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Question Number 8992 Answers: 0 Comments: 0

Question Number 8991 Answers: 1 Comments: 0

prove a^3 +b^3 +c^3 ≥3abc ; ∀a,b,c≥0

$${prove} \\ $$$$\:\:\:\:{a}^{\mathrm{3}} +{b}^{\mathrm{3}} +{c}^{\mathrm{3}} \geqslant\mathrm{3}{abc}\:;\:\forall{a},{b},{c}\geqslant\mathrm{0} \\ $$

Question Number 8988 Answers: 2 Comments: 0

prove Σ_(k=1) ^n k(k+1)=k(k+1)(k+2)/3

$${prove} \\ $$$$\underset{{k}=\mathrm{1}} {\overset{{n}} {\sum}}{k}\left({k}+\mathrm{1}\right)={k}\left({k}+\mathrm{1}\right)\left({k}+\mathrm{2}\right)/\mathrm{3} \\ $$

Question Number 8985 Answers: 1 Comments: 0

solve the value of x log_x 3=81

$$\mathrm{solve}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$\mathrm{log}_{\mathrm{x}} \mathrm{3}=\mathrm{81} \\ $$

Question Number 8973 Answers: 0 Comments: 0

given that x and y are samples of random variable drawn from a population that is normally distributed find the joint distribution of x and y. if x and y are independent find the marginal distributions.

$${given}\:{that}\:{x}\:{and}\:{y}\:{are}\:{samples}\: \\ $$$${of}\:{random}\:{variable}\:{drawn}\:{from}\:{a}\: \\ $$$${population}\:{that}\:{is}\:{normally}\:{distributed} \\ $$$${find}\:{the}\:{joint}\:{distribution}\:{of}\:{x}\:{and}\:{y}.\: \\ $$$${if}\:{x}\:{and}\:{y}\:{are}\:{independent}\:{find}\:{the} \\ $$$${marginal}\:{distributions}. \\ $$

Question Number 8972 Answers: 2 Comments: 0

A cylindrical can of internal diameter 8cm contains water to a deep of 6cm. 24000 heavy spherical pullet of diameter 2mm are dropped into the can. how far does the water level rise ?

$$\mathrm{A}\:\mathrm{cylindrical}\:\mathrm{can}\:\mathrm{of}\:\mathrm{internal}\:\mathrm{diameter}\:\mathrm{8cm} \\ $$$$\mathrm{contains}\:\mathrm{water}\:\mathrm{to}\:\mathrm{a}\:\mathrm{deep}\:\mathrm{of}\:\mathrm{6cm}.\:\mathrm{24000}\:\mathrm{heavy} \\ $$$$\mathrm{spherical}\:\mathrm{pullet}\:\mathrm{of}\:\mathrm{diameter}\:\mathrm{2mm}\:\mathrm{are}\:\mathrm{dropped} \\ $$$$\mathrm{into}\:\mathrm{the}\:\mathrm{can}.\:\mathrm{how}\:\mathrm{far}\:\mathrm{does}\:\mathrm{the}\:\mathrm{water}\:\mathrm{level}\:\mathrm{rise}\:? \\ $$

Question Number 9060 Answers: 2 Comments: 0

Question Number 8969 Answers: 0 Comments: 1

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Question Number 8965 Answers: 0 Comments: 1

If xy − x = yz − 2y = xz + 3z = 3 and xyz > 0 What is the value of xyz ?

$${If} \\ $$$${xy}\:−\:{x}\:=\:{yz}\:−\:\mathrm{2}{y}\:=\:{xz}\:+\:\mathrm{3}{z}\:=\:\mathrm{3} \\ $$$${and} \\ $$$${xyz}\:>\:\mathrm{0} \\ $$$${What}\:{is}\:{the}\:{value}\:{of}\:{xyz}\:? \\ $$

