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Question Number 12190    Answers: 1   Comments: 0

Show that, 0.9999999999999 ...... ∞ is equal to 1

$$\mathrm{Show}\:\mathrm{that},\:\:\mathrm{0}.\mathrm{9999999999999}\:......\:\infty\:\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{1} \\ $$

Question Number 12189    Answers: 1   Comments: 0

Find the fraction to the below deimal 4.4444444444444....... ∞

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{fraction}\:\mathrm{to}\:\mathrm{the}\:\mathrm{below}\:\mathrm{deimal} \\ $$$$\mathrm{4}.\mathrm{4444444444444}.......\:\infty \\ $$

Question Number 12185    Answers: 1   Comments: 0

A particle is moving with velocity v=K(yi^ +xj^ ) prove that y^2 =x^2 +constant

$$\mathrm{A}\:\mathrm{particle}\:\mathrm{is}\:\mathrm{moving}\:\mathrm{with}\:\mathrm{velocity} \\ $$$${v}={K}\left({y}\hat {{i}}+{x}\hat {{j}}\right) \\ $$$${prove}\:{that} \\ $$$${y}^{\mathrm{2}} ={x}^{\mathrm{2}} +{constant} \\ $$

Question Number 12201    Answers: 3   Comments: 0

∫(1/(sin(x)))dx

$$\int\frac{\mathrm{1}}{{sin}\left({x}\right)}{dx} \\ $$

Question Number 12291    Answers: 1   Comments: 0

Question Number 12181    Answers: 0   Comments: 0

The value of xyz is 15/2 or 18/5 according as the series a,x,y,z,b are in an A.P. or H.P., then ′a+b′ equals where a, b are +ve integers.

$$\mathrm{The}\:\mathrm{value}\:\mathrm{of}\:{xyz}\:\mathrm{is}\:\mathrm{15}/\mathrm{2}\:\mathrm{or}\:\mathrm{18}/\mathrm{5} \\ $$$$\mathrm{according}\:\mathrm{as}\:\mathrm{the}\:\mathrm{series}\:{a},{x},{y},{z},{b}\:\mathrm{are} \\ $$$$\mathrm{in}\:\mathrm{an}\:\mathrm{A}.\mathrm{P}.\:\mathrm{or}\:\mathrm{H}.\mathrm{P}.,\:\mathrm{then}\:'{a}+{b}'\:\mathrm{equals} \\ $$$$\mathrm{where}\:{a},\:{b}\:\mathrm{are}\:+\mathrm{ve}\:\mathrm{integers}. \\ $$

Question Number 12173    Answers: 2   Comments: 0

Prove that ∀x∈[1,2] ⇒ 1−x^2 ≤ x

$$\boldsymbol{{Prove}}\:\boldsymbol{{that}}\:\forall\boldsymbol{{x}}\in\left[\mathrm{1},\mathrm{2}\right] \\ $$$$\Rightarrow\:\mathrm{1}−\boldsymbol{{x}}^{\mathrm{2}} \:\leqslant\:\boldsymbol{{x}} \\ $$

Question Number 12171    Answers: 1   Comments: 0

∫x^2 ×sgn(2x)dx=?

$$\int\mathrm{x}^{\mathrm{2}} ×\mathrm{sgn}\left(\mathrm{2x}\right)\mathrm{dx}=? \\ $$

Question Number 12170    Answers: 1   Comments: 0

In any △ABC, 2(bc cos A+ca cos B+ab cos C) =

$$\mathrm{In}\:\mathrm{any}\:\bigtriangleup{ABC}, \\ $$$$\:\mathrm{2}\left({bc}\:\mathrm{cos}\:{A}+{ca}\:\mathrm{cos}\:{B}+{ab}\:\mathrm{cos}\:{C}\right)\:= \\ $$

