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Question Number 39236 Answers: 0 Comments: 3

If a petrol tank costs $2000.00 to fill it up at 10°C ,how much extra dollar must I pay to fill up the tank at 50°C,if the petrol costs $50.00 per litre and its cubic expansivity is 9.5×10^(−4) K^(−1) ?

$${If}\:{a}\:{petrol}\:{tank}\:{costs}\:\$\mathrm{2000}.\mathrm{00}\:{to} \\ $$$${fill}\:{it}\:{up}\:{at}\:\mathrm{10}°{C}\:,{how}\:{much}\:{extra} \\ $$$${dollar}\:{must}\:{I}\:{pay}\:{to}\:{fill}\:{up}\:{the}\:{tank} \\ $$$${at}\:\mathrm{50}°{C},{if}\:{the}\:{petrol}\:{costs}\:\$\mathrm{50}.\mathrm{00} \\ $$$${per}\:{litre}\:{and}\:{its}\:{cubic}\:{expansivity} \\ $$$${is}\:\mathrm{9}.\mathrm{5}×\mathrm{10}^{−\mathrm{4}} {K}^{−\mathrm{1}} ? \\ $$$$ \\ $$

Question Number 39235 Answers: 0 Comments: 1

The length of a mercury column in a mercury in glass thermometer is 4cm at triple point.What is the length of the column when the scale indicates temperature of 560K.

$${The}\:{length}\:{of}\:{a}\:{mercury}\:{column} \\ $$$${in}\:{a}\:{mercury}\:{in}\:{glass}\:{thermometer} \\ $$$${is}\:\mathrm{4}{cm}\:{at}\:{triple}\:{point}.{What}\:{is}\:{the} \\ $$$${length}\:{of}\:{the}\:{column}\:{when}\:{the} \\ $$$${scale}\:{indicates}\:{temperature}\:{of}\:\mathrm{560}{K}. \\ $$

Question Number 39231 Answers: 1 Comments: 0

(sin^(−1) x)^2 + (sin^(−1) y)^2 + 2(sin^(−1) x) (sin^(−1) y)= π^2 ,then x^2 +y^2 is equal to?

$$\left({sin}^{−\mathrm{1}} {x}\right)^{\mathrm{2}} +\:\:\left({sin}^{−\mathrm{1}} {y}\right)^{\mathrm{2}} +\:\:\mathrm{2}\left({sin}^{−\mathrm{1}} {x}\right) \\ $$$$\left({sin}^{−\mathrm{1}} {y}\right)=\:\pi^{\mathrm{2}} ,{then}\:{x}^{\mathrm{2}} +{y}^{\mathrm{2}} \:{is}\:{equal}\:{to}? \\ $$

Question Number 39230 Answers: 2 Comments: 0

∫(dα/(sin 2α +sin 3α +sin 5α))=?

$$\int\frac{{d}\alpha}{\mathrm{sin}\:\mathrm{2}\alpha\:+\mathrm{sin}\:\mathrm{3}\alpha\:+\mathrm{sin}\:\mathrm{5}\alpha}=? \\ $$

Question Number 39222 Answers: 1 Comments: 5

Question Number 39218 Answers: 1 Comments: 0

Question Number 39214 Answers: 0 Comments: 1

let f(x)= (e^(−3x) /(x^2 +4)) developp f at integr serie.

$${let}\:{f}\left({x}\right)=\:\frac{{e}^{−\mathrm{3}{x}} }{{x}^{\mathrm{2}} \:+\mathrm{4}} \\ $$$${developp}\:{f}\:\:{at}\:{integr}\:{serie}. \\ $$

Question Number 39204 Answers: 0 Comments: 0

study tbe variation of f(x) =(2x+1)ln(1+e^(−x) ) and give its graph 2) calculate ∫_0 ^4 f(x)dx .

$${study}\:{tbe}\:{variation}\:{of}\:{f}\left({x}\right)\:=\left(\mathrm{2}{x}+\mathrm{1}\right){ln}\left(\mathrm{1}+{e}^{−{x}} \right) \\ $$$${and}\:{give}\:{its}\:{graph} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\:\int_{\mathrm{0}} ^{\mathrm{4}} \:{f}\left({x}\right){dx}\:. \\ $$