Question Number 8958 Answers: 1 Comments: 0

Prove that 1+(1/2)+(1/3)+....+(1/(2009))=2009−((1/2)+(2/3)+(3/4)+...+((2008)/(2009)))

$${Prove}\:{that}\:\mathrm{1}+\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{1}}{\mathrm{3}}+....+\frac{\mathrm{1}}{\mathrm{2009}}=\mathrm{2009}−\left(\frac{\mathrm{1}}{\mathrm{2}}+\frac{\mathrm{2}}{\mathrm{3}}+\frac{\mathrm{3}}{\mathrm{4}}+...+\frac{\mathrm{2008}}{\mathrm{2009}}\right) \\ $$

Question Number 8957 Answers: 0 Comments: 1

Let n be a positive integer such that one of the roofs of the quadratic equation 4x^2 −(4(√3)+4)x+(√3)n−24=0 is an integer Find the value of n

$$\: \\ $$$${Let}\:{n}\:{be}\:{a}\:{positive}\:{integer}\:{such}\:{that}\:{one}\:{of} \\ $$$${the}\:{roofs}\:{of}\:{the}\:{quadratic}\:{equation}\: \\ $$$$\mathrm{4}{x}^{\mathrm{2}} −\left(\mathrm{4}\sqrt{\mathrm{3}}+\mathrm{4}\right){x}+\sqrt{\mathrm{3}}{n}−\mathrm{24}=\mathrm{0}\:{is}\:{an}\:{integer}\: \\ $$$${Find}\:{the}\:{value}\:{of}\:{n}\: \\ $$$$\: \\ $$

Question Number 8955 Answers: 0 Comments: 1

Solve the equation below (√(x−2))=((5x^2 −10x+1)/(x^2 +6x−11))

$${Solve}\:{the}\:{equation}\:{below}\: \\ $$$$\sqrt{{x}−\mathrm{2}}=\frac{\mathrm{5}{x}^{\mathrm{2}} −\mathrm{10}{x}+\mathrm{1}}{{x}^{\mathrm{2}} +\mathrm{6}{x}−\mathrm{11}} \\ $$

Question Number 8956 Answers: 0 Comments: 1

prove that; log_(ab) x=((log_a x−log_b x)/(log_a x+log_b x))

$$\mathrm{prove}\:\mathrm{that}; \\ $$$$\mathrm{log}_{\mathrm{ab}} \mathrm{x}=\frac{\mathrm{log}_{\mathrm{a}} \mathrm{x}−\mathrm{log}_{\mathrm{b}} \mathrm{x}}{\mathrm{log}_{\mathrm{a}} \mathrm{x}+\mathrm{log}_{\mathrm{b}} \mathrm{x}} \\ $$

Question Number 8964 Answers: 0 Comments: 1

Can you solve this problem? lim_(x→∞) ((log (x^3 + (log x)^3 ))/(log (x^2 + (log x)^2 )))

$$\mathrm{Can}\:\mathrm{you}\:\mathrm{solve}\:\mathrm{this}\:\mathrm{problem}? \\ $$$$\underset{{x}\rightarrow\infty} {\mathrm{lim}}\:\frac{\mathrm{log}\:\left({x}^{\mathrm{3}} \:+\:\left(\mathrm{log}\:{x}\right)^{\mathrm{3}} \right)}{\mathrm{log}\:\left({x}^{\mathrm{2}} \:+\:\left(\mathrm{log}\:{x}\right)^{\mathrm{2}} \right)}\: \\ $$

Question Number 8946 Answers: 1 Comments: 0

x−y=1 and x^y =64, what is the value of x+y=...?

$$\mathrm{x}−\mathrm{y}=\mathrm{1}\:\mathrm{and}\:\mathrm{x}^{\mathrm{y}} =\mathrm{64},\:\mathrm{what}\:\mathrm{is}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x}+\mathrm{y}=...? \\ $$

Question Number 8939 Answers: 1 Comments: 0

1) diket lingkaran c dg pers x^2 +y^2 −6x+2y+2=0 diket pula titik d (a,−3). agar d brd di dlm lingkaran nilai a yg memenuhi adalah....

