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Question Number 10227 Answers: 1 Comments: 0

An aeroplane leaves a port P(51°S, 29°E) and after flying 7597 km due north it reached another port R. calculate the. (i) Latitude of R correct to the nearest degree (ii) Radius of parallel of latitude through R to the nearest whole number.

$$\mathrm{An}\:\mathrm{aeroplane}\:\mathrm{leaves}\:\mathrm{a}\:\mathrm{port}\:\mathrm{P}\left(\mathrm{51}°\mathrm{S},\:\:\mathrm{29}°\mathrm{E}\right)\:\mathrm{and} \\ $$$$\mathrm{after}\:\mathrm{flying}\:\mathrm{7597}\:\mathrm{km}\:\mathrm{due}\:\mathrm{north}\:\mathrm{it}\:\mathrm{reached}\: \\ $$$$\mathrm{another}\:\mathrm{port}\:\mathrm{R}.\:\mathrm{calculate}\:\mathrm{the}. \\ $$$$\left(\mathrm{i}\right)\:\mathrm{Latitude}\:\mathrm{of}\:\mathrm{R}\:\mathrm{correct}\:\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{degree} \\ $$$$\left(\mathrm{ii}\right)\:\mathrm{Radius}\:\mathrm{of}\:\mathrm{parallel}\:\mathrm{of}\:\mathrm{latitude}\:\mathrm{through}\:\mathrm{R} \\ $$$$\mathrm{to}\:\mathrm{the}\:\mathrm{nearest}\:\mathrm{whole}\:\mathrm{number}. \\ $$

Question Number 10223 Answers: 3 Comments: 0

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 10216 Answers: 2 Comments: 0

(((√2) +(√4)+...+(√(28)))/((√3)+(√6)+...+(√(42))))=(√x) ⇒x=?

$$\frac{\sqrt{\mathrm{2}}\:+\sqrt{\mathrm{4}}+...+\sqrt{\mathrm{28}}}{\sqrt{\mathrm{3}}+\sqrt{\mathrm{6}}+...+\sqrt{\mathrm{42}}}=\sqrt{\mathrm{x}}\:\Rightarrow\mathrm{x}=? \\ $$

Question Number 10214 Answers: 1 Comments: 1

How many moles of oxygen atom are in 0.50 mol of Ca(ClO3)2

$$\mathrm{How}\:\mathrm{many}\:\mathrm{moles}\:\mathrm{of}\:\mathrm{oxygen}\:\mathrm{atom}\:\mathrm{are}\:\mathrm{in} \\ $$$$\mathrm{0}.\mathrm{50}\:\mathrm{mol}\:\mathrm{of}\:\mathrm{Ca}\left(\mathrm{ClO3}\right)\mathrm{2} \\ $$

Question Number 10213 Answers: 2 Comments: 0

4a−b=60 2(√a)−(√b)=6 ⇒a+b=?

$$\mathrm{4a}−\mathrm{b}=\mathrm{60} \\ $$$$\mathrm{2}\sqrt{\mathrm{a}}−\sqrt{\mathrm{b}}=\mathrm{6} \\ $$$$\Rightarrow\mathrm{a}+\mathrm{b}=? \\ $$

Question Number 10212 Answers: 3 Comments: 0

x+y=12 x×y=16 ⇒(√(x/y))−(√(y/x)) =?

$$\mathrm{x}+\mathrm{y}=\mathrm{12} \\ $$$$\mathrm{x}×\mathrm{y}=\mathrm{16} \\ $$$$\Rightarrow\sqrt{\frac{\mathrm{x}}{\mathrm{y}}}−\sqrt{\frac{\mathrm{y}}{\mathrm{x}}}\:=? \\ $$

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)) = ?

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

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