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AllQuestion and Answers: Page 1970

Question Number 10414    Answers: 2   Comments: 2

Question Number 10409    Answers: 0   Comments: 0

Question Number 10408    Answers: 1   Comments: 0

Question Number 10399    Answers: 0   Comments: 0

Question Number 10398    Answers: 2   Comments: 0

Question Number 10397    Answers: 1   Comments: 1

Question Number 10394    Answers: 1   Comments: 0

∫x×(√(x dx=))

$$\int\mathrm{x}×\sqrt{\mathrm{x}\:\mathrm{dx}=} \\ $$

Question Number 10392    Answers: 1   Comments: 0

find the direction cosines and its angles on 2i − 3j

$${find}\:{the}\:{direction}\:{cosines}\: \\ $$$${and}\:{its}\:{angles}\:{on} \\ $$$$\mathrm{2}{i}\:−\:\mathrm{3}{j}\: \\ $$

Question Number 10391    Answers: 1   Comments: 0

Find the equation of the straight line through (2,3) (i)parallel to (ii)perpendicular to 2x−3y+6=0

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{the}\:\mathrm{straight} \\ $$$$\mathrm{line}\:\mathrm{through}\:\left(\mathrm{2},\mathrm{3}\right)\: \\ $$$$\left(\mathrm{i}\right)\mathrm{parallel}\:\mathrm{to} \\ $$$$\left(\mathrm{ii}\right)\mathrm{perpendicular}\:\mathrm{to}\:\mathrm{2x}−\mathrm{3y}+\mathrm{6}=\mathrm{0} \\ $$

Question Number 10387    Answers: 1   Comments: 0

6 people a, b, c, d, e, and f stand in a line. The number of ways they can stand arranged is equal to 6! If two people have to stand next to each other, but everyone else do not matter, how many combinations combinations are there? e.g. (ab)cdef or cd(ba)ef

$$\mathrm{6}\:\mathrm{people}\:{a},\:{b},\:{c},\:{d},\:{e},\:\mathrm{and}\:{f}\:\mathrm{stand}\:\mathrm{in}\:\mathrm{a}\:\mathrm{line}. \\ $$$$\: \\ $$$$\mathrm{The}\:\mathrm{number}\:\mathrm{of}\:\mathrm{ways}\:\mathrm{they}\:\mathrm{can}\:\mathrm{stand}\:\mathrm{arranged} \\ $$$$\mathrm{is}\:\mathrm{equal}\:\mathrm{to}\:\mathrm{6}! \\ $$$$\: \\ $$$$\mathrm{If}\:\mathrm{two}\:\mathrm{people}\:\mathrm{have}\:\mathrm{to}\:\mathrm{stand}\:\mathrm{next}\:\mathrm{to}\:\mathrm{each}\:\mathrm{other}, \\ $$$$\mathrm{but}\:\mathrm{everyone}\:\mathrm{else}\:\mathrm{do}\:\mathrm{not}\:\mathrm{matter},\:\mathrm{how}\:\mathrm{many}\:\mathrm{combinations} \\ $$$$\mathrm{combinations}\:\mathrm{are}\:\mathrm{there}? \\ $$$$\: \\ $$$$\mathrm{e}.\mathrm{g}.\:\:\:\left({ab}\right){cdef}\:\:\:\:\mathrm{or}\:\:\:\:{cd}\left({ba}\right){ef} \\ $$

Question Number 10381    Answers: 1   Comments: 1

Question Number 10374    Answers: 3   Comments: 0

lim_(x→(π/4)) (((x−(π/4))sin(3x−3(π/4)))/(2(1−sin2x)))=...?

$$\underset{{x}\rightarrow\frac{\pi}{\mathrm{4}}} {\mathrm{lim}}\frac{\left(\mathrm{x}−\frac{\pi}{\mathrm{4}}\right)\mathrm{sin}\left(\mathrm{3x}−\mathrm{3}\frac{\pi}{\mathrm{4}}\right)}{\mathrm{2}\left(\mathrm{1}−\mathrm{sin2x}\right)}=...? \\ $$