Question Number 12169    Answers: 1   Comments: 0

If tan α equals the integral solution of the inequality 4x^2 −16x+15<0 and cos β equals to the slope of the bisector of the first quadrant, then sin (α+β) sin (α−β) is equal to

$$\mathrm{If}\:\:\mathrm{tan}\:\alpha\:\mathrm{equals}\:\mathrm{the}\:\mathrm{integral}\:\mathrm{solution}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{inequality}\:\:\mathrm{4}{x}^{\mathrm{2}} −\mathrm{16}{x}+\mathrm{15}<\mathrm{0}\:\mathrm{and}\: \\ $$$$\mathrm{cos}\:\beta\:\:\mathrm{equals}\:\mathrm{to}\:\mathrm{the}\:\mathrm{slope}\:\mathrm{of}\:\mathrm{the}\:\mathrm{bisector} \\ $$$$\mathrm{of}\:\mathrm{the}\:\mathrm{first}\:\mathrm{quadrant},\:\mathrm{then}\: \\ $$$$\mathrm{sin}\:\left(\alpha+\beta\right)\:\mathrm{sin}\:\left(\alpha−\beta\right)\:\mathrm{is}\:\mathrm{equal}\:\mathrm{to} \\ $$

Question Number 12161    Answers: 0   Comments: 2

Question Number 12160    Answers: 1   Comments: 0

Two angles of a triangle are cot^(−1) 2 and cot^(−1) 3. Then the third angle is

$$\mathrm{Two}\:\mathrm{angles}\:\mathrm{of}\:\mathrm{a}\:\mathrm{triangle}\:\mathrm{are}\:\mathrm{cot}^{−\mathrm{1}} \mathrm{2} \\ $$$$\mathrm{and}\:\mathrm{cot}^{−\mathrm{1}} \mathrm{3}.\:\mathrm{Then}\:\mathrm{the}\:\mathrm{third}\:\mathrm{angle}\:\mathrm{is} \\ $$

Question Number 12156    Answers: 1   Comments: 0

If the ratio of the students that pass a test to those that fail is in ratio 4:1, If 9 students were chosen at random, what is the probability that exactly 7 passed the test.

$$\mathrm{If}\:\mathrm{the}\:\mathrm{ratio}\:\mathrm{of}\:\mathrm{the}\:\mathrm{students}\:\mathrm{that}\:\mathrm{pass}\:\mathrm{a}\:\mathrm{test}\:\mathrm{to}\:\mathrm{those}\:\mathrm{that}\:\mathrm{fail}\:\mathrm{is}\:\mathrm{in}\:\mathrm{ratio}\:\mathrm{4}:\mathrm{1}, \\ $$$$\mathrm{If}\:\:\mathrm{9}\:\mathrm{students}\:\mathrm{were}\:\mathrm{chosen}\:\mathrm{at}\:\mathrm{random},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{probability}\:\mathrm{that}\:\mathrm{exactly} \\ $$$$\mathrm{7}\:\mathrm{passed}\:\mathrm{the}\:\mathrm{test}. \\ $$

Question Number 12155    Answers: 1   Comments: 0

Find the 35th derivative of (2x^3 + 5x^4 )^(60)

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{35th}\:\mathrm{derivative}\:\mathrm{of}\:\:\left(\mathrm{2x}^{\mathrm{3}} \:+\:\mathrm{5x}^{\mathrm{4}} \right)^{\mathrm{60}} \\ $$

Question Number 12148    Answers: 0   Comments: 13

Question Number 12144    Answers: 1   Comments: 0

(1/(1+1^2 +1^4 ))+(2/(1+2^2 +2^4 ))+(3/(1+3^2 +3^4 ))+.....∞=?

$$\frac{\mathrm{1}}{\mathrm{1}+\mathrm{1}^{\mathrm{2}} +\mathrm{1}^{\mathrm{4}} }+\frac{\mathrm{2}}{\mathrm{1}+\mathrm{2}^{\mathrm{2}} +\mathrm{2}^{\mathrm{4}} }+\frac{\mathrm{3}}{\mathrm{1}+\mathrm{3}^{\mathrm{2}} +\mathrm{3}^{\mathrm{4}} }+.....\infty=? \\ $$