Question Number 39203 Answers: 0 Comments: 0

study and give the graph of f(x) = (e^(−x^2 ) /(x^2 +3 e^x ))

$${study}\:{and}\:{give}\:{the}\:{graph}\:{of}\: \\ $$$${f}\left({x}\right)\:=\:\:\frac{{e}^{−{x}^{\mathrm{2}} } }{{x}^{\mathrm{2}} \:+\mathrm{3}\:{e}^{{x}} } \\ $$

Question Number 39177 Answers: 2 Comments: 2

Question Number 39175 Answers: 1 Comments: 0

Question Number 39174 Answers: 1 Comments: 0

Question Number 39173 Answers: 0 Comments: 0

Given that A and B are two independent Events where P(A) = (4/5) and P(A ∪ B) = ((13)/5) . find a) P(A∩B) b) P(A∣B). hence draw tree Diagram for each posible out come

$${Given}\:{that}\:{A}\:{and}\:{B}\:{are}\:{two} \\ $$$${independent}\:{Events}\: \\ $$$${where}\:{P}\left({A}\right)\:=\:\frac{\mathrm{4}}{\mathrm{5}}\:{and}\: \\ $$$${P}\left({A}\:\cup\:{B}\right)\:=\:\frac{\mathrm{13}}{\mathrm{5}}\:. \\ $$$$\left.{find}\:{a}\right)\:{P}\left({A}\cap{B}\right) \\ $$$$\left.\:\:\:\:\:\:\:\:\:{b}\right)\:{P}\left({A}\mid{B}\right). \\ $$$${hence}\:{draw}\:{tree}\:{Diagram} \\ $$$${for}\:{each}\:{posible}\:{out}\:{come} \\ $$

Question Number 39172 Answers: 1 Comments: 1

find the angle between 3i − 4j and i − j

$${find}\:{the}\:{angle}\:{between}\: \\ $$$$\mathrm{3}{i}\:−\:\mathrm{4}{j}\:{and}\:{i}\:−\:{j} \\ $$

Question Number 39171 Answers: 1 Comments: 0

Given that y = 3x^4 and x increases at the rate of 34% . find the percentage increase in y. [hint: using Bionomial method]

$${Given}\:{that}\: \\ $$$${y}\:=\:\mathrm{3}{x}^{\mathrm{4}} \:{and}\:{x}\:{increases} \\ $$$${at}\:{the}\:{rate}\:{of}\:\mathrm{34\%}\:. \\ $$$${find}\:{the}\:{percentage}\:{increase} \\ $$$${in}\:{y}. \\ $$$$\left[{hint}:\:{using}\:{Bionomial}\:\right. \\ $$$$\left.{method}\right] \\ $$

Question Number 39166 Answers: 1 Comments: 1

Find the value of k if (2,k) ,(3,4) and (6,4) are collinear. hence find the equation on the line 3i − j with the above points

$${Find}\:{the}\:{value}\:{of}\:{k}\:{if} \\ $$$$\left(\mathrm{2},{k}\right)\:,\left(\mathrm{3},\mathrm{4}\right)\:{and}\:\left(\mathrm{6},\mathrm{4}\right)\:{are} \\ $$$${collinear}. \\ $$$${hence}\:{find}\:{the}\:{equation}\:{on} \\ $$$${the}\:{line}\:\mathrm{3}{i}\:−\:{j}\:{with}\:{the}\:{above} \\ $$$${points} \\ $$

Question Number 39165 Answers: 0 Comments: 4

calculate ∫_0 ^∞ (dt/(1+t^(4 ) +t^6 ))

$${calculate}\:\:\int_{\mathrm{0}} ^{\infty} \:\:\:\:\frac{{dt}}{\mathrm{1}+{t}^{\mathrm{4}\:} \:+{t}^{\mathrm{6}} } \\ $$

Question Number 39170 Answers: 0 Comments: 0

Find the value of k if (d/dx)(f(x))= 6 when x = −1 and f(x) = 3x^3 − kx^2 + 1 if f(2) = 8 find one factor of f(x) and hence Evaluate lim_(x→∞) (f(x)).

