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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

Question Number 10317 Answers: 2 Comments: 0

Solve for x. 3^(2x) = 18x please i need workings.

$$\mathrm{Solve}\:\mathrm{for}\:\mathrm{x}. \\ $$$$\mathrm{3}^{\mathrm{2x}} \:=\:\mathrm{18x} \\ $$$$\mathrm{please}\:\mathrm{i}\:\mathrm{need}\:\mathrm{workings}. \\ $$

Question Number 10318 Answers: 1 Comments: 0

If 12, x, y and 4 provides a sequence such that the first 3 of the numbers are in arithmetic progression. Calculate the (a) Possible values of x and y (b) The sum of the A.P (c) The product of the last 3 numbers of the G.P

$$\mathrm{If}\:\mathrm{12},\:\mathrm{x},\:\mathrm{y}\:\mathrm{and}\:\mathrm{4}\:\mathrm{provides}\:\mathrm{a}\:\mathrm{sequence}\:\mathrm{such}\:\mathrm{that} \\ $$$$\mathrm{the}\:\mathrm{first}\:\mathrm{3}\:\mathrm{of}\:\mathrm{the}\:\mathrm{numbers}\:\mathrm{are}\:\mathrm{in}\:\mathrm{arithmetic} \\ $$$$\mathrm{progression}.\:\mathrm{Calculate}\:\mathrm{the}\: \\ $$$$\left(\mathrm{a}\right)\:\mathrm{Possible}\:\mathrm{values}\:\mathrm{of}\:\mathrm{x}\:\mathrm{and}\:\mathrm{y} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{The}\:\mathrm{sum}\:\mathrm{of}\:\mathrm{the}\:\mathrm{A}.\mathrm{P} \\ $$$$\left(\mathrm{c}\right)\:\mathrm{The}\:\mathrm{product}\:\mathrm{of}\:\mathrm{the}\:\mathrm{last}\:\mathrm{3}\:\mathrm{numbers}\:\mathrm{of} \\ $$$$\mathrm{the}\:\mathrm{G}.\mathrm{P} \\ $$

Question Number 10309 Answers: 0 Comments: 0

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

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

Question Number 10303 Answers: 0 Comments: 1

Question Number 10294 Answers: 3 Comments: 0

A student needs at least three notebooks and three pencils. Notebooks cost #60 and pencil #36 and the student has #360 to spend. The student decides to spend as much as possible of his #360. (a) How many ways can he spend his money (b) Does any of the ways give him change ??? if so, how much ?

$$\mathrm{A}\:\mathrm{student}\:\mathrm{needs}\:\mathrm{at}\:\mathrm{least}\:\mathrm{three}\:\mathrm{notebooks}\:\mathrm{and} \\ $$$$\mathrm{three}\:\mathrm{pencils}.\:\mathrm{Notebooks}\:\mathrm{cost}\:#\mathrm{60}\:\mathrm{and}\:\mathrm{pencil} \\ $$$$#\mathrm{36}\:\mathrm{and}\:\mathrm{the}\:\mathrm{student}\:\mathrm{has}\:#\mathrm{360}\:\mathrm{to}\:\mathrm{spend}.\:\mathrm{The} \\ $$$$\mathrm{student}\:\mathrm{decides}\:\mathrm{to}\:\mathrm{spend}\:\mathrm{as}\:\mathrm{much}\:\mathrm{as}\:\mathrm{possible} \\ $$$$\mathrm{of}\:\mathrm{his}\:#\mathrm{360}. \\ $$$$\left(\mathrm{a}\right)\:\mathrm{How}\:\mathrm{many}\:\mathrm{ways}\:\mathrm{can}\:\mathrm{he}\:\mathrm{spend}\:\mathrm{his}\:\mathrm{money} \\ $$$$\left(\mathrm{b}\right)\:\mathrm{Does}\:\mathrm{any}\:\mathrm{of}\:\mathrm{the}\:\mathrm{ways}\:\mathrm{give}\:\mathrm{him}\:\mathrm{change}\:??? \\ $$$$\mathrm{if}\:\mathrm{so},\:\mathrm{how}\:\mathrm{much}\:? \\ $$

Question Number 10290 Answers: 1 Comments: 0

3×3!+4×4!+...+12×12!=?

$$\mathrm{3}×\mathrm{3}!+\mathrm{4}×\mathrm{4}!+...+\mathrm{12}×\mathrm{12}!=? \\ $$

Question Number 10289 Answers: 1 Comments: 0

((9−x^2 )/x)+3=((x−3)/3)⇒Σx=?

$$\frac{\mathrm{9}−\mathrm{x}^{\mathrm{2}} }{\mathrm{x}}+\mathrm{3}=\frac{\mathrm{x}−\mathrm{3}}{\mathrm{3}}\Rightarrow\Sigma\mathrm{x}=? \\ $$$$ \\ $$

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