Question Number 10369    Answers: 1   Comments: 1

Find the sum of the series 2 + 5 + 8 + 12 ... n

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{series} \\ $$$$\mathrm{2}\:+\:\mathrm{5}\:+\:\mathrm{8}\:+\:\mathrm{12}\:...\:\mathrm{n}\: \\ $$

Question Number 10364    Answers: 1   Comments: 0

1+2+3+4+5+6+7+8+9+10+11 = x^y The sum of all possible solutions of x and y is ...

$$\mathrm{1}+\mathrm{2}+\mathrm{3}+\mathrm{4}+\mathrm{5}+\mathrm{6}+\mathrm{7}+\mathrm{8}+\mathrm{9}+\mathrm{10}+\mathrm{11}\:=\:{x}^{{y}} \\ $$$$\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solutions}\:\mathrm{of}\:{x}\:\mathrm{and}\:{y}\:\mathrm{is}\:... \\ $$

Question Number 10363    Answers: 1   Comments: 0

ΔABC with AB = 5, BC = 7, CA = 8 Find the value of (sin A + sin B + sin C) . (cot (A/2) + cot (B/2) + cot (C/2))

$$\Delta{ABC}\:\mathrm{with}\:{AB}\:=\:\mathrm{5},\:{BC}\:=\:\mathrm{7},\:{CA}\:=\:\mathrm{8} \\ $$$$\mathrm{Find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of} \\ $$$$\left(\mathrm{sin}\:{A}\:+\:\mathrm{sin}\:{B}\:+\:\mathrm{sin}\:{C}\right)\:.\:\left(\mathrm{cot}\:\frac{{A}}{\mathrm{2}}\:+\:\mathrm{cot}\:\frac{{B}}{\mathrm{2}}\:+\:\mathrm{cot}\:\frac{{C}}{\mathrm{2}}\right) \\ $$

Question Number 10362    Answers: 0   Comments: 0

An helium atom has a mass of 6.64 × 10^(−27) kg and a charge Q is +2 electon. Compare the magnitude of the electric repulsion to that of the gravitational attraction between them.

$$\mathrm{An}\:\mathrm{helium}\:\mathrm{atom}\:\mathrm{has}\:\mathrm{a}\:\mathrm{mass}\:\mathrm{of}\:\mathrm{6}.\mathrm{64}\:×\:\mathrm{10}^{−\mathrm{27}} \mathrm{kg}\:\mathrm{and}\:\mathrm{a}\:\mathrm{charge} \\ $$$$\mathrm{Q}\:\mathrm{is}\:+\mathrm{2}\:\mathrm{electon}.\:\mathrm{Compare}\:\mathrm{the}\:\mathrm{magnitude}\:\mathrm{of}\:\mathrm{the}\:\mathrm{electric}\: \\ $$$$\mathrm{repulsion}\:\mathrm{to}\:\mathrm{that}\:\mathrm{of}\:\mathrm{the}\:\mathrm{gravitational}\:\mathrm{attraction}\:\mathrm{between}\:\mathrm{them}. \\ $$

Question Number 11166    Answers: 1   Comments: 1

Question Number 10360    Answers: 3   Comments: 0

Solve for x in the equation. 3^x + 4^x + 5^x = 6^x

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}\:\mathrm{in}\:\mathrm{the}\:\mathrm{equation}. \\ $$$$\mathrm{3}^{\mathrm{x}} \:+\:\mathrm{4}^{\mathrm{x}} \:+\:\mathrm{5}^{\mathrm{x}} \:=\:\mathrm{6}^{\mathrm{x}} \\ $$

Question Number 10355    Answers: 1   Comments: 1

What is the escape velocity from the surface of a planet with two third of the earth′s gravity but the same radius.

$$\mathrm{What}\:\mathrm{is}\:\mathrm{the}\:\mathrm{escape}\:\mathrm{velocity}\:\mathrm{from}\:\mathrm{the}\:\mathrm{surface} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{planet}\:\mathrm{with}\:\mathrm{two}\:\mathrm{third}\:\mathrm{of}\:\mathrm{the}\:\mathrm{earth}'\mathrm{s} \\ $$$$\mathrm{gravity}\:\mathrm{but}\:\mathrm{the}\:\mathrm{same}\:\mathrm{radius}. \\ $$