$${Find}\:{the}\:{value}\:{of}\:{k}\:{if}\: \\ $$$$\frac{{d}}{{dx}}\left({f}\left({x}\right)\right)=\:\mathrm{6}\:{when}\:{x}\:=\:−\mathrm{1}\: \\ $$$${and}\:{f}\left({x}\right)\:=\:\mathrm{3}{x}^{\mathrm{3}} \:−\:{kx}^{\mathrm{2}} \:+\:\mathrm{1}\: \\ $$$${if}\:{f}\left(\mathrm{2}\right)\:=\:\mathrm{8}\:{find}\:{one}\:{factor}\:{of} \\ $$$${f}\left({x}\right)\:{and}\:{hence}\:{Evaluate} \\ $$$$\underset{{x}\rightarrow\infty} {{lim}}\left({f}\left({x}\right)\right). \\ $$

Question Number 39156 Answers: 1 Comments: 0

Question Number 39142 Answers: 1 Comments: 0

F(x) = x^3 −9x^2 +24x+c=0 has three real and distinct roots α , β & γ . Q.1 → Possible value of c is : Q.2 → If [α]+[β]+[γ]= 8 then c is : Q.3 → If [α]+[β]+[γ]=7 then c is : Options for the above 3 Q. → a) (−20,−16) b) (−20,−18) c) (−18,−16) d) none of these. [.] = greatest integer function.

$$\mathrm{F}\left({x}\right)\:=\:{x}^{\mathrm{3}} −\mathrm{9}{x}^{\mathrm{2}} +\mathrm{24}{x}+{c}=\mathrm{0}\:{has}\:\mathrm{three} \\ $$$$\mathrm{real}\:\mathrm{and}\:\mathrm{distinct}\:\mathrm{roots}\:\alpha\:,\:\beta\:\&\:\gamma\:. \\ $$$$\mathrm{Q}.\mathrm{1}\:\rightarrow\:\mathrm{Possible}\:\mathrm{value}\:\mathrm{of}\:\mathrm{c}\:\mathrm{is}\:: \\ $$$$\mathrm{Q}.\mathrm{2}\:\rightarrow\:\mathrm{If}\:\left[\alpha\right]+\left[\beta\right]+\left[\gamma\right]=\:\mathrm{8}\:\mathrm{then}\:\mathrm{c}\:\mathrm{is}\:: \\ $$$$\mathrm{Q}.\mathrm{3}\:\rightarrow\:\mathrm{If}\:\left[\alpha\right]+\left[\beta\right]+\left[\gamma\right]=\mathrm{7}\:\mathrm{then}\:\mathrm{c}\:\mathrm{is}\:: \\ $$$$ \\ $$$$\mathrm{Options}\:\mathrm{for}\:\mathrm{the}\:\mathrm{above}\:\mathrm{3}\:\mathrm{Q}.\:\rightarrow \\ $$$$\left.\mathrm{a}\left.\right)\:\left(−\mathrm{20},−\mathrm{16}\right)\:\:\:\:\:\:\:\:\mathrm{b}\right)\:\left(−\mathrm{20},−\mathrm{18}\right) \\ $$$$\left.\mathrm{c}\left.\right)\:\left(−\mathrm{18},−\mathrm{16}\right)\:\:\:\:\:\:\:\:\:\mathrm{d}\right)\:\mathrm{none}\:\mathrm{of}\:\mathrm{these}. \\ $$$$ \\ $$$$\left[.\right]\:=\:\mathrm{greatest}\:\mathrm{integer}\:\mathrm{function}. \\ $$

Question Number 39135 Answers: 1 Comments: 2

calculate A(λ) = ∫_0 ^λ ((ln(x+(√(1+x^2 ))))/(√(1+x^2 ))) dx 2) calculate ∫_0 ^1 ((ln(x+(√(1+x^2 ))))/(√(1+x^2 )))dx

$${calculate}\:{A}\left(\lambda\right)\:=\:\int_{\mathrm{0}} ^{\lambda} \:\:\:\frac{{ln}\left({x}+\sqrt{\left.\mathrm{1}+{x}^{\mathrm{2}} \right)}\right.}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}\:{dx} \\ $$$$\left.\mathrm{2}\right)\:{calculate}\:\int_{\mathrm{0}} ^{\mathrm{1}} \:\frac{{ln}\left({x}+\sqrt{\left.\mathrm{1}+{x}^{\mathrm{2}} \right)}\right.}{\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }}{dx} \\ $$