$$\left.\mathrm{1}\right)\:\mathrm{diket}\:\mathrm{lingkaran}\:\mathrm{c}\:\mathrm{dg}\:\mathrm{pers}\:\mathrm{x}^{\mathrm{2}} +\mathrm{y}^{\mathrm{2}} −\mathrm{6x}+\mathrm{2y}+\mathrm{2}=\mathrm{0} \\ $$$$\mathrm{diket}\:\mathrm{pula}\:\mathrm{titik}\:\mathrm{d}\:\left(\mathrm{a},−\mathrm{3}\right).\:\mathrm{agar}\:\mathrm{d}\:\mathrm{brd}\:\mathrm{di}\:\mathrm{dlm}\:\mathrm{lingkaran} \\ $$$$\mathrm{nilai}\:\mathrm{a}\:\mathrm{yg}\:\mathrm{memenuhi}\:\mathrm{adalah}.... \\ $$

Question Number 8938 Answers: 0 Comments: 0

Question Number 8924 Answers: 1 Comments: 2

Question Number 8933 Answers: 1 Comments: 0

3x+3y+2z=1,x+2y=4,10y+3z=−2, 2x−3y−z=5

$$\mathrm{3x}+\mathrm{3y}+\mathrm{2z}=\mathrm{1},\mathrm{x}+\mathrm{2y}=\mathrm{4},\mathrm{10y}+\mathrm{3z}=−\mathrm{2}, \\ $$$$\mathrm{2x}−\mathrm{3y}−\mathrm{z}=\mathrm{5} \\ $$

Question Number 8934 Answers: 1 Comments: 0

find the value of x. 3^(x+1) =2^(x+2)

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\:\mathrm{x}. \\ $$$$\mathrm{3}^{\mathrm{x}+\mathrm{1}} =\mathrm{2}^{\mathrm{x}+\mathrm{2}} \\ $$

Question Number 8921 Answers: 0 Comments: 0

Question Number 8917 Answers: 0 Comments: 0

Proposed by Rasheed Soomro. What will be possible minimum area of a quadrilateral, whose all the sides touch a circle of radius r ?

$$\mathrm{Proposed}\:\mathrm{by}\:\mathrm{Rasheed}\:\mathrm{Soomro}. \\ $$$$\mathrm{What}\:\mathrm{will}\:\mathrm{be}\:\mathrm{possible}\:\mathrm{minimum}\:\mathrm{area} \\ $$$$\mathrm{of}\:\mathrm{a}\:\mathrm{quadrilateral},\:\mathrm{whose}\:\mathrm{all}\:\mathrm{the}\:\mathrm{sides} \\ $$$$\mathrm{touch}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{of}\:\mathrm{radius}\:\:\mathrm{r}\:? \\ $$

Question Number 8916 Answers: 1 Comments: 2

Question Number 8914 Answers: 0 Comments: 2

∫ ∣x∣ dx

$$\int\:\mid\mathrm{x}\mid\:\mathrm{dx} \\ $$

Question Number 8905 Answers: 1 Comments: 0

find the value of x 3^x =9x

$$\mathrm{find}\:\mathrm{the}\:\mathrm{value}\:\mathrm{of}\:\mathrm{x} \\ $$$$\mathrm{3}^{\mathrm{x}} \:=\mathrm{9x} \\ $$

Question Number 8893 Answers: 1 Comments: 2

if log_x a,log_(x ) b,log_x c are the term of A.P prove that c^2 =(ac)log_(a ) b

$$\mathrm{if}\:\mathrm{log}_{\mathrm{x}} \mathrm{a},\mathrm{log}_{\mathrm{x}\:} \mathrm{b},\mathrm{log}_{\mathrm{x}} \mathrm{c}\:\mathrm{are}\:\mathrm{the}\:\mathrm{term}\:\mathrm{of}\:\mathrm{A}.\mathrm{P} \\ $$$$\mathrm{prove}\:\mathrm{that}\:\mathrm{c}^{\mathrm{2}} =\left(\mathrm{ac}\right)\mathrm{log}_{\mathrm{a}\:} \mathrm{b} \\ $$

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