{4}\sqrt{\mathrm{4}\sqrt{\mathrm{4}....}}}}\:=\mathrm{y} \\ $$$$\Rightarrow\mathrm{x}^{\mathrm{2}} −\mathrm{y}=? \\ $$

Question Number 10204 Answers: 1 Comments: 0

x^2 p^2 +xyp−6y^2 =0

$${x}^{\mathrm{2}} {p}^{\mathrm{2}} +{xyp}−\mathrm{6}{y}^{\mathrm{2}} =\mathrm{0} \\ $$

Question Number 10200 Answers: 0 Comments: 0

Question Number 10198 Answers: 0 Comments: 0

An aeroplane leaves a port (51^° S, 29^° E) and after flying 759 km due north. it reaches another point R. calculate: (i) Latitude of R correct to the nearest degree (ii) Radius of the parallel of latitude through R to the nearest whole number.

$$\mathrm{An}\:\mathrm{aeroplane}\:\mathrm{leaves}\:\mathrm{a}\:\mathrm{port}\:\left(\mathrm{51}^{°} \mathrm{S},\:\:\mathrm{29}^{°} \mathrm{E}\right)\:\mathrm{and} \\ $$$$\mathrm{after}\:\mathrm{flying}\:\mathrm{759}\:\mathrm{km}\:\mathrm{due}\:\mathrm{north}.\:\mathrm{it}\:\mathrm{reaches} \\ $$$$\mathrm{another}\:\mathrm{point}\:\mathrm{R}.\:\mathrm{calculate}: \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Latitude}\:\mathrm{of}\:\mathrm{R}\:\mathrm{correct}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{degree} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Radius}\:\mathrm{of}\:\mathrm{the}\:\mathrm{parallel}\:\mathrm{of}\:\mathrm{latitude}\:\mathrm{through} \\ $$$$\mathrm{R}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{whole}\:\mathrm{number}. \\ $$

Question Number 10197 Answers: 1 Comments: 0

^3 (√(x−2))+^3 (√(8x−16))=16⇒x=?

$$\:^{\mathrm{3}} \sqrt{\mathrm{x}−\mathrm{2}}+^{\mathrm{3}} \sqrt{\mathrm{8x}−\mathrm{16}}=\mathrm{16}\Rightarrow\mathrm{x}=? \\ $$

Question Number 10196 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 10193 Answers: 1 Comments: 0

x=^3 (√(11+(√(57)))) +^3 (√(11−(√(57)))) ⇒ x^3 −12x=?

$$\mathrm{x}=^{\mathrm{3}} \sqrt{\mathrm{11}+\sqrt{\mathrm{57}}}\:\:+\:^{\mathrm{3}} \sqrt{\mathrm{11}−\sqrt{\mathrm{57}}} \\ $$$$\Rightarrow\:\mathrm{x}^{\mathrm{3}} −\mathrm{12x}=? \\ $$

Question Number 10191 Answers: 1 Comments: 0

∫_0 ^( π) sin(x)^(cos(x)) dx

$$\int_{\mathrm{0}} ^{\:\pi} \mathrm{sin}\left({x}\right)^{\mathrm{cos}\left({x}\right)} {dx} \\ $$

Question Number 10190 Answers: 0 Comments: 3

Question Number 10188 Answers: 0 Comments: 1

Question Number 10186 Answers: 0 Comments: 0

Prove ln (1+(1/n))^n =[1−(1/(2(n+1)))+(1/(2∙3(n+1)^2 ))−(1/(3∙4(n+1)^3 ))+..]

$$\mathrm{Prove} \\ $$$$\mathrm{ln}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{n}}\right)^{{n}} =\left[\mathrm{1}−\frac{\mathrm{1}}{\mathrm{2}\left({n}+\mathrm{1}\right)}+\frac{\mathrm{1}}{\mathrm{2}\centerdot\mathrm{3}\left({n}+\mathrm{1}\right)^{\mathrm{2}} }−\frac{\mathrm{1}}{\mathrm{3}\centerdot\mathrm{4}\left({n}+\mathrm{1}\right)^{\mathrm{3}} }+..\right] \\ $$

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 10175 Answers: 1 Comments: 0

Question Number 10172 Answers: 1 Comments: 0

x^x =2^(24) , y^y =3^(18) ⇒((2y+3x)/(y−x))=?

$$\mathrm{x}^{\mathrm{x}} =\mathrm{2}^{\mathrm{24}} \:,\:\mathrm{y}^{\mathrm{y}} =\mathrm{3}^{\mathrm{18}} \Rightarrow\frac{\mathrm{2y}+\mathrm{3x}}{\mathrm{y}−\mathrm{x}}=? \\ $$

Question Number 10184 Answers: 2 Comments: 0

if a_− =2i+3j . b_− =19−15j and c_− =5i−7j. find the value of x such that xa_− + yc_− =b

$${if}\:\underset{−} {{a}}\:=\mathrm{2}{i}+\mathrm{3}{j}\:.\:\underset{−} {{b}}=\mathrm{19}−\mathrm{15}{j}\:{and}\: \\ $$$$\underset{−} {{c}}\:=\mathrm{5}{i}−\mathrm{7}{j}.\:{find}\:{the}\:{value}\:{of}\:{x}\:{such} \\ $$$${that}\:{x}\underset{−} {{a}}\:+\:{y}\underset{−} {{c}}\:={b} \\ $$$$ \\ $$

Question Number 10170 Answers: 1 Comments: 0

y . f(xy) = f(x) x,y ∈ R If f(4) = 1006, so f(2012) = ?

