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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=?

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

Question Number 10286    Answers: 1   Comments: 0

2000g of water at 100°C is poured into a copper calorimeter 150g of water at 10°C. The temperature of the mixture is 45°C. Calculate the thermal capaity of tbe vessel. specific heat capacity of copper = 400 specific heat capacity of water = 4200

$$\mathrm{2000g}\:\mathrm{of}\:\mathrm{water}\:\mathrm{at}\:\mathrm{100}°\mathrm{C}\:\mathrm{is}\:\mathrm{poured}\:\mathrm{into}\:\mathrm{a}\: \\ $$$$\mathrm{copper}\:\mathrm{calorimeter}\:\mathrm{150g}\:\mathrm{of}\:\mathrm{water}\:\mathrm{at}\:\mathrm{10}°\mathrm{C}. \\ $$$$\mathrm{The}\:\mathrm{temperature}\:\mathrm{of}\:\mathrm{the}\:\mathrm{mixture}\:\mathrm{is}\:\mathrm{45}°\mathrm{C}. \\ $$$$\mathrm{Calculate}\:\mathrm{the}\:\mathrm{thermal}\:\mathrm{capaity}\:\mathrm{of}\:\mathrm{tbe}\:\mathrm{vessel}. \\ $$$$\mathrm{specific}\:\mathrm{heat}\:\mathrm{capacity}\:\mathrm{of}\:\mathrm{copper}\:=\:\mathrm{400} \\ $$$$\mathrm{specific}\:\mathrm{heat}\:\mathrm{capacity}\:\mathrm{of}\:\mathrm{water}\:=\:\mathrm{4200} \\ $$

Question Number 10282    Answers: 1   Comments: 1

210 cm^3 of Nitrogen at a pressure of 400 mmHg and 100 cm^3 of carbon(iv)oxide at a pressure of 350 mmHg were introduce into a 200 cm^3 vessel. what is the total pressure in the vessel.

$$\mathrm{210}\:\mathrm{cm}^{\mathrm{3}} \:\mathrm{of}\:\mathrm{Nitrogen}\:\mathrm{at}\:\mathrm{a}\:\mathrm{pressure}\:\mathrm{of}\:\mathrm{400}\:\mathrm{mmHg} \\ $$$$\mathrm{and}\:\mathrm{100}\:\mathrm{cm}^{\mathrm{3}} \:\mathrm{of}\:\mathrm{carbon}\left(\mathrm{iv}\right)\mathrm{oxide}\:\mathrm{at}\:\mathrm{a}\:\mathrm{pressure}\: \\ $$$$\mathrm{of}\:\mathrm{350}\:\mathrm{mmHg}\:\mathrm{were}\:\mathrm{introduce}\:\mathrm{into}\:\mathrm{a}\:\mathrm{200}\:\mathrm{cm}^{\mathrm{3}} \\ $$$$\mathrm{vessel}.\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{total}\:\mathrm{pressure}\:\mathrm{in}\:\mathrm{the}\:\mathrm{vessel}. \\ $$

Question Number 10277    Answers: 2   Comments: 0

How can kerosine be heated ???. please give reasons.

$$\mathrm{How}\:\mathrm{can}\:\mathrm{kerosine}\:\mathrm{be}\:\mathrm{heated}\:???.\: \\ $$$$\mathrm{please}\:\mathrm{give}\:\mathrm{reasons}. \\ $$

Question Number 10268    Answers: 2   Comments: 0

Question Number 10265    Answers: 1   Comments: 0

From the top of a 100 m high building, a man observes the top of a tree at an angle of depression 30°. If the tree is 50 m tall, the angle of depression of the foot of the tree is viewed by the man is ?

$$\mathrm{From}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{100}\:\mathrm{m}\:\mathrm{high}\:\mathrm{building},\:\mathrm{a}\:\mathrm{man} \\ $$$$\mathrm{observes}\:\mathrm{the}\:\mathrm{top}\:\mathrm{of}\:\mathrm{a}\:\mathrm{tree}\:\mathrm{at}\:\mathrm{an}\:\mathrm{angle}\:\mathrm{of} \\ $$$$\mathrm{depression}\:\mathrm{30}°.\:\mathrm{If}\:\mathrm{the}\:\mathrm{tree}\:\mathrm{is}\:\mathrm{50}\:\mathrm{m}\:\mathrm{tall},\:\mathrm{the} \\ $$$$\mathrm{angle}\:\mathrm{of}\:\mathrm{depression}\:\mathrm{of}\:\mathrm{the}\:\mathrm{foot}\:\mathrm{of}\:\mathrm{the}\:\mathrm{tree}\:\mathrm{is} \\ $$$$\mathrm{viewed}\:\mathrm{by}\:\mathrm{the}\:\mathrm{man}\:\mathrm{is}\:? \\ $$

Question Number 10250    Answers: 1   Comments: 1

Question Number 10245    Answers: 1   Comments: 0

prove that determinant ((1,1,1),(x,y,z),(x^2 ,y^2 ,z^2 ))=(x−y)(y−z)(z−y)

$$\mathrm{prove}\:\mathrm{that}\: \\ $$$$\begin{vmatrix}{\mathrm{1}}&{\mathrm{1}}&{\mathrm{1}}\\{\mathrm{x}}&{\mathrm{y}}&{\mathrm{z}}\\{\mathrm{x}^{\mathrm{2}} }&{\mathrm{y}^{\mathrm{2}} }&{\mathrm{z}^{\mathrm{2}} }\end{vmatrix}=\left(\mathrm{x}−\mathrm{y}\right)\left(\mathrm{y}−\mathrm{z}\right)\left(\mathrm{z}−\mathrm{y}\right) \\ $$

Question Number 10248    Answers: 2   Comments: 0

solve the value of x logx^2 =(x/(25))

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$\:\:\:\mathrm{logx}^{\mathrm{2}} =\frac{\mathrm{x}}{\mathrm{25}} \\ $$

Question Number 10243    Answers: 0   Comments: 0

solve the eqution determinant (((x−3),1,(−1)),((−7),(x+5),(−1)),((−6),6,(x−1)))=0

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{eqution} \\ $$$$\:\:\:\:\:\begin{vmatrix}{\mathrm{x}−\mathrm{3}}&{\mathrm{1}}&{−\mathrm{1}}\\{−\mathrm{7}}&{\mathrm{x}+\mathrm{5}}&{−\mathrm{1}}\\{−\mathrm{6}}&{\mathrm{6}}&{\mathrm{x}−\mathrm{1}}\end{vmatrix}=\mathrm{0} \\ $$$$ \\ $$

Question Number 10242    Answers: 2   Comments: 1

f(x)=((sin(x+n))/(cos(x−n))) if f(x)=1, n=??

$${f}\left({x}\right)=\frac{\mathrm{sin}\left({x}+{n}\right)}{\mathrm{cos}\left({x}−{n}\right)} \\ $$$$\mathrm{if}\:{f}\left({x}\right)=\mathrm{1},\:\:{n}=?? \\ $$

Question Number 10241    Answers: 0   Comments: 1

∫_a ^( a+δ) ((sin(x))/(cos(x+δ)))dx = ???

$$\int_{{a}} ^{\:{a}+\delta} \frac{\mathrm{sin}\left({x}\right)}{\mathrm{cos}\left({x}+\delta\right)}{dx}\:=\:??? \\ $$

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