Question Number 12141    Answers: 1   Comments: 0

∫ sin(x^4 )cos(x^2 ) dx

$$\int\:\mathrm{sin}\left(\mathrm{x}^{\mathrm{4}} \right)\mathrm{cos}\left(\mathrm{x}^{\mathrm{2}} \right)\:\mathrm{dx} \\ $$

Question Number 12139    Answers: 2   Comments: 0

Find the area of the region between the graphs of f(x) = 3x^3 − x^2 − 10x and g(x) = − x^3 + 2x

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{area}\:\mathrm{of}\:\mathrm{the}\:\mathrm{region}\:\mathrm{between}\:\mathrm{the}\:\mathrm{graphs}\:\mathrm{of}\:\mathrm{f}\left(\mathrm{x}\right)\:=\:\mathrm{3x}^{\mathrm{3}} \:−\:\mathrm{x}^{\mathrm{2}} \:−\:\mathrm{10x} \\ $$$$\mathrm{and}\:\mathrm{g}\left(\mathrm{x}\right)\:=\:−\:\mathrm{x}^{\mathrm{3}} \:+\:\mathrm{2x} \\ $$

Question Number 12137    Answers: 0   Comments: 0

Question Number 12130    Answers: 1   Comments: 0

∫(√(a+x/a−x )) −(√(a−x/a+x))

$$\int\sqrt{{a}+{x}/{a}−{x}\:} \\ $$$$−\sqrt{{a}−{x}/{a}+{x}} \\ $$

Question Number 12127    Answers: 1   Comments: 1

Question Number 12126    Answers: 1   Comments: 0

Question Number 12132    Answers: 1   Comments: 0

Given that 1° = 0.017 rad Use f(a) = sin(a) to find an approximate value for sin(29)°.

$$\mathrm{Given}\:\mathrm{that}\:\:\mathrm{1}°\:=\:\mathrm{0}.\mathrm{017}\:\mathrm{rad} \\ $$$$\mathrm{Use}\:\:\mathrm{f}\left(\mathrm{a}\right)\:=\:\mathrm{sin}\left(\mathrm{a}\right)\:\mathrm{to}\:\mathrm{find}\:\mathrm{an}\:\mathrm{approximate}\:\mathrm{value}\:\mathrm{for}\:\mathrm{sin}\left(\mathrm{29}\right)°. \\ $$

Question Number 12131    Answers: 0   Comments: 0

a cube has a rib ABCD.EFGH, the midle point P on BF so that BP = PF, and the midle point Q on FG so that FQ = QG how long projection point C to APQH field ?

$${a}\:{cube}\:{has}\:{a}\:{rib}\:{ABCD}.{EFGH},\:{the}\:{midle}\:{point}\:{P}\:\:{on}\:{BF}\:{so}\:{that}\:{BP}\:=\:{PF}, \\ $$$${and}\:{the}\:{midle}\:{point}\:{Q}\:{on}\:{FG}\:{so}\:{that}\:{FQ}\:=\:{QG} \\ $$$${how}\:{long}\:{projection}\:{point}\:{C}\:{to}\:{APQH}\:{field}\:? \\ $$

Question Number 12111    Answers: 0   Comments: 0

show that: Σ_(n=0) ^∞ (((−1)^n )/(n!))=(1/e) please show your working

$$\mathrm{show}\:\mathrm{that}: \\ $$$$\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}} }{{n}!}=\frac{\mathrm{1}}{{e}} \\ $$$$\mathrm{please}\:\mathrm{show}\:\mathrm{your}\:\mathrm{working} \\ $$

Question Number 12109    Answers: 0   Comments: 0

show that: Σ_(n=1) ^∞ (((−1)^(n+1) )/n)=ln(2) please show your working

$$\mathrm{show}\:\mathrm{that}: \\ $$$$\underset{{n}=\mathrm{1}} {\overset{\infty} {\sum}}\frac{\left(−\mathrm{1}\right)^{{n}+\mathrm{1}} }{{n}}=\mathrm{ln}\left(\mathrm{2}\right) \\ $$$$\mathrm{please}\:\mathrm{show}\:\mathrm{your}\:\mathrm{working} \\ $$

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