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Question Number 170911    Answers: 1   Comments: 0

A manufacturing company produces containers(jugs) of the same kind. Two similar containers of height 1.5cm and 8cm were selected and filled with orange juice for some athletes. Determine the quantity of orange juice in the smaller container if the bigger one contained 7liters.

$$\boldsymbol{\mathrm{A}}\:\boldsymbol{\mathrm{manufacturing}}\:\boldsymbol{\mathrm{company}}\:\boldsymbol{\mathrm{produces}} \\ $$$$\boldsymbol{\mathrm{containers}}\left(\boldsymbol{\mathrm{jugs}}\right)\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{same}}\:\boldsymbol{\mathrm{kind}}.\:\boldsymbol{\mathrm{Two}} \\ $$$$\boldsymbol{\mathrm{similar}}\:\boldsymbol{\mathrm{containers}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{height}}\:\mathrm{1}.\mathrm{5}\boldsymbol{\mathrm{cm}} \\ $$$$\boldsymbol{\mathrm{and}}\:\mathrm{8}\boldsymbol{\mathrm{cm}}\:\boldsymbol{\mathrm{were}}\:\boldsymbol{\mathrm{selected}}\:\boldsymbol{\mathrm{and}}\:\boldsymbol{\mathrm{filled}}\:\boldsymbol{\mathrm{with}} \\ $$$$\boldsymbol{\mathrm{orange}}\:\boldsymbol{\mathrm{juice}}\:\boldsymbol{\mathrm{for}}\:\boldsymbol{\mathrm{some}}\:\boldsymbol{\mathrm{athletes}}.\:\boldsymbol{\mathrm{Determine}} \\ $$$$\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{quantity}}\:\boldsymbol{\mathrm{of}}\:\boldsymbol{\mathrm{orange}}\:\boldsymbol{\mathrm{juice}}\:\boldsymbol{\mathrm{in}}\:\boldsymbol{\mathrm{the}} \\ $$$$\boldsymbol{\mathrm{smaller}}\:\boldsymbol{\mathrm{container}}\:\boldsymbol{\mathrm{if}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{bigger}}\:\boldsymbol{\mathrm{one}} \\ $$$$\:\boldsymbol{\mathrm{contained}}\:\mathrm{7}\boldsymbol{\mathrm{liters}}. \\ $$

Question Number 170910    Answers: 0   Comments: 0

Question Number 170909    Answers: 0   Comments: 4

1!+2!+3!+....+20000!=?

$$\mathrm{1}!+\mathrm{2}!+\mathrm{3}!+....+\mathrm{20000}!=? \\ $$

Question Number 170906    Answers: 2   Comments: 0

Question Number 170904    Answers: 0   Comments: 0

show that the padel equation of the curve x = acos𝛉 βˆ’acos 2𝛉 , y = 2asin 𝛉 βˆ’asin 2𝛉 is 9(r^2 βˆ’a^2 ) = 8p^2

$$\:\:\:\boldsymbol{\mathrm{show}}\:\boldsymbol{\mathrm{that}}\:\boldsymbol{\mathrm{the}}\:\boldsymbol{\mathrm{padel}}\:\boldsymbol{\mathrm{equation}}\:\boldsymbol{\mathrm{of}}\:\:\boldsymbol{{the}} \\ $$$$\:\:\:\boldsymbol{\mathrm{curve}}\:\:\:\boldsymbol{\mathrm{x}}\:=\: \boldsymbol{{a}\mathrm{cos}\theta}\:βˆ’\boldsymbol{\mathrm{acos}}\:\mathrm{2}\boldsymbol{\theta}\:\:, \\ $$$$\:\boldsymbol{\mathrm{y}}\:=\:\mathrm{2}\boldsymbol{\mathrm{a}}\mathrm{sin}\:\boldsymbol{\theta}\:βˆ’\boldsymbol{\mathrm{a}}\mathrm{sin}\:\mathrm{2}\boldsymbol{\theta}\:\:\mathrm{is}\:\mathrm{9}\left(\mathrm{r}^{\mathrm{2}} βˆ’\mathrm{a}^{\mathrm{2}} \right)\:=\:\mathrm{8}{p}^{\mathrm{2}} \\ $$

Question Number 170902    Answers: 0   Comments: 2

prove that sec((2Ο€)/7)+sec((4Ο€)/7)+sec((8Ο€)/7)=βˆ’4

$${prove}\:{that} \\ $$$${sec}\frac{\mathrm{2}\pi}{\mathrm{7}}+{sec}\frac{\mathrm{4}\pi}{\mathrm{7}}+{sec}\frac{\mathrm{8}\pi}{\mathrm{7}}=βˆ’\mathrm{4} \\ $$$$ \\ $$

Question Number 170900    Answers: 0   Comments: 0

Question Number 170893    Answers: 0   Comments: 0

Question Number 170894    Answers: 0   Comments: 0

Question Number 170891    Answers: 0   Comments: 1

Question Number 170888    Answers: 0   Comments: 0

Question Number 170890    Answers: 2   Comments: 0

Find the equation of a circle which touches the line xβˆ’3y+13 = 0 and passes through the points (6, 3) and (4, βˆ’1).