Question Number 10353    Answers: 0   Comments: 0

show that α^4 =−3hα^2 −gα and deduce that Σα^4 =−3hΣα^2 −gΣα and find Σα^2 ,Σα^3 ,Σα^4 in term of g and h.

$$\mathrm{show}\:\mathrm{that}\:\alpha^{\mathrm{4}} =−\mathrm{3h}\alpha^{\mathrm{2}} −\mathrm{g}\alpha\:\mathrm{and}\:\mathrm{deduce} \\ $$$$\mathrm{that}\:\Sigma\alpha^{\mathrm{4}} =−\mathrm{3h}\Sigma\alpha^{\mathrm{2}} −\mathrm{g}\Sigma\alpha\:\mathrm{and}\:\mathrm{find}\: \\ $$$$\Sigma\alpha^{\mathrm{2}} ,\Sigma\alpha^{\mathrm{3}} ,\Sigma\alpha^{\mathrm{4}} \:\:\mathrm{in}\:\mathrm{term}\:\mathrm{of}\:\mathrm{g}\:\mathrm{and}\:\mathrm{h}. \\ $$

Question Number 10352    Answers: 0   Comments: 0

show that α^3 =−3hα−g and use the similar expression to α,γ to deduce that α^3 =−3hΣα −g

$$\mathrm{show}\:\mathrm{that}\:\alpha^{\mathrm{3}} =−\mathrm{3h}\alpha−\mathrm{g}\:\:\:\mathrm{and}\:\:\mathrm{use}\:\mathrm{the}\: \\ $$$$\mathrm{similar}\:\mathrm{expression}\:\mathrm{to}\:\:\alpha,\gamma\:\:\mathrm{to}\:\mathrm{deduce}\: \\ $$$$\mathrm{that}\:\alpha^{\mathrm{3}} =−\mathrm{3h}\Sigma\alpha\:−\mathrm{g} \\ $$

Question Number 10347    Answers: 2   Comments: 0

A=1+2+3+...+n−2 B=15+16+.....+n A−B=42⇒n=?

$$\mathrm{A}=\mathrm{1}+\mathrm{2}+\mathrm{3}+...+\mathrm{n}−\mathrm{2} \\ $$$$\mathrm{B}=\mathrm{15}+\mathrm{16}+.....+\mathrm{n} \\ $$$$\mathrm{A}−\mathrm{B}=\mathrm{42}\Rightarrow\mathrm{n}=? \\ $$

Question Number 10340    Answers: 0   Comments: 1

A=1×2 +2×4 +3×6+...+14×28 B=1×3 +2×3 +...+14×29 ⇒B=?

$$\mathrm{A}=\mathrm{1}×\mathrm{2}\:+\mathrm{2}×\mathrm{4}\:+\mathrm{3}×\mathrm{6}+...+\mathrm{14}×\mathrm{28} \\ $$$$\mathrm{B}=\mathrm{1}×\mathrm{3}\:+\mathrm{2}×\mathrm{3}\:+...+\mathrm{14}×\mathrm{29} \\ $$$$\Rightarrow\mathrm{B}=? \\ $$

Question Number 10339    Answers: 2   Comments: 0

A=1×2 + 2×3 +3×4+...+10×11 B=3×8 +6×12 +9×16+...+30×44 ⇒(A/B)=?

$$\mathrm{A}=\mathrm{1}×\mathrm{2}\:+\:\mathrm{2}×\mathrm{3}\:+\mathrm{3}×\mathrm{4}+...+\mathrm{10}×\mathrm{11} \\ $$$$\mathrm{B}=\mathrm{3}×\mathrm{8}\:+\mathrm{6}×\mathrm{12}\:+\mathrm{9}×\mathrm{16}+...+\mathrm{30}×\mathrm{44} \\ $$$$\Rightarrow\frac{\mathrm{A}}{\mathrm{B}}=? \\ $$

Question Number 10324    Answers: 1   Comments: 0

Question Number 10323    Answers: 1   Comments: 0

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