Question Number 39127 Answers: 0 Comments: 1

Given the lines l_1 : x + y = 5 and l_2 : y = 4x and l_3 ; 4x + y − 1 =0 show that l_(2 ) is perpendicular to l_3 . find the point coordinates if x + 2y = 5 is colliner to l_1

$${Given}\:{the}\:{lines} \\ $$$${l}_{\mathrm{1}} :\:\:{x}\:+\:{y}\:=\:\mathrm{5}\:{and}\:{l}_{\mathrm{2}} :\:{y}\:=\:\mathrm{4}{x} \\ $$$${and}\:{l}_{\mathrm{3}} ;\:\mathrm{4}{x}\:+\:{y}\:−\:\mathrm{1}\:=\mathrm{0} \\ $$$${show}\:{that}\:{l}_{\mathrm{2}\:} \:{is}\:{perpendicular} \\ $$$${to}\:{l}_{\mathrm{3}} . \\ $$$${find}\:{the}\:{point}\:{coordinates} \\ $$$${if}\:{x}\:+\:\mathrm{2}{y}\:=\:\mathrm{5}\:{is}\:{colliner}\:{to}\:{l}_{\mathrm{1}} \\ $$

Question Number 39144 Answers: 1 Comments: 0

f(x) = 3x^3 − 2x + k has factor (x − 1) find the value of k. with these value evaluate a) (d/(dx ))(f(x)_ ) b) ∫_5 ^2 (f(x))

$${f}\left({x}\right)\:=\:\mathrm{3}{x}^{\mathrm{3}} \:−\:\mathrm{2}{x}\:+\:{k}\:{has}\: \\ $$$${factor}\:\left({x}\:−\:\mathrm{1}\right)\:\: \\ $$$${find}\:{the}\:{value}\:{of}\:{k}. \\ $$$${with}\:{these}\:{value}\: \\ $$$${evaluate} \\ $$$$\left.{a}\right)\:\frac{{d}}{{dx}\:}\left({f}\left({x}\right)_{} \right) \\ $$$$\left.{b}\right)\:\int_{\mathrm{5}} ^{\mathrm{2}} \left({f}\left({x}\right)\right) \\ $$

Question Number 39121 Answers: 0 Comments: 5

Find domain of (1+(1/x))^x ? Also prove thatL_(x→0^+ ) (1+(1/x))^x = 1 ?

$$\mathrm{Find}\:\mathrm{domain}\:\mathrm{of}\:\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}} \:? \\ $$$$\mathrm{Also}\:\mathrm{prove}\:\mathrm{that}\underset{{x}\rightarrow\mathrm{0}^{+} } {\mathrm{L}}\:\left(\mathrm{1}+\frac{\mathrm{1}}{{x}}\right)^{{x}} \:=\:\mathrm{1}\:? \\ $$

Question Number 39120 Answers: 1 Comments: 1

let A_n = ∫_1 ^n (([(√(1+x^2 ))] −[x])/x^2 ) dx (n integr ≥1) 1) calculate A_n 2) find lim_(n→+∞) A_n

$${let}\:{A}_{{n}} =\:\int_{\mathrm{1}} ^{{n}} \:\frac{\left[\sqrt{\mathrm{1}+{x}^{\mathrm{2}} }\right]\:−\left[{x}\right]}{{x}^{\mathrm{2}} }\:{dx}\:\:\left({n}\:{integr}\:\geqslant\mathrm{1}\right) \\ $$$$\left.\mathrm{1}\right)\:{calculate}\:{A}_{{n}} \\ $$$$\left.\mathrm{2}\right)\:{find}\:{lim}_{{n}\rightarrow+\infty} \:{A}_{{n}} \: \\ $$

Question Number 39119 Answers: 0 Comments: 1

calculate ∫_(−∞) ^(+∞) ((x^2 cos(4x))/((x^2 +1)^2 ))dx

$${calculate}\:\:\int_{−\infty} ^{+\infty} \:\:\:\frac{{x}^{\mathrm{2}} \:{cos}\left(\mathrm{4}{x}\right)}{\left({x}^{\mathrm{2}} \:+\mathrm{1}\right)^{\mathrm{2}} }{dx} \\ $$

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