$$\mathrm{Find}\:\mathrm{the}\:\mathrm{equation}\:\mathrm{of}\:\mathrm{a}\:\mathrm{circle}\:\mathrm{which} \\ $$$$\mathrm{touches}\:\mathrm{the}\:\mathrm{line}\:{x}βˆ’\mathrm{3}{y}+\mathrm{13}\:=\:\mathrm{0}\: \\ $$$$\mathrm{and}\:\:\mathrm{passes}\:\mathrm{through}\:\mathrm{the}\:\mathrm{points}\:\left(\mathrm{6},\:\mathrm{3}\right) \\ $$$$\mathrm{and}\:\left(\mathrm{4},\:βˆ’\mathrm{1}\right). \\ $$

Question Number 170889    Answers: 1   Comments: 1

Question Number 170878    Answers: 1   Comments: 0

Question Number 170868    Answers: 1   Comments: 0

Solve: ∣x βˆ’ 1∣ + ∣x βˆ’ 2∣ β‰₯ 4

$$\mathrm{Solve}:\:\:\:\mid\mathrm{x}\:\:\:βˆ’\:\:\:\mathrm{1}\mid\:\:\:\:+\:\:\:\mid\mathrm{x}\:\:\:\:βˆ’\:\:\:\mathrm{2}\mid\:\:\:\:\geqslant\:\:\:\:\mathrm{4} \\ $$

Question Number 170856    Answers: 1   Comments: 2

in AB^Ξ” C : cos (A)+cos(B)+cos(C)=(7/4) (R/r) =?

$$ \\ $$$$\:\:{in}\:{A}\overset{\Delta} {{B}C}\::\:\:{cos}\:\left({A}\right)+{cos}\left({B}\right)+{cos}\left({C}\right)=\frac{\mathrm{7}}{\mathrm{4}} \\ $$$$\:\:\:\frac{{R}}{{r}}\:=? \\ $$

Question Number 170855    Answers: 1   Comments: 0

⌊xβŒ‹= log_2 (4^( x) βˆ’2^( x) βˆ’1)β‡’ ⌊ 4^( x) βŒ‹=?

$$ \\ $$$$\:\:\:\lfloor{x}\rfloor=\:{log}_{\mathrm{2}} \left(\mathrm{4}^{\:{x}} βˆ’\mathrm{2}^{\:{x}} βˆ’\mathrm{1}\right)\Rightarrow\:\lfloor\:\mathrm{4}^{\:{x}} \rfloor=? \\ $$$$ \\ $$

Question Number 181349    Answers: 0   Comments: 0

Question Number 170872    Answers: 1   Comments: 0

Question Number 170871    Answers: 1   Comments: 0

Why is it equal? (1/2)∫_0 ^Ο€ sin^(2p) udu=∫_0 ^(Ο€/2) sin^(2p) udu

$${Why}\:{is}\:{it}\:{equal}? \\ $$$$\frac{\mathrm{1}}{\mathrm{2}}\underset{\mathrm{0}} {\overset{\pi} {\int}}{sin}^{\mathrm{2}{p}} {udu}=\underset{\mathrm{0}} {\overset{\frac{\pi}{\mathrm{2}}} {\int}}{sin}^{\mathrm{2}{p}} {udu} \\ $$

Question Number 170849    Answers: 1   Comments: 0

2x+(√x)=(1/2) 8x+(1/( (√x)))=?

$$\mathrm{2}{x}+\sqrt{{x}}=\frac{\mathrm{1}}{\mathrm{2}} \\ $$$$\mathrm{8}{x}+\frac{\mathrm{1}}{\:\sqrt{{x}}}=? \\ $$

Question Number 170847    Answers: 0   Comments: 1

Question Number 170844    Answers: 2   Comments: 0

solve x^2 +(√(3βˆ’x))=3

$${solve}\:{x}^{\mathrm{2}} +\sqrt{\mathrm{3}βˆ’{x}}=\mathrm{3} \\ $$

Question Number 170843    Answers: 1   Comments: 0

Question Number 170838    Answers: 1   Comments: 0

if a<b, show that a<((mb+na)/(m+n))<b a,b,m,n are arbitrary constants

$$\mathrm{if}\:{a}<{b},\:\mathrm{show}\:\mathrm{that}\:{a}<\frac{{mb}+{na}}{{m}+{n}}<{b} \\ $$$${a},{b},{m},{n}\:\mathrm{are}\:\mathrm{arbitrary}\:\mathrm{constants} \\ $$

Question Number 170836    Answers: 2   Comments: 1

x^3 βˆ’ 2x^2 βˆ’ 5x + 6 = 0 Ξ±^3 + Ξ²^3 + Ξ³^3 = ?

$${x}^{\mathrm{3}} \:βˆ’\:\mathrm{2}{x}^{\mathrm{2}} \:βˆ’\:\mathrm{5}{x}\:+\:\mathrm{6}\:=\:\mathrm{0}\:\:\:\:\:\:\:\:\:\:\:\:\alpha^{\mathrm{3}} \:+\:\beta^{\mathrm{3}} \:+\:\gamma^{\mathrm{3}} \:=\:? \\ $$

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