$${y}\:.\:{f}\left({xy}\right)\:=\:{f}\left({x}\right)\:\:\:\:\:\:\:\:{x},\mathrm{y}\:\in\:\mathbb{R} \\ $$$$\mathrm{If}\:{f}\left(\mathrm{4}\right)\:=\:\mathrm{1006},\:\mathrm{so}\:{f}\left(\mathrm{2012}\right)\:=\:? \\ $$

Question Number 10169 Answers: 1 Comments: 0

((2013)/1) + ((2013)/(1+2)) + ((2013)/(1+2+3)) + ... + ((2013)/(1+2+3+...+2012)) = ?

$$\frac{\mathrm{2013}}{\mathrm{1}}\:+\:\frac{\mathrm{2013}}{\mathrm{1}+\mathrm{2}}\:+\:\frac{\mathrm{2013}}{\mathrm{1}+\mathrm{2}+\mathrm{3}}\:+\:...\:+\:\frac{\mathrm{2013}}{\mathrm{1}+\mathrm{2}+\mathrm{3}+...+\mathrm{2012}}\:=\:? \\ $$

Question Number 10168 Answers: 0 Comments: 0

If the roots of quadratic equation ax^2 + bx + c = 0 were within the interval [0,1], the maximum value from (((2a−b)(a−b))/(a(a−b+c))) is ...

$$\mathrm{If}\:\mathrm{the}\:\mathrm{roots}\:\mathrm{of}\:\mathrm{quadratic}\:\mathrm{equation} \\ $$$${ax}^{\mathrm{2}} \:+\:{bx}\:+\:{c}\:=\:\mathrm{0} \\ $$$$\mathrm{were}\:\mathrm{within}\:\mathrm{the}\:\mathrm{interval}\:\left[\mathrm{0},\mathrm{1}\right], \\ $$$$\mathrm{the}\:\mathrm{maximum}\:\mathrm{value}\:\mathrm{from} \\ $$$$\frac{\left(\mathrm{2}{a}−{b}\right)\left({a}−{b}\right)}{{a}\left({a}−{b}+{c}\right)}\:\:\:\:\mathrm{is}\:... \\ $$

Question Number 10166 Answers: 1 Comments: 1

Question Number 10159 Answers: 1 Comments: 2

Question Number 10157 Answers: 1 Comments: 0

the difference of two number is 3. if the sum of their reciprocal is (7/(10)) . find the numbres

$${the}\:{difference}\:{of}\:{two}\:{number}\:{is}\:\mathrm{3}. \\ $$$${if}\:{the}\:{sum}\:{of}\:{their}\:{reciprocal}\:{is}\: \\ $$$$\frac{\mathrm{7}}{\mathrm{10}}\:.\:{find}\:{the}\:{numbres} \\ $$

Question Number 10155 Answers: 1 Comments: 0

solve for x sin(x) − (√(3cos(x))) = 1

$$\mathrm{solve}\:\mathrm{for}\:\mathrm{x} \\ $$$$\mathrm{sin}\left(\mathrm{x}\right)\:−\:\sqrt{\mathrm{3cos}\left(\mathrm{x}\right)}\:=\:\mathrm{1} \\ $$

Question Number 10154 Answers: 0 Comments: 0

The sum of the first term of sequence is given by S_n = 5n^2 − 2n. A sequence U_1 , U_2 , U_3 .... is defined by U_t = S_t − S_(t − 1) . Express U_t in terms of it simplest form. and show that sequences is linear (AP). (a) Find the sum S_n of the n terms of the sequence r^(th ) term is 4 × 2^(−1) (b) The value of n for which the difference between S_n and less than 10^(−4)

$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{term}\:\mathrm{of}\:\mathrm{sequence}\:\mathrm{is}\: \\ $$$$\mathrm{given}\:\mathrm{by}\:\:\mathrm{S}_{\mathrm{n}} \:=\:\mathrm{5n}^{\mathrm{2}} \:−\:\mathrm{2n}.\:\mathrm{A}\:\mathrm{sequence}\:\: \\ $$$$\mathrm{U}_{\mathrm{1}} ,\:\mathrm{U}_{\mathrm{2}} ,\:\mathrm{U}_{\mathrm{3}} \:....\:\mathrm{is}\:\mathrm{defined}\:\mathrm{by}\:\mathrm{U}_{\mathrm{t}} \:=\:\mathrm{S}_{\mathrm{t}} \:−\:\mathrm{S}_{\mathrm{t}\:−\:\mathrm{1}} . \\ $$$$\mathrm{Express}\:\mathrm{U}_{\mathrm{t}} \:\mathrm{in}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{it}\:\mathrm{simplest}\:\mathrm{form}.\:\mathrm{and} \\ $$$$\mathrm{show}\:\mathrm{that}\:\mathrm{sequences}\:\mathrm{is}\:\mathrm{linear}\:\left(\mathrm{AP}\right). \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{S}_{\mathrm{n}} \:\mathrm{of}\:\mathrm{the}\:\mathrm{n}\:\mathrm{terms}\:\mathrm{of}\:\mathrm{the}\: \\ $$$$\mathrm{sequence}\:\mathrm{r}^{\mathrm{th}\:} \:\mathrm{term}\:\mathrm{is}\:\mathrm{4}\:×\:\mathrm{2}^{−\mathrm{1}} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:\mathrm{n}\:\mathrm{for}\:\mathrm{which}\:\mathrm{the}\:\mathrm{difference} \\ $$$$\mathrm{between}\:\mathrm{S}_{\mathrm{n}} \:\mathrm{and}\:\mathrm{less}\:\mathrm{than}\:\mathrm{10}^{−\mathrm{4}} \\ $$

Question Number 10152 Answers: 0 Comments: 0

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